three essays in international finance a ...bg767pr7175...cheol encouraged me and my ﬁrst advisor,...

THREE ESSAYS IN INTERNATIONAL FINANCE

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ECONOMICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Brian Byongju Lee

August 2011

This dissertation is online at: http://purl.stanford.edu/bg767pr7175

© 2011 by Byong-Ju Lee. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

ii

http://purl.stanford.edu/bg767pr7175

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Ronald McKinnon, Primary Adviser


Kyle Bagwell


Han Hong

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

This thesis consists of three essays on international finance.

The first essay is ”Exchange rates and Fundamentals”. A new open interest rate parity

condition that takes account of economic fundamentals is developed from stochastic

discount factors (SDFs) of two countries. Through this parity condition, business

cycles or fundamentals are linked to exchange rates. Key empirical findings from this

parity condition are as follows. First, this model beats the random walk hypothesis:

economic fundamentals explain exchange rate movements for high interest rate cur-

rencies. Exchange rates of low interest rate currencies act like a random walk because

they are less correlated with fundamentals owing to their low risk. For example, U.S.

business cycles explain the direction of changes in exchange rates against the dollar.

The same thing is true for Japan. Second, this model resolves the forward premium

puzzle: the forward premium puzzle is not a general characteristic as regarded in

previous studies. It happens when the risk awareness of investors is low, during eco-

nomic expansions and for low risk currencies.

The second essay is ”Carry Trade and Global Financial Instability”. Carry trade,

an opportunistic investment strategy that takes advantage of interest rate differential

across countries, is identified the cause of the large-scale depreciations of peripheral

currencies in the later half of 2008. A simultaneous equations model, which is derived

from a conceptual partial equilibrium model for a local foreign exchange market, is

estimated from a cross-sectional sample. The results suggest that the larger appreci-

ation of the yen than the dollar was brought about by a lack of the local supply of

the yen rather than a more severe crunch of yen credits.

The third essay is ”The Economic Origin of Letters of Credit”. This essay discusses

iv

the economic origin of letters of credit, an instrument widely used in international

trade. A game theoretical analysis shows that letters of credit improve efficiency in

trade settlements, increasing returns in trade. A few notable facts on letters of credit

are discussed. First, the new institution is adopted by merchant banks to maximize

their profits and in the process, an improvement in efficiency of international trans-

actions is obtained. Second, the organization established by the legacy institution,

bills of exchange, played a critical role in adopting the new institution. Third, the

legal enforcement is not essential in this economic institution. Finally, two drivers

are identified that improve efficiency of transactions: concentration and projection.

v

Acknowledgements

I have been interested in economics since I was in my alma mater, KAIST in Korea.

Although the school did not offer an economics program, I took a few economics

courses during my study there. My advisor then, Prof. Yu Pyung-il and Kim Jae-

Cheol encouraged me and my first advisor, Prof. Chae Kyung-Chol was always kind

and patient to support me.

After spending seven years in career, I came to Stanford, initially for the master

program in statistics. I met my advisor Prof. McKinnon in his international finance

class. Since then, he guided and supported through Ph.D admission to completion of

the Ph.D. program. He led and challenged me in the academic area and I am very

grateful for his generous RAships through the program. I am enormously in indebted

to him.

Throughout the program, helps from Prof. Kyle Bagwell, Prof. Han Hong, Prof.

Stefan Nagel, Prof. Darrell Duffie and Prof. Mordecai Kurz were pivotal. They ex-

tended their kindness beyond my surprise.

I appreciate friendship with Nadeem, David, Paul and Ray at Stanford.

My wife, Kunyoung Park, has been a great advisor and a talented secretary to me

and a caring mother to my two sons, kindhearted Jaeryoung and confident Seryoung.

My family is expecting a precious boy in December. My mother-in-law Mrs. K.I.

Kim and father-in-law Mr. J.D. Park have been always with my family whenever we

vi

needed helps.

I thank my parents for encouragements and supports despite all the hardships they

had. Lastly, my mother, Hong Sung-Pyo is the greatest leader in my life.

vii

Contents

Abstract iv

Acknowledgements vi

1 Exchange rates and Fundamentals 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Fundamental Open Interest Parity and its Implications . . . . . 12

1.2.1 Stochastic Discount Factors . . . . . . . . . . . . . . . . . . 12

1.2.2 The Fundamental Open Interest Parity . . . . . . . . . . . . 14

1.2.3 The Forward Premium Puzzle . . . . . . . . . . . . . . . . . 18

1.3 Estimations of the fundamental open parity condition . . . . . . . . 19

1.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.3.2 Evidences against the Random Walk Hypothesis . . . . . . . 24

1.3.3 The Fundamental Open Interest Parity with Factors . . . . . 34

1.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

1.4.1 Carry Trade Returns . . . . . . . . . . . . . . . . . . . . . . 41

1.4.2 The Forward Premium Puzzle . . . . . . . . . . . . . . . . . 43

1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2 Carry Trade and Global Financial Instability 55

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.2 Conceptual Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3 Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

viii

2.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3 The Economic Origin of Letters of Credit 77

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.2 Letters of Credit and Bills of Exchange . . . . . . . . . . . . . . . . 83

3.3 A Theoretic Model of Letters of Credit . . . . . . . . . . . . . . . . . 89

3.3.1 A Game Model . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.3.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A Appendix to Chapter 1 107

A.1 Details on data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.1.1 U.S. durables . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.1.2 U.S. nondurables . . . . . . . . . . . . . . . . . . . . . . . . 107

A.1.3 U.S. Market returns . . . . . . . . . . . . . . . . . . . . . . 108

A.1.4 U.S. population . . . . . . . . . . . . . . . . . . . . . . . . . 108

A.1.5 Japanese durables . . . . . . . . . . . . . . . . . . . . . . . . 108

A.1.6 Japanese nondurables . . . . . . . . . . . . . . . . . . . . . . 108

A.1.7 Japanese Market returns . . . . . . . . . . . . . . . . . . . . 108

A.1.8 Japanese population . . . . . . . . . . . . . . . . . . . . . . . 108

A.1.9 Business Cycles . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.2 Derivation of Fundamental Open Interest Parity . . . . . . . . . . . 109

A.3 Preference behind the Linear Factor Model . . . . . . . . . . . . . . 111

ix

List of Tables

1.1 Evidences against the Random Walk hypothesis: United States . . . 27

1.2 Evidence against the Random Walk hypothesis: Japan . . . . . . . . 28

1.3 The simple FOIP model with Net Returns: United States . . . . . . 30

1.4 The simple FOIP model with Net Returns: Japan . . . . . . . . . . 31

1.5 Logistic Regression on the NBER Business Cycle Data with the three

factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.6 Estimation of Linear Factor Models for the United States . . . . . . 36

1.7 Estimation of Linear Factor Models for Japan . . . . . . . . . . . . . 38

1.8 Estimation of Linear Factor Models with the FOIP . . . . . . . . . . 40

1.9 Carry Trade Returns in dollars . . . . . . . . . . . . . . . . . . . . . 44

1.10 Carry Trade Returns in Japanese yen . . . . . . . . . . . . . . . . . 45

1.11 Forward Premium Puzzle Regressions under the OIP . . . . . . . . . 49

1.12 Forward Premium Puzzle Regressions without subtracting the U.S.

rate from foreign rates . . . . . . . . . . . . . . . . . . . . . . . . . . 50

1.13 Decomposition of the forward premium puzzle coefficient . . . . . . . 52

2.1 Returns on carry trades . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.2 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.1 Payoffs of the Game . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

x

List of Figures

1.1 Trade Weighted U.S. Exchange Index and U.S. Business Cycles . . . 2

1.2 Japanese Nondurable Consumption Growth and Growth of Durable

Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 The Dollar-Yen Exchange rate . . . . . . . . . . . . . . . . . . . . . 10

1.4 Currency Portfolios for the Japanese yen and Australian dollar . . . 22

1.5 Variability of Currencies across Currency Portfolios . . . . . . . . . . 23

1.6 Predicted Probabilities of Contraction by the three Factors . . . . . 33

1.7 The yen’s position in U.S. currency portfolios and the dollar’s position

in Japanese currency portfolios . . . . . . . . . . . . . . . . . . . . . 42

1.8 The U.S. interest rate and the average interest rate of the portfolio

with lowest interest rate currencies (portfolio 1) . . . . . . . . . . . . 47

2.1 The yen/New Zealand dollar exchange rate and Japanese banks’ claims

on New Zealand banks . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.2 Domestic Demand and Supply . . . . . . . . . . . . . . . . . . . . . 61

2.3 Foreign Demand and Supply . . . . . . . . . . . . . . . . . . . . . . 62

2.4 An Equilibrium with an Increase of Foreign Claims . . . . . . . . . . 63

2.5 Unwinding Carry Trades . . . . . . . . . . . . . . . . . . . . . . . . . 71

2.6 The Unwinding Scenario for the euro and pound sterling . . . . . . . 72

2.7 The Unwinding Scenario for the yen . . . . . . . . . . . . . . . . . . 73

2.8 The residual analysis of equations . . . . . . . . . . . . . . . . . . . 74

2.9 The cases for Australia and Korea . . . . . . . . . . . . . . . . . . . 75

3.1 Issue and Acceptance of Bills of Exchange . . . . . . . . . . . . . . . 85

xi

3.2 Settlement of Bills of Exchange . . . . . . . . . . . . . . . . . . . . . 86

3.3 Issuing a Letter of Credit . . . . . . . . . . . . . . . . . . . . . . . . 88

3.4 Negotiation of a Letter of Credit . . . . . . . . . . . . . . . . . . . . 90

3.5 The Structure of the Game . . . . . . . . . . . . . . . . . . . . . . . 92

xii

Chapter 1

Exchange rates and Fundamentals

1.1 Introduction

Exchange rates are a central topic of the literature of international finance. Many

efforts have been made on the question whether exchange rates can be predicted.

There are two distinct theoretical approaches to this matter: the macroeconomic

approach and the asset pricing approach. The macroeconomic approach includes

monetary models, equilibrium models and portfolio balance models. Exchange rates

in those models are derived from conditions such as the purchasing power parity or

the long-term balance of current accounts. The failure of the models in predicting or

explaining the short-to-mid term movements of exchange rates is well known.1 One

of the earliest models in the macroeconomic approach is the monetary model. The

monetary approach encompasses the flexible prices model, the stick prices model and

the hybrid model, in all of which the purchasing power parity provides the link be-

tween exchange rates and fundamentals. Meese and Rogoff (1983) find that monetary

models perform worse than a simple random walk model. A key prediction of the

monetary approach regarding economic fundamentals is that the dollar depreciates

during U.S. economic contractions. This prediction is inconsistent with historical

dollar exchange rates, as shown in Figure 1.1. The dollar has appreciated during U.S.

contractions in terms of the trade-weighted index. A possible cause of the failure

1For developments in exchange rate theories and empirical studies, see Sarno and Taylor (2002).

1

CHAPTER 1. EXCHANGE RATES 2

1980 1990 2000 2010

40

60

80

100

120

Year

Inde

x

Figure 1.1: Trade Weighted U.S. Exchange Index and U.S. Business Cycles

Note: The figure shows the trade weighted exchange index against U.S. business cyclesbetween January 1973 and October 2010. Contractions are marked by shaded areas. Thedata is from the U.S. Federal Reserves.

of the model is that exchange rates are not the equilibrating element for the above

conditions in such a time horizon. In order to accept purchasing power parity as

a valid theory of exchange rate determination, it is required that arbitrage actions

through goods or international trade should be more forceful than any other force

that impacts exchange rates. This is clearly not the case by a stylized fact in cur-

rency transactions: the transaction volume in currency markets is much greater than

is required by needs of commodity trade.

Another view of exchange rates is that exchange rates are prices that achieve

the balance of current accounts. This view is clearly rejected from experiences of

sustained global imbalances of current accounts. Since exchange rates affect the


prices of any cross-border transactions, exchange rates for a certain time horizon

are affected by the most active class of transactions for such a horizon. Since any

disequilibrium of prices on tradable goods or commodities can be fixed by adjustments

in local prices and proportions of foreign demand and supply are relatively small

compared with domestic volumes, it is unlikely that adjustments in exchange rates

happen due to a disequilibrium in commodity markets. Even within financial markets,

an exchange rate cannot achieve an equilibrium in every asset offered across the

border. For example, if government bonds, corporate bonds and stocks are available

to foreign investment, an exchange rate cannot equilibrate all the markets at once.

It is likely that the exchange rate equilibrates the market of an asset that is most

actively traded by foreign investors. This argument provides a rationale for the asset

pricing approach, in which exchange rates are adjusted to equilibrate the market

for domestic government bonds, which are more actively traded by foreign investors

owing to relatively lower asymmetry of information than any other private class of

financial assets.

The simplest model of the asset pricing approach is the open interest parity (OIP).

The OIP can be stated in this form:

∆st+1 + it+1 − i$t+1 = ϵt+1,where Et [ϵt+1] = 0. (1.1)

∆st+1 is the depreciation rate of the dollar, or ∆st+1 = Log [St+1]−Log [St], where St

is the nominal exchange rate denoted by the dollar amount for a unit of the Japanese

yen. The terms it+1 and i$t+1 are the Japanese and U.S. nominal interest rates for

bonds that mature at the beginning of period t+1 although the rates are known at the

beginning of period t. Note that expectation on ϵt+1 is with respect to the physical

measure, not the risk neutral measure. Clearly, if investors are not risk neutral, the

OIP does not hold. The attempt to use the OIP as the theory of exchange rate

determination has been far from a success. It rather reinforced the pessimistic view

of exchange rate theory by adding a new puzzle, the forward premium puzzle, which

is an empirical finding that the slope coefficient of the regression of ∆st+1 on (i − i$)

is significantly different from its theoretical prediction, negative unity.


Another attempt in the asset pricing approach is to use stochastic discount factors

(SDFs), notably by Backus, Foresi, and Telmer (2001),

St+1

St

=NJP

t+1

NUSt+1

, (1.2)

where NJPt+1 and NUS

t+1 are nominal stochastic discount factors for Japan and the U.S.,

respectively. This equation is consistent with the observations that the dollar appre-

ciates during U.S. contractions. During U.S. contractions, consumption in the U.S. is

more valuable and hence NUSt+1 is high unless price movements in the U.S. and Japan

cancel the effect. Studies after Backus, Foresi, and Telmer (2001) such as Benigno

and Benigno (2008), Backus, Gavazzoni, Telmer, and Zin (2010) and Martin (2010)

postulate that the above equation holds by assuming that the global financial markets

are complete.

The theoretical contribution of this paper is to derive an open interest parity

condition using the equation (1.2), while completely specifying the term ϵt+1 in the

OIP condition (1.1) in terms of economic fundamentals. Here, economic fundamentals

refer to business cycles of the two countries and business cycles can be expressed by

consumption growth.

From this new theoretical finding, I go further to investigate the two most in-

triguing issues in exchange rate economics: the exchange disconnect anomaly and the

forward premium puzzle. Following Lustig and Verdelhan (2007), the present study

performs an empirical probe into portfolios of currencies rather than into an indi-

vidual currency. Exempt from idiosyncratic risk of individual currencies and perhaps

more importantly, changing characteristics of a currency, the portfolio approach helps

identify the cause of the puzzle and the anomaly. In particular, I confirm Lustig and

Verdelhan (2007)’s finding that a low interest rate currency is equivalent to a low

risk asset in the financial market. Lustig and Verdelhan (2007) use Sharpe ratios,

consumption beta and a regression on OIP residuals to make this point. The present

study uses differences in returns in currency investments by phases of business cy-

cles. The approach in this study is simpler but displays a clearer relation between

exchange rates and business cycles. Low interest rate currencies are less correlated


with economic fundamentals and hence, their exchange rates more or less act like

a random walk. By this argument, the exchange rate disconnect puzzle is nothing

but a logical outcome in asset markets, where low risk assets are less correlated with

economic fundamentals than high risk assets.

The second issue, the forward premium puzzle, is associated with seemingly abnor-

mal risk-taking by investors. High interest rate currencies are predicted to depreciate

according to the OIP but in reality these currencies frequently appreciate. Hence the

markets respond in the opposite direction to the prediction of forward premia. I find

that the forward premium puzzle appears only in low risk situations, such as for low

interest rate currencies and during economic expansions, supporting the view that

investors rationally take risk in low risk situations for high returns. As in any other

financial market, nondiversifiable risk or business cycle risk is valued in the currency

market. To someone oblivious to this risk factor, returns in the currency market,

which are determined by realized exchange rates, seem to act randomly or against

economic intuitions.

A new open interest parity condition derived from SDFs is:

∆st+1 + it+1 − i$t+1 =(cJP − cUS

)+(mJP

t+1 −mUSt+1

)+(∆qUS

t+1 −∆qJPt+1

)+ ηt+1, (1.3)

where mt = Log[

Mt

E[Mt]

]for each country with Mt being the real stochastic discount

factor and ∆q is the inflation rate. cJP and cUS are constants. I sketch the deriva-

tion of the above equation in the next section and Appendix A.2 contains a proof.

From now on I refer to this equation as the fundamental open interest rate parity

(FOIP). This parity condition explicitly specifies the residual term of the textbook

OIP, ϵt+1. While the textbook OIP is derived under the assumption of risk neutrality

of investors, the FOIP assumes only rational expectations. Clearly the textbook OIP

is not necessarily correct if investors are risk-averse and therefore, the expectation of

the right-hand side of the FOIP is not necessarily zero. Stochastic discount factors

depend on business cycles of both countries and investors are assumed to be homoge-

nous. For instance, mUSt+1 is high during U.S. contractions and so, the model predicts


appreciation of the dollar during U.S. contractions, consistent with the empirical ob-

servation in Figure 1.1. For empirical studies, one can model the SDF with business

cycle data such as the National Bureau of Economic Research (NBER) business cycle

dating.

Alternatively, one can express the stochastic discount factor in terms of asset

pricing factors. Asset pricing factors used by Yogo (2006) and Lustig and Verdelhan

(2007) are consumption growth for durable goods, consumption growth of nondurable

goods and the value-weighted market return. The last term η is a consequence of

incomplete markets. Therefore, under the incomplete market, the future exchange

rate cannot be precisely predicted even with perfect knowledge of SDFs and future

inflation. Performing empirical investigation on portfolios of currencies, rather than

individual currencies, neutralizes the impact of the market incompleteness, delivering

robust results.

This equation sheds a new light on the forward premium anomaly. If today’s

interest rate is not correlated with future fundamentals and the inflation rate, the

regression coefficient should be negative unity. There are two factors that resolve the

puzzle: fundamentals and inflation, although the two are not necessarily mutually

exclusive.

The above idea on the relationship of exchange rates with fundamentals puts

forward a new explanation to carry trade returns. Burnside, Eichenbaum, Kleshchel-

ski, and Rebelo (2006) find that carry trades have higher return-to-risk ratios than

the market portfolio in the U.S. stock market. Burnside, Eichenbaum, Kleshchelski,

and Rebelo (2008) attribute these extraordinary returns to the peso problem, more

precisely, a high SDF value when the peso event takes place or the high interest

currencies depreciate. However, Farhi, Fraiberger, Gabaix, Rancire, and Verdelhan

(2009) report that only a quarter of carry trade excess returns are accounted for by

the risk premia for disastrous events. Lustig and Verdelhan (2007) link the high yield

of high interest rate currencies to the consumption risk premium, applying the same

rationale that explains the high risk premium of stocks with a high book-to-market

ratio against low book-to-market ratio stocks. The high yield of high interest rate

currencies or high book-to-market ratio stocks is a compensation for bearing the low


realized yield for these investment vehicles during economic contractions in the U.S.

They find that high interest currencies are more correlated with consumption shocks

of nondurable goods and more decisively, with shocks of durable goods, consumption

of which is more closely related to business cycles, as shown by Yogo (2006).

During U.S. contractions, mUSt+1 is high and foreign currencies depreciate without

any domestic factor movements in foreign countries by (1.3). Since the impact of U.S.

domestic factors is common to all foreign currencies, reactions of foreign currencies

depend on responses of foreign fundamentals against the development in the U.S. It is

shown in the section II that low interest currencies depreciate less than high interest

rate currencies. This observation can be explained by the FOIP (1.3) if a country

with a low interest rate experiences a more severe slowdown in its economy than a

country with a high interest rate. This reaction is required to make depreciations of

the low interest rate currencies less than depreciations of high interest rate currencies.

The comparison is between the country with a low interest rate and a high interest

rate country. Therefore, a country with a low interest rate currency such as Japan

is more likely to experience a recession when the U.S. does. Lustig and Verdelhan

(2007) arrive at the same result under the assumption of complete markets and log-

normality of the SDFs and interest rates. Synchronization of business cycles among

advanced countries is strong evidence that the low interest rate currencies, usually

currencies from advanced economies, perform better or depreciate less during a U.S.

recession.2 Hence, a long position in those currencies is less risky than its counterpart

in higher interest rate currencies. More precisely, if Japan experiences a contraction

when the U.S. does, the yen is a low risk asset for U.S. investors. However, Japan

may have a contraction that is not synchronized with the U.S. economy. If this is the

case, the U.S. is not necessarily a low risk currency for Japanese investors.

One may be puzzled by the argument that the Japanese yen is a low risk currency

since foreign currencies are in general volatile assets and the yen-dollar exchange

rate is not particularly stable. In the financial market, nondiversifiable risk is priced

2This synchronization can be explained by adoptions of the Taylor rule by advanced economies.Backus, Gavazzoni, Telmer, and Zin (2010) incorporate this structure to explain the forward pre-mium puzzle, employing asymmetric responses to exchange rate changes. Their argument is consis-tent with the dollar standard by McKinnon (2005).


because diversifiable risk can be reduced by forming a portfolio. Nondiversifiable risk

in consumption is related to business cycles. Therefore, the correct measure of risk is

not the volatility of the exchange rate or the Sharpe ratio but the correlation between

exchange rate movements and business cycles.

I compare the synchronization of U.S. business cycles with Japanese ones because

Japan has been trapped at near zero interest rates since 1996. Since then, the U.S. has

experienced two contractions at almost the same time as Japan. Four U.S. contrac-

tions since 1980 almost coincided with Japanese counterparts as shown in Figure 1.2.

The upper panel of the figure shows Japanese consumption shocks against U.S. busi-

ness cycles and the lower panel shows the same data against Japanese business cycles.

The long-term swing in growth of stocks of durables shown in the lower panel is very

similar to the U.S. case reported by Yogo (2006), confirming with the case of another

country his argument that stocks of durable goods are a good indicator of business

cycles. The movements of Japanese factors are in line with those expected from coun-

tries with low interest rate currencies. The yen appreciated against the dollar only in

the recent contraction in 2009-10, however very drastically(see Figure 1.3). During

the contraction in 2001, the dollar gained against the yen but the dollar appreciated

by 1.37% in the trade-weighted index while it appreciated against the yen only by

0.74%. The contraction in 1991-2 matched the conjectured pattern of drops in con-

sumption growth in Japan and a depreciation of the dollar against the yen. The yen

was one of lowest interest rate currencies at that time.

The argument about synchronization does not specify causality between U.S. con-

tractions and Japanese downturns. There are many possible scenarios in a contraction

in the U.S. spreads to Japan. Identifying the channel which generates the correla-

tion in business cycles between the two countries is an interesting subject but that

is not the focus of the asset pricing approach of the exchange rate. One may offer

an ad-hoc explanation for some particular turns of events. For instance, during the

2007-8 recession, the banking crisis in the U.S. resulted in a shortage of liquidity in

the market. Concerned about the heightened counterparty risk, Japanese investors

withdrew their credit from currency investments, making the yen shoot up against

all currencies, including the dollar. This was expected by investors because prior to


(a) Against U.S. Business Cycles

1990 2000 2010

-2

-1

0

1

2

3

Year

Perc

entp

erQ

uart

er

NondurablesDurables

(b) Against Japanese Business Cycles

1990 2000 2010

-2

-1

0

1

2

3

Year

Perc

entp

erQ

uart

er

Figure 1.2: Japanese Nondurable Consumption Growth and Growth of Durable Stock

Note: The figures show real growth rates of nondurable consumption and the stock ofdurables of Japanese households against (a) U.S. business cycles from the NBER (b) Japanesebusiness cycles from the Economic and Social Research Institute (ESRI) of the Japanese gov-ernment. Contractions are marked by shaded areas.


1990 2000 2010

100

150

200

250

Year

Ï�$

Figure 1.3: The Dollar-Yen Exchange rate

Note: U.S. business cycle Contractions are marked by shaded areas.

this incident credit had been cheap in Japan owing to the near zero interest rate. For

example, take the Japanese yen as the home currency. During the 1997-8 Asian crisis,

currencies of neighboring Asian countries depreciated drastically, reducing demand

for Japanese goods from the affected countries and improving their price competi-

tiveness over Japan. This brought a recession to Japan in late 1997 and 1998. In the

eyes of Japanese investors, high interest currencies depreciated during the Japanese

recession. For these two episodes, the causality flows in the opposite directions, from

the domestic economy to the foreign currency in the case of the recent U.S. contrac-

tion and in the reverse way for the Asian crisis to Japanese investors. The predicted

correlation was nonetheless realized for both cases.

The portfolio approach for empirical research opens a new approach to studies of


exchange rates. Most studies before Lustig and Verdelhan (2007) have focused on

movements of an individual currency. Those studies are comparable to researches on

the domestic financial market that aim to explain the movement of a single stock.

The focus of the finance literature shifted from a single asset to a portfolio of assets

which is formed by assets with similar characteristics such as book-to-market value

ratio or size (Fama and French (1992)). Rationales of this shift are (1) characteristics

of an individual asset change over time, making a single asset a moving target and

(2) theories suggest that returns should depend on characteristics rather than ticker

names. Applying these principles to the foreign exchange market, previous studies

that attempt to link exchange rates to fundamentals are doomed to disappointment

unless characteristics of currencies have been unchanged over time, and currencies

readily react to fundamentals like high risk assets, an improbable situation. In this

paper, I choose interest rates of currencies as a key characteristic, forming portfolios

by grouping currencies with similar interest rate levels for each period. Alternatively,

one can choose credit ratings or previous default history to find whether these char-

acteristics earn excess returns and the excess returns are related to macroeconomic

risks. If currencies frequently switch portfolios, reactions of foreign currencies against

changes in fundamentals of the home country may not be obvious to researchers who

are unaware of the link between interest rates of currencies and their responses to

business cycles of the home country.

This paper is organized as follows. In Section 1.2, theoretical outcomes of the

FOIP are stated in relation to the international financial market. In Section 1.3,

two forms of the FOIP, the simple FOIP and the FOIP with factors, are estimated.

Section 1.4 identifies the cause of the forward premium anomaly and the source of

high returns in the carry trade. Section 1.5 offers conclusions.


1.2 The Fundamental Open Interest Parity and its

Implications

Consumption based asset pricing models derive the pricing kernel or the stochastic

discount factor from the intertemporal decision on consumption. The basic principle is

that the benefit or marginal utility from today’s consumption should equal the benefit

from saving or consumption tomorrow. Therefore, the price between consumption

today and consumption tomorrow is determined by the ratio of marginal utility today

and tomorrow, or the stochastic discount factor (SDF). Marginal utility, in turn,

depends on aggregate consumption and aggregate asset returns if agents are assumed

to be homogenous. The SDF of the home country can be translated into the SDF

of the foreign country through the exchange rate. Therefore, causality flows from

economic fundamentals to the SDFs and another causality flows from the SDFs to

the exchange rate. These two can be linked to tie the exchange rate to fundamentals.

In this section, a theoretical link between SDFs and the exchange rate is established

and then its implications for the forward premium puzzle are presented.

1.2.1 Stochastic Discount Factors

Given the real SDF Mt+1, the Euler equation, which prices the real gross return of

asset i, Ri,t+1 to 1, is

Et [Mt+1Ri,t+1] = 1. (1.4)

Or in terms of the excess return Rei,t+1, the Euler equation is

Et

[Mt+1R

ei,t+1

]= 0, (1.5)

where Rei,t+1 = Ri,t+1 − Rf

t+1 with Rft+1 being the real risk free rate. Yogo (2006)

derives a close form of the SDF in terms of preference and consumption factors from

the consumer’s problem and performs a generalized method of moments (GMM)

estimation on the moment conditions (1.5). A brief review on Yogo (2006)’s work

is in Appendix A.3. Lustig and Verdelhan (2007) apply Yogo (2006)’s framework to


the international financial market, using currency portfolios sorted by interest rates

as test assets. The numeraire of equation (1.4) is U.S. nondurable goods. To study

the nominal exchange rate, I change the numeraire to the U.S. dollar. Let QUSt be the

U.S. price level at time t and Nt+1 be the nominal SDF. The nominal gross return of

asset i, Ii,t+1, is equal toQUS

t+1

QUSt

Ri,t+1. Hence,

1 = Et [Mt+1Ri,t+1] = Et

[Mt+1

(QUS

t+1

QUSt

)−1

Ii,t+1

]= Et [Nt+1Ii,t+1] , (1.6)

where the nominal SDF Nt+1 is defined by Nt+1 ≡ Mt+1

(QUS

t+1

QUSt

)−1

. If the dollar asset i

is available to Japanese investors, the return of the asset in yen, IJPi,t+1, is set by IUSi,t+1=

IJPi,t+1St+1

St, where St is the spot exchange rate at t expressed as the dollar amount per

yen. Applying this relationship,

1 = Et

[NUS

t+1IUSi,t+1

]= Et

[NUS

t+1IJPi,t+1

St+1

St

]= Et

[(NUS

t+1

St+1

St

)IJPi,t+1

]. (1.7)

Therefore, for Japanese investors,(NUS

t+1St+1

St

)is a nominal SDF because it satisfies

the Euler equation. Define

NJP,It+1 =

(NUS

t+1

St+1

St

), (1.8)

with superscript I standing for "imputed."

If financial markets are complete, there is a unique stochastic discount factor for

Japanese investors. Therefore, this imputed SDF should be the SDF for Japanese

investors. If the market is incomplete, there are multiple SDFs that price traded

assets. Suppose one derives a Japanese nominal stochastic factor, designated by

NJapan,Ct+1 using Japanese fundamentals as one does for the U.S. SDF. Then

Et

[(NJP,I

t+1 −NJP,Ct+1

)IJPi,t+1

]= 0 ∀ i, (1.9)

for any asset has a single price at t. If the market is complete, NJapan,It+1 = NJapan,C

t+1


since the payoffs of assets span the entire space of states of nature (Cochrane (2005)).

Equation (1.9) can be also tested as a moment condition in GMM estimation by the

orthogonality test. A rejection of the test is a sign of inaccuracy in estimating the

SDFs, possibly caused by missing pricing factors. Alternatively, it can be attributed

to the situation that U.S. investors and Japanese investors do not share the same

probability measure, a violation of rationale expectations.

1.2.2 The Fundamental Open Interest Parity

The difference between the two SDFs is an interesting object but it has been treated

as a purely theoretical construct and has rarely been a subject of studies of ex-

change rates. Cochrane (2005) offers an excellent theoretical exhibition on this topic.

Given NJP,It+1 and NJP,C

t+1 , I define ∆N JPt+1=NJP,I

t+1 -NJP,Ct+1 . If there is a nominal risk

free asset in Japan, then its gross return IJP,ft+1 = 1

Et[NJP,It+1 ]

= 1

Et[NJP,Ct+1 ]

. Therefore,

Et

[∆NJP

t+1

]=0. Clearly, an asset that pays ∆NJP

t+1 is not traded.3 Since ∆NJPt+1 is

not traded, the valuation of a hypothetical asset that pays ∆NJPt+1 at t+1 is dif-

ferent between U.S. investors and Japanese investors and hence, there is an arbi-

trage opportunity. This is how the arbitrage is executed: sell an asset to U.S. in-

vestors that pays ∆NJPt+1St+1 in dollar at t+1 and sell to Japanese investors an asset

that pays −∆NJPt+1 in yen at t+1. At t+1, the arbitrageur has no net cash flows

from the two transactions. At t, he receives Et

[NUS

t+1∆NJPt+1St+1

]=StEt

[NJP,I

t+1 ∆NJPt+1

]in dollar from U.S. investors, or equivalently, Et

[NJP,I

t+1 ∆NJPt+1

]in yen and he also

receives Et

[NJP,C

t+1

(−∆NJP

t+1

)]from Japanese investors. His net cash flow at t is

Et

[NJP,I

t+1 ∆NJPt+1

]-Et

[NJP,C

t+1

(∆NJP

t+1

)]=Et

[(∆NJP

t+1

)2], which is always positive if the

markets are not complete. Like any other arbitrage opportunity, the arbitrage stems

from the difference in valuations for the same asset. Here, U.S. investors’ valuation

of the future cash flow ∆NJPt+1St+1 in dollars in today’s yen is greater than Japanese

investors’ valuation of the future cash flow ∆NJPt+1. The reason is that ∆NJP

t+1 pays well

3∆NJPt+1 belongs to a space which is orthogonal to the payoff space as shown in equation (1.9)

and the only way that ∆NJPt+1 belongs to the payoff space, that is, is traded in the market, is the

trivial case, ∆NJPt+1 = 0.


when the U.S. investors’ SDF in terms of the yen is greater than that of Japanese in-

vestors (NJP,It+1 >NJP,C

t+1 or NUSt+1

St+1

St> NJP,C

t+1 ). Using the analogy of insurance, ∆NJPt+1

is an insurance that pays well when U.S. investors are more pinched than Japanese

investors. This finding implies that there is an unexploited arbitrage opportunity if

the markets are incomplete and arbitrageurs fully understand well both SDFs from

the U.S. and from Japan.

Under the asset pricing framework, SDFs are a meter that values consumption

growth risk and the major component of consumption growth risk is uncertainty in

economic fundamentals. If markets were complete and the SDFs were well under-

stood, the exchange rate would be related to fundamentals through the SDFs (see

equation (1.8)) and there would be no exchange rate disconnect puzzle. Therefore,

under complete markets, the exchange rate disconnect puzzle is just a symptom of re-

searchers’ lack of understanding of the specific form of SDFs. More precisely, it repre-

sents our lack of answers to questions of how agents measure consumption growth risk,

and how or whether consumption growth risk depends on economic fundamentals, al-

though these questions are still valid under incomplete markets. A more realistic view

would be that markets are incomplete. From equation (1.8) and ∆NJPt+1=NJP,I

t+1 -NJP,Ct+1 ,

I can express (NJP,C

t+1 +∆NJPt+1

)=

(NUS

t+1

St+1

St

). (1.10)

It is possible that the exchange rate can be disconnected from fundamentals if

∆NJPt+1 is large enough. But if that were true, then there would be an unexploited

arbitrage opportunity of which profit depends on the magnitude of Et

[(∆NJP

t+1

)2]. A

probable situation is that arbitrageurs do not fully understand the SDFs and hence

cannot trade upon the SDFs. When financial institutions become confident of their

understanding of SDFs, they will trade upon the difference of the SDFs and by

this process, the market will become less incomplete, thereby reducing the degree of

disconnect between the exchange rate and economic fundamentals. By comparing

Et[ (∆Nt+1)2 ] across countries or over period of time, one can check the degree of

market completeness or our progress in understanding the SDFs or locate a pair of

countries that offers arbitrage opportunities.


Using the formula Nt+1 ≡ Mt+1

(QUS

t+1

QUSt

)−1

and (1.10), I derive the following equa-

tion in Appendix A.2 for the dollar/yen exchange rate which links the SDFs of the

two countries to the exchange rate:

∆st+1 + it+1 − i$t+1 =(cJP − cUS

)+(mJP

t+1 −mUSt+1

)+(∆qUS

t+1 −∆qJPt+1

)+ ηt+1, (1.11)

where mt = Log[

Mt

E[Mt]

]for each country and ∆q is the inflation rate. it+1 and i$t+1 are

nominal risk-free rates in Japan and the U.S., respectively. cJP and cUS are constants

and they are close to zero if inflations are not correlated with real SDFs and expected

inflations are mild. The constant term in the above equation can be ignored if the

two countries have similar correlations between inflation and real SDF, and similar

expected inflations(see Appendix A.2 for details). The exchange rate is the dollar

amount for a unit of yen. During U.S. contractions, the U.S. SDF is high because

marginal consumption is more valuable during recessions than during economic ex-

pansions. Therefore, the above fundamental open interest parity (FOIP) asserts that

during U.S. contractions, the dollar appreciates. The parity condition is derived un-

der very mild assumptions of rational expectations and logarithmic approximation of

the SDFs. Rational expectations by investors in both countries are required so that

they share the same probability measure. Unlike other studies like Backus, Foresi,

and Telmer (2001), complete markets are not assumed here. On the contrary, the

issue of complete markets is explicitly addressed by the term ηt+1, which is equal to

IJP,ft+1 ∆NJPt+1 where IJP,ft+1 is the Japanese nominal risk free return. Even with perfect

knowledge of the SDFs of both countries, the exchange rate cannot be predicted if the

market is not complete. The FOIP is readily estimable with the moment condition

(1.9) using realized gross returns of Japanese assets {IJPi,t+1} as instruments because

IJPi,t+1’s are orthogonal to the residual term ηt+1 if the log of SDF is correctly estimated

(see equation (1.9)).

The log of SDFs, mUSt+1 and mJP

t+1 can be restated in terms of asset pricing factors.

First, I restate a loglinearization approximation from Appendix II of Yogo (2006).

The log deviation of stochastic discount factor from its mean, Log[

Mt

E[Mt]

], can be


approximated by

−mt ≈ −k + b1∆ct + b2∆dt + b3rw,t, (1.12)

where k is a constant and b’s are factor loadings in linear asset pricing models. ∆ct,

∆dt, and rw,t are nondurable consumption growth, durable consumption growth and

the market return, respectively(for details on preference behind this equation, see

Appendix A.3 ). In a more concise notation,

mt = k − b′f, (1.13)

where b′ = (b1, b2, b3 ) and f ′=(ft,1, ft,2, ft,3)=(∆ct,∆dt, rw,t). The FOIP with factors

is derived by plugging factor models above into equation (1.11):

∆st+1 + it+1 − i$t+1 =(kJP − kUS

)+(bUS′fUS

t+1 − bJP′fJPt+1

)+(∆qUS

t+1 −∆qJPt+1

)+ ηt+1.

(1.14)

kJPand kUS are constants for Japan and the U.S. Factors from each country describe

economic conditions in their countries.

If indicators of stages of business cycles are available, we can put them into equa-

tion (1.11) to get a simple form of the FOIP:

∆st+1 + it+1 − i$t+1 =(cJP − cUS

)+(βJPBJP

t+1 − βUSBUSt+1

)+(∆qUS

t+1 −∆qJPt+1

)+ ηt+1,

(1.15)

where BUSt+1 is 1 if the U.S. is in a contraction at period t+1 and 0 otherwise. Similarly

BJPt+1 is related to Japanese business cycles. βJP and βUS are positive parameters. For

example, one can apply U.S. business cycle data available from the NBER. I refer

to the above equation as the simple FOIP model. Since business cycles are serially

correlated, we can use the above equation in predicting the exchange rate by plugging

in a simple model of business cycle prediction, Bt+1 = αBt + δt+1 for each country,

∆st+1 + it+1 − i$t+1 =(cJP − cUS

)+(αJPβJPBJP

t − αUSβUSBUSt

)+ ξt+1, (1.16)

where ξt+1 =(∆qUS

t+1 −∆qJPt+1

)+ ηt+1 + βJPδJPt+1 + βUSδUS

t+1.


1.2.3 The Forward Premium Puzzle

The forward premium puzzle is an empirical finding that the estimated value of a2 in

the following equation is greater than 0, while the theory predicts negative unity.

∆st+1 = a1 + a2(it+1 − i$t+1

)+ νt+1. (1.17)

Note that although risk-free rates, i$t+1 and it+1 are indexed by t+1, they are known

at t. Exchange rate St is expressed by units of dollar per yen. Backus, Foresi, and

Telmer (2001) examine whether affine term structure models can resolve the forward

premium anomaly. The affine term structure models express the log of the SDF as a

linear form of state variables. They conclude that affine models cannot replicate the

forward premium puzzle without a series flaw such as negative interest rates.

The estimate of a2,a2, is expressed by sample moments denoted by subscript T:

a2 =CovT

[∆st+1,

(it+1 − i$t+1

)]VarT

[(it+1 − i$t+1

)] . (1.18)

Insert the factor FOIP model into the above formula, giving

a2 =CovT

[∆st+1,

(iUt+1 − i$t+1

)]VarT

[(iUt+1 − i$t+1

)]= −1 +

CovT[(bUS′fUS − bJP′fJP

),(iUt+1 − i$t+1

)]VarT

[(iUt+1 − i$t+1

)]+

CovT[(∆qUS

t+1 −∆qJPt+1

),(iUt+1 − i$t+1

)]VarT

[(iUt+1 − i$t+1

)]+

CovT[ηt+1,

(iUt+1 − i$t+1

)]VarT

[(iUt+1 − i$t+1

)] . (1.19)

The fourth term on the right-hand side converges to zero since the U.S. and

foreign interest is known at t. Since the first term is negative unity, the forward

premium puzzle takes place only if the nominal interest rate differential predicts

future fundamentals or inflation. This issue is revisited with empirical analyses in

Section 1.4.


1.3 Estimations of the fundamental open parity

condition

1.3.1 Data

In this subsection, I outline the procedure to obtain data from various sources. Ap-

pendix refsec1a1 documents sources and details of the data. Data used in estimation

are largely factor data and return data. Business cycle data are obtained from the

NBER for the U.S. and the Economic and Social Research Institute (ESRI) of the

Japanese government for Japan. The U.S. data for durable service is calculated from

the raw data obtained from the Bureau of Economic Analysis. The U.S. data for

nondurable consumption are generated by the Fisher quantity index from price and

quantity data from the National Income and Product Accounts (NIPA) tables. Both

consumption data are divided by population and their growth rates are used as fac-

tors. For Japanese data, data from the ESRI are used to correspond to their U.S.

counterparts. All consumption data are in real terms and are aggregated in a chained-

type quantity index if necessary. Exchange rate data and interest rate data are from

the Global Financial Data website. All but 5 interest rates are for 3-month sovereign

bonds.

Some samples with available exchange rate and interest rate data are excluded

from portfolio formation. If a country is under a special circumstance, which dis-

rupts the operation of its financial market, I exclude the currency of the country for

a certain period. I use three filters to exclude a currency for a particular quarter:

capital controls, defaults and abnormal interest rates. Lustig and Verdelhan (2007)

used Quinn (1997)’s index for capital control. Since quarterly data are used here and

the sample period covers a very recent quarter (the fourth quarter of 2009), a new

benchmark is devised to measure capital openness, and the index takes into account

that capital openness may change over time. The index is foreign banks’ assets and

liabilities against the country of interest divided by its exports and imports. If either

asset position data or trade data is not available for a particular quarter, the sam-

ple of the country with missing data is excluded for the quarter. Among countries


with available data, countries with the lowest 5% in the index are excluded for the

period. Countries in defaulted state are also removed from the pool. The default

data are obtained from Panizza and Borensztein (2008) and Chambers, Ontko, and

Beers (2010). I apply recovery rates from defaults to the yield of the quarters when

defaults are declared and defaulted countries are excluded until they emerge from

the default. The recovery rates are from Duggar (2009). If the matching recovery

rate for a country is available, the recovery rate for that country is applied. If the

matching data is not available, the average recovery rate 31% is applied.4 If the exact

date of default is not available but the year of default is available, I assume that the

default took place in the first quarter and ended in the last quarter of the reported

years. There are 12 cases of sovereign default in the sample. There are more reported

defaults or restructuring in bank debts but these events do not involve loss in invest-

ments in sovereign bonds denominated in local currencies, although accompanying

depreciations of the currencies under financial distress render very low returns for

investments in the affected currencies. For financial distresses other than sovereign

defaults, it is not necessary to adjust the yield.

The last reason to exclude samples is abnormal interest rates. Among 7800 avail-

able records of interest rates for 102 countries during the 1982:1∼2009:4 period, there

are 80 records or 1% of total samples which have interest rates higher than 110 per-

cents per annum. Those observations with such high interest rates are dropped from

the sample. A very high interest rate is a sign of financial distresses where the market

for the security is not liquid and the market price of the security may not reflect the

fundamentals. Since currency portfolios in this study are formed by currencies with

similar interest rate levels with equal weights, adding currencies with abnormally high

interest rates to the portfolio would have increased heterogeneity within the portfolio

and extremely high or low yields of those currencies would have corrupted the pricing

information contained in other currencies in the same group.

There are 60 currencies on average available to create currency portfolios. Earlier

4These recovery rates are lower than the 70% used by Lustig and Verdelhan (2007). Sinceportfolios in this study are rebalanced every three months, the recovery rate after one month ascalculated by Duggar (2009) is more applicable than higher recovery rates after work-out periods.Work-outs on average take two years, reported by Singh (2003).


periods have fewer currencies with a minimum of 35 currencies and recent periods

have more currencies with a maximum of 81 currencies. During the 2008-2009 period,

eligible currencies dropped to 69 currencies. For each quarter, eligible currencies that

pass three filters described above, are sorted by opening levels of interest rates. Fol-

lowing Lustig and Verdelhan (2007), I create 8 portfolios by levels of opening interest

rates. For portfolio 1, currencies with lowest interest rates are assigned and for port-

folio 8, currencies with highest interest rates are assigned. The number of currencies

in the two outermost portfolios is the rounded number of eligible currencies divided

by 8 for each portfolio. The remaining currencies are clustered by using a squared

Euclidean distance function to minimize heterogeneity within a portfolio. Therefore,

the number of currencies in each portfolio may be different, even for portfolios for

the same period. By assigning the pre-defined number of currencies in the outermost

portfolios, the influence of outlying currencies is extenuated. For example, for the

first quarter of 2000, there are 72 eligible currencies and the numbers of currencies in

portfolios from portfolio 1 to 8 are 9, 8, 14, 6, 11, 7, 8, and 9.

Given a currency, the portfolio to which a currency belongs changes over time.

Figure 1.4 shows the portfolios to which the Japanese yen and Australian dollar be-

long over time. While the yen stays in low interest rate portfolios, the Australian

dollar changes frequently. The portfolio approach is valuable especially when curren-

cies often change their characteristics in the global financial market, or in the context

of this study, when they frequently switch portfolios they belong to. One can mea-

sure variability of a currency across currency portfolios by observing the standard

deviation of its portfolio numbers. Figure 1.5 presents positions of all 95 currencies in

terms of their standard deviations and means of portfolio numbers. The vertical line

and horizontal line are the mean values of the means and the standard deviations,

respectively. The figure suggests that characteristics of currencies vary considerably.

Variability is high for currencies in the medium range of interest rates. Therefore, the

portfolio approach is valuable in studying exchange rates in terms of characteristics

of currencies.

Combining the interest rate and the rate of appreciation of a currency over a

quarter, I obtain the realized yield for a long position in a currency. By using the


1980 1990 2000 20100

2

4

6

8

JapanAustralia

Figure 1.4: Currency Portfolios for the Japanese yen and Australian dollar

Note: The figure shows currency portfolios that each currency belongs to over time. Currencyportfolios are numbered from 1 to 8 and portfolio 1 is the group of lowest interest ratecurrencies and portfolio 8 is the group of highest interest rate currencies. The Australiandollar is once excluded from portfolio formation in the 1980s by the filtering standard ofcapital openness, which is marked by 0 in the figure.


Japan

Germany

Canada

United Kingdom

Australia

Denmark

Turkey

Brazil

MexicoPhilippines

Korea

Iceland

2 4 6 8Mean

0.5

1.0

1.5

2.0

2.5

Standard Deviation

Figure 1.5: Variability of Currencies across Currency Portfolios

Note: For each currency, the y-axis is the standard deviation of the portfolio numbers of itover time. The x-axis is the mean of the portfolio numbers. A high value of the standarddeviation for a currency implies that the currency frequently changes its position in theglobal financial market.


same weight for currencies within a portfolio, I calculate the realized nominal yield of

a portfolio. For the factor model, real excess returns are used. They are obtained by

subtracting the risk free rate of the home country from nominal yields of portfolios

and then deflate them with the inflation rate of nondurable goods. The portfolios

studied here are formed every quarter using the quarterly return data, while Lustig

and Verdelhan (2007) form annual portfolios based upon 3-month treasury bill rates.

Therefore, the portfolios here describe the practice of currency markets more closely.

The data used in estimation are on a quarterly basis for 1982:1-2009:4. For currency

portfolios for Japanese investors, the Japanese nominal interest rate and inflation rate

are applied.

1.3.2 Evidences against the Random Walk Hypothesis

The fundamental open interest parity predicts that the dollar is strong during U.S.

contractions and weak during expansions. Therefore, investments in foreign currencies

have high yields during expansions and low yields during contractions. This prediction

is well supported by the data of three currencies and portfolios, as shown in Table 1.1.

In the first panel of the table, returns on investments in foreign currencies and foreign

currency portfolios are calculated by phase of business cycles in the same period

and the second panel reports the returns matched with the preceding period. The

first panel is consistent with (1.15) and the second panel is in line with (1.16). In

all currency portfolios and currencies, returns during expansions are greater than

returns during contractions. The gap is greater for portfolios of high interest rate

currencies than for portfolios of low interest rate currnecies. The well-known random

walk hypothesis on exchange rates asserts that exchange rates cannot be predicted

by data from the previous period. This hypothesis is directly contradictory to the

observations in the second panel. A simple forecast model of the exchange rate that

is consistent with (1.16) is:

St+1

St

I£t+1 ≥ 1 if the U.S. is in expansions at t (1.20)

St+1

St

I£t+1 < 1 if the U.S. is in contractions at t,


where I£i,t+1 is the gross return on a foreign currency bond in its own currency that

matures at the beginning of period t+1. The returns are known at period t. St+1 is

the exchange rate at t+1, expressed by the dollar amount for a unit of the foreign

currency. The simple forecast model predicts that returns on foreign currencies are

positive if the home country is in expansions and negative in contractions. The

fourth row of the second panel reports results of the simple model. The simple

model predicts directions of exchange rate movements with a reasonable degree of

accuracy (68%), rejecting the random walk hypothesis5, as shown in the p-value

in the next row. Note that the p-values are calculated for the sign test under the

null hypothesis that the returns are a random walk. The Meese and Rogoff (1983)

hypothesis that exchange rates follow a random walk performs worse than the simple

FOIP models because the interest rate level sets the baseline for the future exchange

rate and phases of business cycles affect the movements of the exchange rate from the

baseline. One important fact from the table is that phases of business cycles predict

future exchange rate movements of high interest rate currencies more accurately than

the low interest rate currencies. Note that low interest rate currencies have a narrow

gap between returns during expansions and during contractions, and their returns are

less dependent on business cycles. These are the defining characteristic of low risk

assets. A low risk asset is not necessarily an asset of low volatility in returns. It is

an asset with low correlation with consumption growth risk, which is determined by

economic fundamentals.6 A currency with low interest rates such as the yen may have

higher daily volatility than other high interest rate currencies under a managed peg by

the monetary authorities but as long as the currency is more weakly correlated with

U.S. business cycles than other assets, it is a low risk asset. Since low interest rate

currencies are less correlated with fundamentals owing to their low macroeconomic

risk, they seem to be disconnected from economic fundamentals. A somewhat agnostic

5The original random work hypothesis is that E [∆st] = 0 or St+1

St≥ 1 with 50% probability.

Here, I use the null hypothesis St+1

StI£i,t+1 ≥ 1 with 50% probability.

6Consumption growth risk depends on the difference in consumption levels between expansion andcontraction phases of business cycles. For example, elements that affect the difference are technologyand preference in real business cycle models. In general, any element that affects consumptionallocation can be regarded as fundamental.


outcome from previous studies on exchange rates such as Meese and Rogoff (1983)

and numerous studies following theirs are now no longer surprising because (1) they

choose currencies with low interest rates out of globally available currencies7 and (2)

a single currency can be subject to idiosyncratic risks of the two countries linked

by the exchange rate and therefore the impact of fundamentals may not have been

clearly pronounced.

The upper panel of the table reports the same quantity with the lower panel but

returns in a period are classified by business cycle phase of the current period, while

the lower panel classifies returns by business cycle phase of the preceding period. The

lower panel is interesting because it provides an evidence against the random walk

hypothesis by predicting future directions of exchange rate movements by the current

economic status. The upper panel is meaningful since it provides a direct evidence of

validity of the FOIP.

The power of the simple form of the FOIP as a predictor of future exchange rate

movements is not limited to the case of the U.S. The same analysis is applied to Japan

and very similar results are obtained, as presented in Table 1.2. In the Japanese case,

the theoretical model (the upper panel) is more powerful than the prediction model

(the lower panel) and the high interest rate currencies show a clear link to business

cycles and the low interest rate currencies present a weaker relationship with business

cycles. This pattern is consistent with the view that investments in low interest rate

currencies are a hedge for consumption growth risk. Practically, the best hedge one

can obtain in the market for consumption growth risk or business cycle risk is not an

asset that pays well during contractions but an asset whose payoff is less correlated

with business cycles. Low interest rate currencies play this role as shown in their low

difference in yields between expansions and contractions, or equivalently in the low

predictability of their returns by business cycles.

The simple form of the FOIP in (1.20), analyzed in Tables 1.1 and 1.2 is consistent

7For example, Meese and Rogoff (1983) use the dollar exchange rate against the mark, yen andpound, and Evans and Lyons (2005) use the rate against the euro. Most of them are classified as lowinterest rate currencies in the global standard. The yen’s average location on the set of portfoliossorted by interest rate is 1.26. The currencies of Germany and the United Kingdom are located at.92 and 3.55, respectively. The average location is 4.5 since there are 8 portfolios.


Table 1.1: Evidences against the Random Walk hypothesis: United States

1 2 3 4 5 6 7 8

Returns during Expansions 6.23 8.38 7.41 3.15 6.10 6.11 8.66 6.04 7.04 5.94 7.88

Returns during Contractions 2.35 -2.41 1.12 1.75 0.01 2.64 1.65 -1.48 4.91 1.09 -2.54

Difference in Returns 3.88 10.79 6.29 1.40 6.08 3.47 7.01 7.52 2.13 4.85 10.42

Matching Ratio by Business cycles 0.51 0.62 0.57 0.62 0.65 0.64 0.70 0.72 0.71 0.63 0.69

P-value under the Random Walk

Hypothesis0.39 0.01 0.05 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00


Returns during Contractions 1.27 -6.93 -2.15 1.09 -0.96 0.98 0.42 -3.13 3.05 0.72 -5.28




Hypothesis0.32 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Panel B: Business cycles predict returns

Panel A: Business cycles explain returns

Currency PortfoliosJapan GermanyUK

Note: Returns are in annualized percents on quarterly currency investments. They are thesum of interest gains and appreciations of the investment currency. Currency portfoliosare formed by grouping currencies of similar interest rate levels. Portfolio 1 is the group ofcurrencies with low interest rates and group 8 is the group of highest interest rate currencies.Business cycle data for the U.S. is from the NBER. The first panel reports the statistics underthe assumption that the current business cycle explains returns in currency investments. Thesecond panel is consistent with the theoretical prediction that exchange rates can be predictedin the FOIP. The matching ratio by business cycles is the proportion of the period when therealized returns agree with the predictions by the simple model, that is, the realized returnsare negative during contractions and positive during expansions. The p-values are calculatedunder the null hypothesis that the random walk is the true model of returns.


Table 1.2: Evidence against the Random Walk hypothesis: Japan

1 2 3 4 5 6 7 8


Returns during Contractions -7.22 -8.19 -3.79 -7.73 -7.84 -5.29 -5.28 -7.30 -7.72 -5.94 -11.24




Hypothesis0.00 0.00 0.01 0.02 0.01 0.01 0.00 0.02 0.00 0.00 0.01


Returns during Contractions -2.61 -2.03 -2.51 -4.32 -2.97 -1.31 -0.80 -3.21 1.10 -0.83 -5.81




Hypothesis0.05 0.02 0.02 0.11 0.08 0.08 0.00 0.11 0.08 0.04 0.11



Currency PortfoliosUS GermanyUK

Note: Business cycle data for Japan are from the Economic and Social Research Institute(ESRI) of the Japanese government. See the note for Table 1.1 for details.


with the theoretical FOIP and powerful in predicting future exchange rate movements,

especially for high interest rate currencies. A more consistent model with the FOIP

uses the interest rate differential between the home currency and foreign currencies.

Using interest rate differentials is equivalent to assuming that the true funding cost

of currency investments is the risk free rate of the home currency. The performance

of the empirical model depends on the validity of this assumption. Tables 1.3 and 1.4

report results of the model with interest rate differentials, which is stated below:

St+1

St

I£t+1

I$t+1

≥ 1 if the U.S. is in expansions at t (1.21)

St+1

St

I£t+1

I$t+1

< 1 if the U.S. is in contractions at t,

while Table 1.4 has the yen as the home currency. From the two tables, it is found

that the effectiveness of the FOIP model is reduced but still significant. The fact that

the model disregarding the funding cost performs better suggests that the Treasury

rate is not a good proxy for the funding cost. Since interest rates for 3-month bonds

used here are heavily affected by the federal funds rate, the interest rates may not

necessarily reflect the true funding cost to the investors. The situation is similar for

the Japanese rate, which has been near zero by the policy mandate of the Bank of

Japan.

Until this point, the simple FOIP model using the NBER business cycle dating

is shown to be a decent predictor of exchange rate movements and the simple FOIP

model beats the random walk hypothesis. This implies that exchange rates are readily

linked to economic fundamentals. Following Yogo (2006) and Lustig and Verdelhan

(2007), I choose three factors, nondurable consumption growth, durable consump-

tion growth and market returns to express economic fundamentals. Yogo (2006)

establishes the theoretical link of these factors to the SDF through the investor’s

intertemporal consumption problem. Yogo (2006) argues that the three factors are

linked with NBER business cycle dating using a figure, similar to Figure 1.2. I esti-

mate a logistic model to investigate the link between the three factors and the NBER


Table 1.3: The simple FOIP model with Net Returns: United States

1 2 3 4 5 6 7 8

Net Returns during Expansions 1.26 3.31 2.39 -1.68 1.13 1.15 3.57 1.08 2.04 0.98 2.83

Net Returns during Contractions -2.68 -7.20 -3.84 -3.25 -4.90 -2.40 -3.35 -6.32 -0.24 -3.88 -7.33




Hypothesis0.80 0.02 0.39 0.89 0.15 0.11 0.00 0.01 0.00 0.02 0.00






Hypothesis0.75 0.00 0.20 0.75 0.11 0.04 0.00 0.01 0.00 0.01 0.00



Currency PortfoliosJapan GermanyUK

Note: Net Returns are in annualized percents on currency investments, taking the U.S. riskfree rate as a funding cost. See the note of Table 1.1


Table 1.4: The simple FOIP model with Net Returns: Japan

1 2 3 4 5 6 7 8

Net Returns during Expansions 4.11 6.70 4.32 0.75 3.77 4.10 7.09 3.32 6.53 3.00 7.93





Hypothesis0.01 0.01 0.11 0.08 0.02 0.15 0.00 0.05 0.01 0.00 0.04






Hypothesis0.11 0.04 0.05 0.15 0.11 0.25 0.01 0.20 0.15 0.02 0.15



Currency PortfoliosUS GermanyUK

Note: Net Returns are in annualized percents on currency investments, taking the Japaneserisk free rate as a funding cost. Business cycle data for Japan are from the Economic andSocial Research Institute (ESRI) of the Japanese government. See the note for Table 1.1 fordetails.


Table 1.5: Logistic Regression on the NBER Business Cycle Data with the threefactors

Estimate Standard Error P-value

145 71.5 0.043

251 76.9 0.001

15 4.3 0.001

c

d

m

Note: The table reports the logistic regression estimates of the equation (1.22), whichmatches the NBER business cycle data with a logistic model with three factors.

business cycle data, using the following equation:

Bt =1

1 + Exp [−α− βc∆ct − βd∆dt − βmrw,t]+ ϵt. (1.22)

Bt is an indicator of business cycles at period t with unity representing a contraction

and zero otherwise. As shown in Table 1.5, all of the three factors are significant

in explaining business cycles by the NBER. The predicted probability of contraction

is plotted in Figure 1.6 with contractions in the NBER data marked by shaded ar-

eas. During expansions in 1980s and 2000s, the predictions by the regression closely

trace the NBER data but register high probabilities of contraction for some periods

during the expansion in 1990s. However, the periods are not ruled as contractions

by the NBER. Since the NBER’s Business Cycle Dating Committee incorporates an

extensive set of data in their decisions, the three factors are likely to fall short of

the full diagnosis by the NBER. Therefore, the selected three factors should not be

considered to be exhaustive and a new factor can be found by searching variables

that reduce the residual of the logistic regression here. In this study, I rather focus

on establishing the link between fundamentals and exchange rates than searching for

a better set of factors.


1990 2000 20100.0

0.2

0.4

0.6

0.8

1.0

Year

Pred

icte

dPr

obab

ility

ofC

ontr

actio

n

Figure 1.6: Predicted Probabilities of Contraction by the three Factors

Note: The figure shows probabilities of contraction given three asset pricing factors. Theprobabilities are calculated from the logistic regression of the NBER business cycle data onthe three factors. Contractions are marked by shaded areas.


1.3.3 The Fundamental Open Interest Parity with Factors

The FOIP with factors is only testable if two sets of SDFs from the two countries are

available. The log of the SDF is expressed in a linear form of three factors above, as

shown in Appendix A.3. Estimation on the SDF is to find values of parameters in

the linear factor model that explain returns on assets. In the asset pricing literature,

portfolios of assets with similar characteristics are formed and used as test assets in

estimation in order to focus on characteristics related to nondiversifiable risks. These

characteristics are the book to market value ratios and sizes of stocks in the equity

market, or interest rates in the international bond market. As test assets, portfolios

of individual assets fend off the effect of idiosyncratic risks to which individual assets

are exposed and allow researchers to concentrate on characteristics of assets rather

than names of assets. For example, a change in the interest rate of a currency may

put a once high interest currency into a portfolio of low interest rate currencies.

An approach that takes one currency as a target of research falls prey to changing

characteristics of the currency in response to the position of its interest rate in the

contemporary global financial market, let alone idiosyncratic pricing errors from the

single exchange rate, which cannot be averaged out without forming a portfolio.

This empirical approach is consistent with theoretical lessons from the asset pric-

ing literature: (1) what matters or is priced in the market is nondiversifiable risk,

which is more pronounced by forming a portfolio, against the idiosyncratic risk of

an individual asset and (2) this nondiversifiable risk is compensated for because the

risk is associated with consumption growth risk. An investment position which gives

agent’s future marginal utility a wild swing should be compensated accordingly while

an asset position that anchors down future consumption should be valued or have

a low expected return. Yogo (2006) and Lustig and Verdelhan (2007) confirm that

average high yields of portfolios such as small stocks, value stocks or high interest rate

currencies are nothing but a compensation of high consumption growth risk associated

with those portfolios during contractions.

The generalized method of moments (GMM) is used to estimate SDFs and test

theoretical predictions. GMM uses moment conditions to estimate parameters. The


following moment conditions are used:(RUS,Excess

t

)−(RUS,Excess

t

) (fUSt − µUS

f

)′bUS = 0 (N × 1) (1.23)

fUSt − µUS

f = 0 (F × 1) (1.24)(RJP,Excess

t

)−(RJP,Excess

t

) (fJPt − µJP

f

)′bJP = 0 (N × 1) (1.25)

fJPt − µJP

f = 0 (F × 1) (1.26)((∆st + it − i$t

)− k −

(aUS

(bUS′fUS

t

)− aJP

(bJP′fJP

t

))−(∆qUS

t −∆qJPt))

Ut = 0, (M×1)

(1.27)

where N,F, and M are the number of test assets, factors and instruments for the

FOIP, respectively. RUS,Excesst is the real excess returns on currency portfolios for U.S.

investors and RJP,Excesst is the real excess returns for Japanese investors. The excess

return on the ith portfolio is expressed by

RUS,Excesst,i =

∑currency j∈ith portfolio

(St,j

St−1,j

Ijt − I$t

). (1.28)

fUSt is the vector of U.S. consumption factors and µUS

f is the vector of the means of

those factors. fJPt and µJP

f are defined similarly. bUS and bJP are factor loadings for

factors of the U.S. and Japan, respectively.

The most basic model is a linear factor model on the U.S., which is composed

of equation (1.23) and (1.24). Equation (1.23) is pricing errors of the test assets

and Equation (1.24) estimates the means of factors. Appendix D of Yogo (2006)

derives condition (1.23). Lustig and Verdelhan (2007) estimate exactly the same

model with two methods, a two-stage procedure by Fama and MacBeth (1973) and

a GMM procedure as a robustness check. I parameterize the model in terms of

factor loading (b) rather than factor prices (λ) where λ = Σffb with Σff being the

factor covariance matrix. Similarly, the Japanese SDF is estimated by equations

(1.25) and (1.26). Tables 1.6 and 1.7 show the two separate estimations of the linear

factor models for the U.S. and Japan, respectively. Moment conditions (1.23) and

(1.24) are used for the U.S. and conditions (1.25) and (1.26) are for Japan. Five


Table 1.6: Estimation of Linear Factor Models for the United States

CAPM CCAPM DCAPM EZ-CCAPM EZ-DCAPM

Factor prices (b)

Nondurables - -154.644 -105.608 -122.353 39.660

- (46.015) (51.112) (78.883) (121.816)

Durables - - 121.867 - -178.635

- - (51.774) - (134.298)

Market 10.790 - - 10.415 10.053

(5.370) - - (4.994) (7.987)

Statistics

MAE 0.197 0.150 0.155 0.138 0.141

R2

0.394 0.600 0.630 0.665 0.684

P-value for the entire estimation 0.408 0.047 0.285 0.294 0.780

P-value for asset pricing 0.451 0.133 0.419 0.561 0.910

Note: This table shows GMM estimation for the moment conditions (1.23) and (1.24). Eachcolumn has a model which employs different sets of factors. The spectral density matrixis estimated by Andrews and Monahan (1992)’s kernel estimation method. Test assetsare eight currency portfolios formed by similarity of interest rates. Mean average error(MAE) is in percent per quarter. The p-value for the entire estimation is the p-value forthe overidentifying test on the entire moment conditions with the degree of freedom beingthe number of test assets - the number of factors. The p-value for asset pricing is from theorthogonality test on the asset pricing errors under the null hypothesis that the returns ofcurrency portfolios are explained by the linear factor model.

combinations of factors are estimated here. They are the CAPM, CCAPM, DCAPM,

EZ-CCAPM and EZ-DCAPM, designated here per Lustig and Verdelhan (2007)’s

naming rules. The CAPM and CCAPM models use a single factor, market returns

and nondurable consumption growth respectively. The DCAPM and EZ-CCAPM

model use two factors, durable and nondurable consumption growth for the DCAPM

and nondurable consumption and market returns from the EZ-CCAPM. The EZ-

CCAPM model is proposed by Epstein and Zin (1991). Finally, the EZ-DCAPM

uses all of the three factors. Yogo (2006) applies a restriction on parameters on the

three-factor model, but here those restrictions are not applied because estimation of

the structural parameter is not the focus of this study.

There are a few points worth mentioning about GMM estimation. Once moment

conditions are set by an economic theory, the most crucial element in GMM estimation

is estimating the spectral density matrix at frequency zero. Andrews and Monahan

(1992)’s kernel estimation method is employed here and the bandwidth parameter is


determined by their automatic criteria with the quadratic spectral kernel as a kernel

function. Andrews and Monahan (1992)’s approach is different from Andrews (1991)

in that it applies a vector autoregressive structure (VAR) to make the spectral density

function flatter before estimating the spectral density matrix at frequency zero. Yogo

(2006) uses den Haan and Levin (2000)’s method which applies a vector autoregressive

structure on moment residuals and then treats residuals from the VAR model as white

noise. The method determines the autoregressive structure based on information

criteria such as the Akaike (1973) information criterion (AIC). den Haan and Levin

(2000)’s method is very sensitive to even precision errors. For instance, although there

is no great difference between the selected model and the second best model in terms

of the information criteria, the estimate of the spectral density matrix is significantly

different if the second best model is chosen for a few moment conditions and this

difference can be brought into the estimation even by different precisions in numerical

calculation. It is possible that two types of computer software with different numerical

precisions give out very different estimates.8 Therefore, I set the VAR structure to

a fixed number for Andrews and Monahan (1992)’s method. Since moment residuals

of the asset pricing do not have long tails, I set the autoregressive order to two.

I also ignore the cross autoregressive property because spurious estimation of cross

autoregressive structure makes the estimated variance of the moment residuals so

great that no model is rejected under any circumstances.

For the U.S., the EZ-DCAPM has the greatest R-square and the model is not

rejected by the test of overidentifying conditions as shown in Table 1.6. The p-

value for the entire estimation is the usual test of overidentifying conditions with the

degree of freedom equal to the number of test assets + the number of factors - the

number of estimated parameters. Note that the number of parameters is the double

of the factors employed since factor loadings and population means of the factors

are estimated. For both the U.S. and Japan, the market return factor is significant

in explaining returns on the currency portfolios. The model with only nondurable

8I found this peculiarity while replicating Yogo (2006). My program selected a different vectorautoregressive (VAR) structure with Yogo (2006) but his selected VAR structure has very similarinformation criteria values to the result of my program. The two different VAR structures producevery different estimates on parameters by the GMM procedure.


Table 1.7: Estimation of Linear Factor Models for Japan


Factor prices (b)

Nondurables - -50.276 44.918 -36.277 -60.043

- (46.321) (55.313) (87.250) (78.915)

Durables - - -87.884 - 89.249

- - (41.193) - (62.303)

Market 15.713 - - 14.991 12.360

(5.512) - - (6.437) (7.886)

Statistics

MAE 0.231 0.316 0.248 0.198 0.114

R2

0.251 -0.071 0.236 0.548 0.855

P-value for the entire estimation 0.487 0.001 0.177 0.333 0.566

P-value for asset pricing 0.897 0.002 0.189 0.716 0.772

Note: This table shows GMM estimation for the moment conditions (1.25) and (1.26). Seethe note for Table 1.6 for details.

consumption growth (CCAPM) is rejected for the U.S. as well as for Japan. For both

countries, the models with multiple factors are not rejected but the model with all

of the three factors (EZ-DCAMP) are the most significant in explaining the returns

in currency portfolios, with the maximum R-square and p-value for both countries. I

conclude that the EZ-DCAPM is the best model in explaining the returns in currency

portfolios for the U.S. and Japan among the models with the three potential pricing

factors.

The results of the two tables confirm that fundamentals explain returns on cur-

rency investments. In the previous subsection, fundamentals are expressed whether

the economy of the funding currency is in contraction or not. In this section, three

factors are introduced to represent fundamentals. All results are consistent with the

predictions by the FOIP. If one combines two estimations from individual countries,

here, the U.S. and Japan, the FOIP with factors (1.27) can be directly estimated and

one can check whether the FOIP with factors holds for the dollar/yen exchange rate.

Moment condition (1.27) restates the FOIP with factors. Two scale parameters

aUSand aJP are added here to accommodate differences between the exchange rate

and asset returns. Without these parameters, the model performs very poorly. The

full model with conditions (1.23) to (1.27) is estimated and reported in Table 1.8. As


instruments for equation (1.27), expressed as Ut in the equation, the lagged data for

factors and Japanese portfolio excess returns are used. The theory predicts that the

residual on the FOIP,((∆st + it − i$t

)− k −

(aUS

(bUS′fUS

t

)− aJP

(bJP′fJP

t

))−(∆qUS

t −∆qJPt))

,

is orthogonal to the Japanese asset returns. A test of orthogonality on GMM models

developed by Eichenbaum, Hansen, and Singleton (1988) is applied and the last row

of Table 1.8 reports the p-value of the test under the null hypothesis that the orthog-

onality condition holds. In this case, the moment condition which uses the Japanese

portfolio returns as instruments is tested. All but CCAPM are rejected at the 5%

confidence level. The high p-values under the random walk hypothesis imply that

condition (1.27) as an empirical equation for the exchange rate is worse than the ran-

dom walk model. The goodness-of-fit statistics for the U.S. and Japanese portfolios

are largely unaffected by introducing the FOIP equation.

The outcome of the orthogonality test seems to suggest that the FOIP condition

fails to be a practical theory for the bilateral exchange rate. However, this inter-

pretation is incorrect because both the yen and the dollar are a low interest rate

currency to investors of the other country as shown in Figure 1.7. The Dollar is on

average at 2.3th portfolio in currency portfolios available to Japanese investors and

the yen is at 1.3th portfolio to U.S. investors. There are 8 portfolios for each country

and therefore, the average position is 4.5. The realized returns of the low interest

currencies should be less correlated with economic fundamentals of the country of

the funding currency. Therefore, the yen exchange rate movement to U.S. investors

should be largely uncorrelated with U.S. fundamentals since the yen is a low interest

rate currency to U.S. investors. Similarly, the dollar exchange rate should be weakly

correlated with Japanese fundamentals. Hence, the dollar-yen exchange rate acts like

a random walk free from the economic fundamentals of both countries. Since pricing

equations for portfolios of high interest currencies are more informative than the low

interest currencies, the GMM estimation pays more attention to these assets and the

estimated factor loadings reflect this structure. Therefore, any predicted movement of

the exchange rate between two low interest rate currencies is simply spurious. Then,

why does not the GMM estimation procedure simply set the scale parameters aUS

and aJPto zero? The answer lies in the incompleteness of the factors. In the previous


Table 1.8: Estimation of Linear Factor Models with the FOIP


Factor prices (b)

United States

Nondurables - -100.255 -9.795 -95.499 -103.388

- (30.937) (33.427) (72.557) (111.109)

Durables - - 98.410 - -57.607

- - (33.439) - (142.280)

Market 9.851 - - 10.915 12.869

(3.912) - - (4.607) (6.192)

Japan

Nondurables - 0.763 1.662 -67.609 -71.142

- (28.681) (43.236) (59.019) (59.143)

Durables - - -58.984 - 86.053

- - (30.763) - (50.127)

Market 9.908 - - 11.110 11.577

(4.011) - - (4.620) (6.081)

Statistics

United States

MAE 0.197 0.150 0.156 0.138 0.137

R2

0.394 0.600 0.630 0.665 0.683

Japan

MAE 0.231 0.316 0.248 0.198 0.114

R2

0.251 -0.071 0.236 0.548 0.855

P-value under the random walk hypothesis 0.946 0.682 0.851 0.462 0.254

p-value for the entire model 0.079 0.004 0.006 0.196 0.608

p-value for the orthogonality test 0.001 0.138 0.000 0.004 0.013

Note: This table shows a GMM estimation for the moment conditions (1.23) to (1.27). Thep-value under the random walk hypothesis reports the probability of matches in directionsbetween the predicted exchange rate movements and the realized ones under the null hypoth-esis that the model does not have any prediction power. The p-value for the orthogonalitytest is the probability that the test statistic gives as extreme or more extreme value thanthe observed test statistic if the moment condition (1.27) holds using returns of currencyportfolios available to Japanese investors.


subsection, I show that the three factors are not totally satisfactory for predicting

U.S. business cycles by the NBER. Since there are missing factors, the residual of

the FOIP condition includes the missing factors and the returns in Japanese assets

react to these missing factors, thereby distorting the moment condition between the

Japanese assets and the residual of the FOIP equation. This result suggests that

further search for factors that account for business cycles is warranted.

1.4 Discussions

1.4.1 Carry Trade Returns

Carry trade is a currency trading strategy that borrows in a low interest rate currency

and invests in a high interest rate currency. In the context of this study, carry trade is

equivalent to selling portfolio 1 and buying portfolios with higher numbers. Table 1.9

reports the realized returns and the predicted returns of carry trades. First, the

actual nominal returns and predicted nominal returns are derived. The predictions

are based upon the linear factor model for the U.S. and in particular, the estimate

for the EZ-DCAPM is used. The upper panel of the table shows that the linear

factor model explains successfully the returns of currency investments for the entire

period. For the golden era of carry trade, defined here as being between the first

quarter of 2000 and the last quarter of 2007, portfolio 1 has lower realized returns

than its predictions and portfolios 6,7, and 8 have higher realized returns than their

predictions from the linear factor model. This finding is translated into returns of

carry trade in the lower panel. There are no significant differences in realized returns

and predicted returns during the entire sample period. A carry trade strategy would

have earned an extra 0.9% per annum over its predicted return if the dollar had

been used as a funding currency and 0.2% over its predicted return if portfolio 1 had

been shorted to fund the investment. These additional returns are so small that they

can be easily justified by the potential risk of the peso problem although the sample

period observes few such incidents.

These results suggest that carry trade is nothing but another vehicle of investments


Yen's average position: 1.3

Dollar's average position: 2.3

1980 1990 2000 20100

2

4

6

8

Year

Por

tfolio

Num

ber

Yen's position in U.S. currency portfoliosDollar's position in Japanese currency portfolios

Figure 1.7: The yen’s position in U.S. currency portfolios and the dollar’s position inJapanese currency portfolios

Note: Currency portfolios are formed by interest rate levels of foreign currencies. U.S.currency portfolios are currency portfolios available to U.S. investors. Portfolio 1 is thegroup of currencies with lowest interest rates and portfolio 8 is the group of currencies withhighest interest rates. The average position is 4.5.


to hedge consumption growth risk. During the golden era of carry trade, the carry

trade strategy paid off more than its fair prices or predicted returns that compensated

consumption risk, as shown in the lower part of panel B. Not only did portfolios 6,7,

and 8 exhibit higher returns than their predictions but portfolios 3, 4, and 5 also

performed better than their predictions by the linear factor model. On average, this

strategy during the era paid 4.4% per annum more than its fair returns if portfolio

1 had been used as a funding source and 2.4% if the dollar had been the used as

a funding source. These observations imply that the currency trading strategy is

not necessarily a superior investment method to domestic assets. The extraordinary

returns during the golden era are balanced by bad performances in the rest of the

sample period. Nonetheless, the period was a lucky streak for carry traders. The cause

of this luck can be attributed to a short contraction and long expansions during this

period. Long positions in high interest rate currencies render high returns during U.S.

expansions like other assets with high consumption growth risk such as value stocks.

The picture for Japanese carry traders is similar and their strategy is boosted by

the near-zero interest rate of the yen, as shown in Table 1.10. During the golden era,

the interest rate of the yen was measly 0.1% per annum and Japan experienced a

very short contraction in 2002 like the U.S. Japanese carry traders enjoyed 6.1% per

annum on the strategy in additional to the fair compensation for consumption growth

risk associated with the strategy. For the entire period, carry trades with the yen as

a funding currency did not pay off more than the risk associated with it, as shown

in the upper part of panel B of the table. For both Japanese and U.S. carry traders,

the golden era was fortuitous but in the long-run, carry trade is compensated for as

much as consumption growth risk associated with it.

1.4.2 The Forward Premium Puzzle

In the previous section, the simple fundamental open interest rate parity model is

shown to be superior to the random walk model. In the simple FOIP model, the

depreciation of a foreign currency is less than the nominal interest rate of the foreign


Table 1.9: Carry Trade Returns in dollars

1 2 3 4 5 6 7 8

The Entire Period (1981:4~2009:3)

Actual Nominal Returns 5.1 0.9 3.1 5.3 5.7 7.6 5.0 6.8 5.3 6.2

Predicted Nominal Returns 2.4 3.9 4.1 5.3 4.6 6.6 6.4 4.3

The Golden Era (2000:1~2007:4)




Dollar as the funding currency

Actual Nominal Returns 0.9 -2.0 0.2 0.7 2.5 -0.1 1.8 0.3 1.1

Predicted Nominal Returns -2.7 -1.2 -1.0 0.2 -0.5 1.6 1.4 -0.8

Portfolio 1 as funding currency

Actual Nominal Returns 0.2 2.2 2.6 4.5 1.9 3.7 2.2 3.1

Predicted Nominal Returns 1.5 1.7 3.0 2.2 4.3 4.1 1.9



Actual Nominal Returns 2.4 -0.9 0.8 3.3 3.5 2.3 5.9 7.8 10.4

Predicted Nominal Returns 0.5 2.7 0.9 3.1 1.6 -1.9 0.7 5.8



Predicted Nominal Returns 2.2 0.4 2.6 1.1 -2.4 0.2 5.3

Currency Portfolios sorted by interest rates

Panel A: Mean Annual Returns on Foreign currency investments

Panel B: Mean Annual Returns on Carry Trade

Risk FreeAverage

Residual

Note: The returns are expressed in percent per annum. The predicted returns are calculatedfrom the predicted returns by the model EZ-DCAPM. Average Residual reports the gapbetween the actual returns and the predicted returns.


Table 1.10: Carry Trade Returns in Japanese yen

1 2 3 4 5 6 7 8


Actual Nominal Returns 2.4 0.7 -0.7 1.3 2.5 4.2 1.1 3.3 1.7 2.5

Predicted Nominal Returns -1.0 0.5 1.7 4.0 2.1 3.8 -0.9 0.4






Actual Nominal Returns 0.7 -3.1 -1.1 0.2 1.8 -1.2 0.9 -0.7 0.2

Predicted Nominal Returns -3.4 -1.9 -0.7 1.7 -0.3 1.4 -3.3 -2.0





Yen as the funding currency

Actual Nominal Returns 6.1 4.8 7.0 8.7 9.3 7.7 12.1 13.6 16.2





Currency Portfolios sorted by interest rates

Panel A: Mean Annual Returns on Foreign currency investments

Panel B: Mean Annual Returns on Carry Trade

Risk FreeAverage

Residual

Note: The returns are expressed in percent per annum. The predicted returns are calculatedfrom the predicted returns by the model EZ-DCAPM. "Average Residual" reports the gapbetween the actual returns and the predicted returns.


currency during expansions and the opposite is true during contractions. The FOIP

model implies that returns on currency investments depend on business cycles. But

degrees of dependence differ across currency portfolios. Portfolios of low interest

rate currencies are less dependent on business cycles of the U.S., while portfolios of

high interest rate currencies depend more strongly on business cycles. In the light

of this finding, I revisit the issue of the forward premium puzzle. The first step is

confirming whether the forward premium puzzle is prevailing in currency markets.

Table 1.11 reports the traditional forward premium puzzle coefficient. The p-values

are calculated for the null hypothesis that the OIP is true or that the coefficient

of (i£-i$) on the regression of ∆s on (i£-i$) is negative unity where i£ stands for

the interest rate of the foreign currency and ∆s is the exchange rate against the

currency. The exchange rate is expressed by the dollar amount for a unit of the

foreign currency. I classify sample periods into three parts: contraction, recovery, and

expansion. Contraction periods are the quarters of economic contraction announced

by the NBER. Recovery periods are quarters that are not in a contraction but the

U.S. interest rate is very close to the average interest rate of the lowest interest rate

currencies. As shown in Figure 1.8, the U.S. interest rate stays close to the average

interest rate of lowest interest rate currencies for a while after contractions. I call

these periods of low U.S. interest rate recovery periods. Finally, expansion periods

are quarters that are neither contraction nor recovery. In other words, expansion

periods have it that the U.S. rate is substantially higher than those of globally lowest

interest rate currencies and that the U.S. economy grows at the same time.

Three currency portfolios and three individual currencies are reported in Ta-

ble 1.11. Among three portfolios, portfolio 1 exhibits the forward premium puzzle for

the entire period at the 5% significance level. In particular, the actions of portfolio 1

during expansion periods drive the puzzle for this portfolio. The three currencies in

the table share a similar pattern with portfolio 1. This shows that the puzzle does not

prevail across all currencies in the global market. The puzzle is an exceptional episode

for low interest rate currencies and the puzzle seems to appear during expansion pe-

riods. A similar estimation without subtracting the U.S. rate from the foreign rate is

reported in Table 1.12, which is more in line with the OIP than Table 1.11. The OIP


1990 2000 20100

2

4

6

8

10

12

Year

%

Portfolio 1United States

Figure 1.8: The U.S. interest rate and the average interest rate of the portfolio withlowest interest rate currencies (portfolio 1)

Note: The U.S. rate is the yield on the Treasury 3-month bond and the foreign rates arebased on similar sovereign bonds.


condition without the U.S. rate has the same parameter under the null hypothesis of

the OIP if the U.S. and foreign rates are not correlated. If the U.S. and foreign rates

are positively correlated, estimated coefficients will be upwardly biased. The null

hypothesis of the OIP for this revised regression is not rejected for the portfolios and

is rejected only for the Japanese yen. Estimates in Table 1.12 are closer to negative

unity than those in the Table 1.11. Therefore, the null hypothesis of the OIP is less

likely to be rejected for the regression equation without the U.S. rate. This is indirect

evidence that the reaction of the error term in the OIP is the cause of the puzzle or

that the error term is correlated to interest rates. This outcome suggests that the

omitted OIP model disregarding the U.S. rate is possibly a better model to check

OIP if the regression assumption that the explanatory variables is not orthogonal to

the error does not hold. Another explanation is that the U.S. rate may not represent

the true funding cost. In two exercises, violations of the OIP are found in the low

interest rate currencies and during expansions.

The cause of the forward premium puzzle for low interest rate currencies can

be explained by the low risk awareness during expansion periods. As the risk free

rate of the dollar increases during expansion periods, the competing low risk assets

such as currency portfolios of low interest rate currencies become less attractive to

investors because of their relatively low yields. Having optimistic prospects, U.S.

investors withdraw funds from low interest rate currencies, causing depreciations of

those currencies. This explanation is also applied to other currency portfolios. In

general, high interest rate currencies do not necessarily depreciate during expansion

periods and if they do, the depreciation is milder than in contraction periods. This

explanation depends on differences in expectations of investors between expansion

periods and other periods. Alternatively, the puzzle can take place if an increase in

the U.S. rate slows its economy down, causing appreciation of the dollar.

The previous explanation can be analyzed by decomposing exchange rate changes.

From the estimation of the FOIP with factors, a nominal exchange rate change can

be decomposed into four parts:

∆st+1 = −(it+1 − i$t+1

)+(k + bUS′fUS


)+(∆qUS

t+1 −∆qJPt+1

)+ ηt+1. (1.29)


Table 1.11: Forward Premium Puzzle Regressions under the OIP

PeriodAppreciation of

the foreign currency

Foreign rate

-U.S. rateEstimate P-value

All 0.17 -2.19 1.25 0.00

Contraction -1.01 -2.38 0.56 0.08

Recovery 3.08 -0.04 -8.54 0.82

Expansion -0.41 -2.81 2.42 0.00

All -0.76 3.44 -0.33 0.18

Contraction -6.78 3.44 -1.37 0.58

Recovery 1.70 5.32 -4.21 0.88

Expansion -0.05 2.86 0.56 0.05

All -10.06 11.98 -0.50 0.07

Contraction -12.41 10.26 -2.25 0.85

Recovery -7.09 15.34 -1.79 0.86

Expansion -10.39 11.36 -0.05 0.01

All 3.23 -2.62 3.64 0.00

Contraction -0.42 -2.38 4.28 0.05

Recovery 9.74 -0.19 -0.04 0.40

Expansion 2.20 -3.42 5.66 0.00

All -0.59 2.36 0.45 0.10

Contraction -9.46 2.62 -2.12 0.62

Recovery 1.03 3.35 -3.50 0.77

Expansion 1.10 1.99 2.72 0.00

All 1.95 -0.55 0.91 0.04

Contraction -4.03 0.21 0.12 0.38

Recovery 6.06 2.37 -4.38 0.80

Expansion 2.17 -1.61 4.40 0.00

Panel F: Germany

Panel B: Currency Portfolio 4

Panel A: Currency Portfolio 1

Panel C: Currency Portfolio 7

Panel E: United Kingdom

Panel D: Japan

Note: The regression equation is ∆st=α+β(i£t − i$t

)+νt, where i£ is the interest rate of a

foreign currency and ∆s is the exchange rate change against the currency, expressed by thedollar amount for a unit of the currency. The null hypothesis for the p-value is the openinterest rate parity or β = -1. The data is for the period 1982:1 to 2009:4.


Table 1.12: Forward Premium Puzzle Regressions without subtracting the U.S. ratefrom foreign rates

PeriodAppreciation of

the foreign currencyForeign rate Estimate P-value

All 0.17 2.75 -0.26 0.17

Contraction -1.01 2.79 -0.05 0.30

Recovery 3.08 2.41 -0.52 0.35

Expansion -0.41 2.85 0.12 0.18

All -0.76 8.38 -0.39 0.16

Contraction -6.78 8.60 -0.37 0.32

Recovery 1.70 7.78 -1.02 0.51

Expansion -0.05 8.51 0.13 0.06

All -10.06 16.92 -1.03 0.54

Contraction -12.41 15.42 -1.48 0.68

Recovery -7.09 17.80 -1.60 0.85

Expansion -10.39 17.01 -0.70 0.25

All 3.23 2.32 1.17 0.02

Contraction -0.42 2.78 0.24 0.33

Recovery 9.74 2.27 0.30 0.22

Expansion 2.20 2.23 2.02 0.02

All -0.59 7.30 -0.30 0.15

Contraction -9.46 7.79 -0.96 0.49

Recovery 1.03 5.81 -1.30 0.57

Expansion 1.10 7.65 0.67 0.02

All 1.95 4.40 -0.47 0.32

Contraction -4.03 5.37 -1.61 0.60

Recovery 6.06 4.83 -1.36 0.57

Expansion 2.17 4.05 2.30 0.04

Panel F: Germany

Panel B: Currency Portfolio 4

Panel A: Currency Portfolio 1

Panel C: Currency Portfolio 7

Panel E: United Kingdom

Panel D: Japan

Note: The regression equation is ∆st = α+ β i£t + ϵt. The null hypothesis for the p-value isβ = -1. The data is for the period 1982:1 to 2009:4.


The first component is the interest rate differential, which drives the forward premium

regression coefficient to negative unity. The second component is the exchange rate

change attributed to fundamentals. The third component is the inflation differential

between the two countries. The last term is the residual of the FOIP. The decomposi-

tion is applied to the EZ-DCAPM model. Since the three factors of the EZ-DCAPM

are far from an exhaustive set of factors that would fully account for business cy-

cles, the last term reflects the missing factors as well as residuals owing to market

incompleteness. Regression results for each component are reported in Table 1.13.

For the dollar-yen exchange rate, the forward premium puzzle happens during ex-

pansion periods. The other two phases cannot reject the null hypothesis that the

slope coefficient of the simple regression ∆st+1 on(it+1 − i$t+1

)is negative unity. For

the expansion period, the contribution of fundamentals to exchange rate changes is

significantly positive. A high interest rate in the U.S. slows down its economy thereby

strengthening the dollar. The last three contractions in the U.S. were preceded by

hikes in its interest rate, as confirmed by Figure 1.8. Therefore, the forward premium

puzzle on the Japanese yen is partly caused by the business cycle response to a high

U.S. rate.

1.5 Conclusions

This paper resolves two issues in international finance: the formidable random walk

hypothesis of exchange rate movements and the mysterious forward premium puzzle.

The major finding here is that both the hypothesis and the puzzle are confined to

low interest rate currencies. Previous studies on these subjects use currencies of

advanced economies such as Japan, Germany or Great Britain against the U.S. dollar.

These currencies have exceptionally low interest rates and therefore, the results using

these currencies cannot be generalized to other currencies, especially ones with higher

interest rates. The empirical results in this paper show that the fundamental open

interest parity—an open interest parity with the error term accounted for by business

cycle risk—is a valid theory to explain the exchange rate movements. This theory is

most effective for currencies with high interest rates because a priori high yields of


Table 1.13: Decomposition of the forward premium puzzle coefficient

Dependent Variable Estimate Std Err Pvalue

Exchange rate 3.26 1.18 0.01

Interest rate differential -1.00 - -

Exchange rate Change owing to fundamentals 1.15 0.74 0.13

Exchange rate Change owing to Inflation -0.05 0.17 0.75

Exchange rate unaccounted by FOIP 3.17 1.45 0.03




Exchange rate Change owing to Inflation 0.00 0.48 1.00





Exchange rate Change owing to Inflation -1.19 0.49 0.02





Exchange rate Change owing to Inflation 0.28 0.27 0.29


Panel A: The whole period (1981:4 ~ 2009:3)

Panel B: Contraction Periods

Panel C: Recovery Periods

Panel D: Expansion Periods

s

bUS ' f US bJP ' f JP

s


s


s


qUS qJP

qUS qJP


qUS qJP


qUS qJP

i i$

i i$

i i$

i i$

Note: The regression equation is Y t=α+β(it − i$t

)+ϵt. Yt are components of exchange rate

decomposition by the FOIP with factors: ∆st+1 = −(it+1 − i$t+1

)+(bUS′fUS


)+(

∆qUSt+1 −∆qJPt+1

)+ ηt+1. The parameter b’s are from the estimation on the EZ - DCAPM

model in Table 1.8. The null hypothesis for the p-values is β = 0. The data is for the period1981:4 to 2009:3.


these currencies are compensations for the high business cycle risk of long positions

in these currencies. On the other hand, low interest rate currencies are less connected

with economic fundamentals. This is not an anomaly but the defining characteristic

of low risk assets, which are less correlated with economic fundamentals than high

risk assets. Risk of assets in the economic sense is measured by their correlations with

business cycles, the risk of which cannot be diversified by forming a portfolio. In the

light of this insight, seeming random walk movements of low interest rate currencies

are no longer puzzling. Since these currencies are low risk assets, they should be

less correlated to business cycles or fundamentals that affect business cycles than

currencies with higher interest rates are.

The benefit of introducing business cycles to exchange rate theories is not limited

to beating the random walk. The forward premium puzzle or violation of the open

interest parity (OIP) is resolved by putting business cycles into the equation. The

textbook OIP is only justifiable if investors are risk neutral or the risk-neutral measure

and the data generating measure coincide. Clearly, either assumption is plausible.

This paper derives a new interest rate parity condition under a mild assumption,

called the fundamental open interest parity (FOIP), which directly accounts for the

residual term of the OIP. However, it is found that the FOIP cannot explain the

U.S.-Japan exchange rate because the single bilateral exchange rate is subject to

idiosyncratic movements by which pricing signals from fundamentals are disrupted

and, more importantly, the dollar and the yen are low interest currencies to each

other for investors of the other country.

The direct implication of the FOIP is that exchange rate movements depend on

phases of business cycles. The forward premium puzzle is found to be pronounced for

low interest rate currencies and during expansions. This timing and currencies of the

forward premium puzzle suggest that the abnormality happens in low risk situations.

Since realized depreciations are less than interest gains in currency investments dur-

ing expansions, as shown in the empirical section, high interest rates in investment

currencies are more likely to be translated into high yields during expansions. The

shift of funds from low interest rate currencies to high interest rate currencies or to

domestic low risk assets during expansions can cause the low interest rate currencies


to depreciate and high interest rate currencies to appreciate, thereby violating the

open interest parity condition. Another channel that drives the forward premium

puzzle is that increases in the U.S. rate during expansions slow down economic activ-

ities in the U.S., thereby influencing the business cycle component in the FOIP and

strengthening the dollar.

The approach used in this paper is heavily influenced by developments in finance

theories, especially consumption-based capital asset pricing models and the portfolio

approach in the empirical asset pricing literature. Previous results on the two issues

were mostly based upon empirical studies of a small set of currencies with similar

characteristics. In the theoretical side of the issues, the derivation of OIP lacked a

careful treatment in the asset pricing aspect of the exchange rate. The present study

offers a new theoretical outcome on exchange rates that is consistent with the asset

pricing theory and sheds a light on the two issues. The forward premium puzzle is

an issue of missing variables in regression if it exists. The random walk hypothesis is

a natural outcome in the asset markets.

Chapter 2

Carry Trade and Global Financial

Instability

2.1 Introduction

A striking development in international finance in the latter half of 2008, in conjunc-

tion with the financial turmoil originated from the United States, is depreciations

of peripheral currencies. While four major international currencies—the U.S. dollar,

the euro, the pound sterling and the Japanese yen, appreciated, peripheral currencies

depreciated, an event consistent with the theory in the previous chapter. Considering

the fact that the domestic financial markets of the four currencies were more or less

in disarray, the strong appearance of the four currencies cannot be easily dismissed as

investors’ collective flights to safety. This study offers a channel by which this incident

is realized. Increases in perceived counterparty risk in financial markets of the four

major currencies caused credit crunches in those markets. The credit crunch made

renewals of credits extended to assets in peripheral countries untenable. Before the

crisis, cheap credits in the four major currencies were exploited to take advantage of

high interest rates in peripheral currencies. This method of opportunistic investments

is called carry trade. One of the well documented episodes of carry trades is the one

between the Japanese yen and the New Zealand dollar (NZD) or other currencies in

the Asia and Pacific region. The yen carry trade was so rewarding at the time that an

55

CHAPTER 2. CARRY TRADE 56

2000 2002 2004 2006 2008

50

60

70

80

90

Exchange rate yen NZD

2000 2002 2004 2006 2008

1500

2000

2500

3000

3500

4000

4500

Banks' claimsMil $

Figure 2.1: The yen/New Zealand dollar exchange rate and Japanese banks’ claimson New Zealand banks

Note: The figures shows yen/New Zealand dollar exchange rate and Japanese banks’ claimson New Zealand banks. The data are from the Bank for International Settlements.

iconic Japanese housewife, Mrs. Watanabe was coined as a driving force behind the

yen carry trade to signify easy and lucrative dimensions of currency trading, which

traditionally has been limited to trading rooms of major global banks.

The drastic depreciation of the New Zealand dollar against the yen along with the

massive flight of yen credit from the country, which is shown in Figure 2.1, supports

the argument that the unwinding of carry trades is the behind this development.

The central question of this study is whether carry trades caused the similar

movements in exchange rates and funds across the world. Before delving into details

of the question, a basic description on carry trades is in order. A carry trade in

foreign exchange markets is a set of profit-seeking transactions to take advantage of

interest rate differentials across countries. A carry trade involves two currencies, a

funding currency and an investment currency. The funding currency is a currency

with a low interest rate and the investment currency is the counterpart of the funding

currency with a high interest rate. An investor employing a carry trade strategy

usually borrows in a funding currency and buys an asset which pays interests in an

investment currency.

The main profit driver of a carry trade is the interest rate differential between


Table 2.1: Returns on carry trades

Funding Currency Returns from Returns of Investment

Funding Investment Appreciation Carry trades Currencies

US Dollar 3.4 10.2 1.1 7.9 Brazil, Mexico, and Canada

Euro 3.2 7.4 1.0 5.2 Iceland, Poland, and Czech Republic

Japanese Yen 0.1 5.3 5.2 10.7 Australia, Korea, and New Zealand

Interest rates

Note: This table reports returns on carry trade for selected countries.

the funding currency and the investment currency and it is sometimes reinforced by

a trend of appreciation of the investment currency. Since this method of investment

incorporates a foreign currency, the main risk factor is sudden discrete depreciation of

the investment currency and/or appreciation of the funding currency. One may argue

that this risk can be hedge by buying the funding currency in the forward market.

Covered interest rate parity dictates that the payoff from the hedging transaction is

exactly the opposite of the original carry trade transaction.1 For instance, investors

borrowed in yen at a very low interest rate and bought high-yield assets denominated

in the New Zealand dollar prior to 2008. Table 2.1 reports that returns on carry

trades, taking each of the three major currencies as an investment currency, from

2002-2007, showing that there had been sufficient incentives for carry trades before

the crisis of 2008. The disrupt aspect of carry trade is that the built-up position can

be abruptly withdrawn at the first glimpse of trouble, leaving investment currencies

vulnerable to sudden depreciations. This incident of unwinding carry trades may

result from a sudden credit crunch in the funding currency, as experienced in the

later half of 2008.

Previous studies on carry trades focus on explaining abnormally high returns

under the traditional asset pricing model or alternatively attribute the excessive re-

turns to market inefficiency. Brunnermeier, Nagel, and Pedersen (2009) explains the

1The set of transactions of borrowing in a funding currency and selling the funding currencyfor an investment currency in the spot market and then depositing the proceeds in the investmentcurrency is equivalent to buying the investment currency in the forward market. Some authorsdefine carry trade by buying the investment currency in the forward market and selling it in thespot market at the maturity of the forward contract.


carry trade return from risk premium on funding liquidity, while Jorda and Taylor

(2009) offers an investment strategy to fend off the 2008 crash, potentially achieving

abnormally high returns in carry trade. Burnside, Eichenbaum, Kleshchelski, and

Rebelo (2008) argue that the high returns of carry trade are compensations for the

peso problem but Farhi, Fraiberger, Gabaix, Rancire, and Verdelhan (2009) argues

that crash risk accounts for only 20 percents of the returns. The previous chapter of

this thesis offers an explanation that high returns of carry trade is nothing but a com-

pensation for high consumption risk associated with the currency trading strategy.

High returns of the strategy prior to the 2008 crash is attributed to long expansions

and a mild recession in the U.S. from 2001 to 2007.

What distinguishes this study with previous ones is that it investigates the causal-

ity between carry trade and exchange rate movements in 2008. It starts with a partial

equilibrium model of the local foreign exchange market and then translates the model

into a simultaneous equations model to estimate the model parameters. A similar the-

oretical approach is taken by Kouri (1981). For estimation, a set of cross-sectional

data is used and a pair of an investment currency and a funding currency constitutes

an observation. The system of simultaneous equation is estimated by the method of

three stage least squares. Based on estimation results, answers to questions regarding

on the aforementioned developments in foreign exchange markets in 2008 are offered.

The result confirms that the depreciations of peripheral currencies were caused by un-

winding of carry trade positions, which had been previously built up. Furthermore, it

is found that there are distinctive characteristics across the four funding currencies:

the U.S. dollar, the euro, the pound sterling and the Japanese yen, and individual

investment currencies reacted differently against each funding currency. The first

notion is instrumental in explaining the huge appreciation of the yen compared with

other funding currency. The second notion explains the differences in magnitudes of

depreciations of investment currencies against each funding currency. The rest of

this essay is organized in the following way. Section 2.2 presents the conceptual par-

tial equilibrium model of the foreign exchange. Section 2.3 translates the conceptual

model into an empirical model. Section 2.4 provides the details of estimation and


results from it. Section 2.5 spells out implications of the findings of this study, an-

swering questions over the unwinding of carry trades. Finally, Section 2.5 concludes.

2.2 Conceptual Model

In this section, a conceptual model for a local foreign exchange market is presented

and through this model, results of empirical estimation are interpreted. The model

describes the market in a framework of supply and demand. There are two groups

of agents: domestic banks and foreign banks. The price in this market is defined

by units of the foreign currency per local currency. Therefore, an appreciation of

the local currency is expressed by an increase of the price. Demand and supply are

measured in terms of the local currency. Demand in this market is a willingness to

take the local currency, paying in the foreign currency.

For domestic banks, their collective demand depends on the price and mercantile

exports. With a high price, which means a high price of the local currency in terms

of the foreign currency, the domestic banks is less willing to exchange their foreign

currency holdings into the local currency. The negative sign in (2.1) expresses this

tendency. Exports represent how much local exporters earn the foreign currency

by selling goods and services. An increase in exports brings additional demand on

the local currency to the market, thereby having a positive impact on the domestic

demand (DD),

DD = fDomestic,Demand[p,Exports].

− +(2.1)

Domestic supply (DS) represents the quantity of the local currency that domestic

banks are willing to purchase given the price and the level of imports. Domestic banks

are more willing to sell the local currency as the local currency becomes dearer in

the market, and therefore, domestic supply increases with the price. Since importers

exchange the local currency into the foreign currency, additional imports drive up the


supply of the local currency in the market,

DS = fDomestic,Supply[p, Import].

+ +(2.2)

Net domestic demand (NDD) is the net demand for the local currency from domestic

banks given a price and, the exports and imports levels:

NDD = DD−DS

= fDomestic[p,Export, Import].

− + −(2.3)

The discussion of domestic demand and supply is expressed in Figure 2.2. When

net domestic demand is less than zero in equilibrium, domestic demand of the local

currency is less than domestic supply, or the foreign banks buy the remaining position

in the local currency. In this case, foreign banks’ claims on domestic banks increase.

In the case that net domestic demand is greater than zero in equilibrium, the foreign

claims decrease because of foreign banks’ additional supply of the local currency.

For foreign banks, they react in the same way for price movements as domes-

tic banks. But their demand and supply are also affected by carry trades. The two

stages of carry trade, building up and unwinding have different effects on demand and

supply of foreign banks. On the one hand, during the build-up stage, foreign carry

traders expand their positions in the local currency, earning profits from the interest

rate differential and occasionally from appreciations. As more private investors like

Mrs. Watanabe jump on the carry trade bandwagon after observing extraordinary

profits from carry trades especially during a peaceful period of the international fi-

nancial market, their investments directly affect foreign banks’ demand of the local

currency.2 On the other hand, unwinding of carry trade releases the local currency

2This assertion can be supported by the traditional asset pricing model by changing risk awarenessof investors. Alternatively, the behavior of “chartists” in behavioral finance can provide a rationale.One of recent studies on exchange rates in the behavioral finace approach is de Grauwe and Grimaldi(2006)


Domestic

Supply

Domestic

Demand

$ inv. currency$ investment currency

Net

Domestic

Demand

Change of Foreign Position

Increase in Foreign

ClaimsDecrease

in Foreign Claims

Figure 2.2: Domestic Demand and Supply

Note: The figure exhibits the determination of net domestic demand. The dollar is theinvestment currency.

to the market as foreign carry traders sell off their positions in the local currency

through their banks. Equations (2.4) and (2.5) shows the demand (FD) and supply

functions (FS) for foreign banks. Net foreign supply (NFS), which is defined by the

difference between foreign supply and foreign demand, is shown in (2.6). A graphical

representation of foreign demand and supply is in Figure 2.3.

FD = fForeign,Demand[p, (Building up carry trade)]

− +(2.4)

FS = fForiegn,Supply[p, (Unwinding carry trade)]

− +(2.5)

NFS = FS− FD

= fForeign[p, (Unwinding carry trade), (Building up carry trade)]

+ + −(2.6)


Foreign

Supply

Foreign

Demand

$ inv. currency$ inv. currency

Net

Foreign

Supply

Change of Foreign Position

Figure 2.3: Foreign Demand and Supply

Note: The figure exhibits the determination of net foreign supply of the local currency.

An equilibrium of the market is defined by the exchange rate and the fund balance

at which net domestic demand and net foreign supply meet. With positive fund

balance in equilibrium, net domestic demand is greater than zero, or equivalently,

domestic demand is greater than domestic supply. In this situation, residual domestic

demand is satisfied by surplus foreign supply of the local currency, and therefore

foreign banks’ claims against domestic banks are reduced. In sum, the positive fund

balance in equilibrium signifies retreating foreign funds from domestic banks. The

flip side of the above argument is that the negative fund balance is associated with

an increase in foreign claims. When carry trade positions are accumulated, foreign

claims against domestic banks increase, thereby resulting in an equilibrium with a

negative fund balance. On the contrary, an equilibrium with a positive fund balance

is associated with unwinding of carry trades. Figure 2.4 shows an equilibrium with a

negative fund balance.


NFS NDD

$ inv. currency

Inflows of

Foreign Investments

Figure 2.4: An Equilibrium with an Increase of Foreign Claims

Note: The figure exhibits the equilibrium of the local currency market with a negative fundbalance, a situation of building up carry trade position.


2.3 Empirical Model

In the previous section, the conceptual model for the local foreign exchange market is

presented. Two functions are derived to describe the aggregate behaviors of domestic

and foreign banks. A meaningful assessment on the impacts of carry trade is possible

only if we have knowledge on these two functions. For further analysis, I assume

linear forms of the functions and attempt to estimate parameters with available data,

employing simplifying assumptions if necessary.

Equations (2.7) and (2.8) are parameterized versions of (2.3) and (2.6) respec-

tively, with subscript i standing for ith sample which is a pair of a funding currency

and an investment currency. Since change between the peak and trough of the ex-

change rate is the main interest of this study, (2.7) and (2.8) are differenced across

the two time points. The peak is the point when the exchange rate was highest in

2008 and the trough is the point when the exchange rate was lowest in 2008 after

the peak. Note that the exchange rate is denoted by units of the foreign currency

per local currency. The local currency is the investment currency and the foreign

currency is the funding currency. For net domestic demand, we obtain (2.9) after

differencing between the two points.

NDDi,t = cNDD + αNDDpi,t + αExExporti,t + αImImporti,t + eNDD,i,t (2.7)

NFSi,t = cNFS + αNFSpi,t + αCarry

(Unwindingi,t − BuildingUpi,t

)+ eNFS,i,t (2.8)

NDDi,trough − NDDi,peak = cNDD + αNDD (pi,trough − pi,peak)+

αEx

(Exporti,trough − Exporti,peak

)+

αIm

(Importi,trough − Importi,peak

)+ eNDD,i

(2.9)

NDDi,trough is the fund balance at the trough, which represents an outflow of foreign

funds. An outflow of foreign funds can be expressed in two ways: a decrease in foreign

claims of foreign banks against domestic banks and/or an increase in domestic banks’

position against foreign banks. We assume that the latter quantity is negligible,

which can be justified by the fact that during the built-up period, the domestic banks’


position on foreign banks is almost zero because of low yields on deposits in funding

currencies, or foreign currencies. We also assume that NDDi,peak, the fund balance at

the peak is very small. This assumption is equivalent to postulating that the foreign

exchange market is balanced at the peak of the exchange rate. Another view on

this assumption is that at the start of the downward exchange rate movement, the

inflow of foreign funds was stopped. With above two assumptions, we can substitute

the right-hand side of (2.9) with the decrease in foreign claims. (pi,trough − pi,peak) is,

by definition, the maximum drop of the exchange rate.(Exporti,trough − Exporti,peak

)and

(Importi,trough − Importi,peak

)are replaced with the difference of exports between

2008 and 2007 and the difference of imports for the same years. These replacements

call for some explanations. Payments for international trade are usually made after

a certain grace period is elapsed from shipments, upon which trade statistics are

based. Therefore, fund flows generated by trade between the peak and the trough is

more related to shipments of the proceeding time period. The peak and the trough

took place in the latter half of 2008 in most of sample countries. Therefore, using

the shipment data is not totally unreasonable. We also postulate that measurement

errors in exports and imports do not correlate with other endogenous variables such

as decreases in foreign claims and the maximum depreciation of the exchange rate.

It is well known that global trade slowed down during the latter half of 2008. The

above postulation on the error is equivalent to assuming that the slowdown was

mainly driven by the lack of demand and that the adjustment of exchange rates

came so unexpectedly that exporters and importers could not adjust their shipments

according to the changed relative prices across countries. In sum, (2.9) is translated

into (2.10), which now can be estimated with available data. The mapping between


parameters of the two equations is shown below:

(Decrease in Foreign Claims) = cNDD + βNDD(Max depreciation of exchange rate)+

βEx∆Export+

βIm∆Import + ϵNDD,i, where

αNDD = −βNDD, αEx = βEx, αIm = βIm.

(2.10)

The second equation of the partial equilibrium model regards net foreign supply.

By differencing between the peak and the trough, we obtain (2.11). The right-hand

side of (2.11) is the same with (2.9) and therefore renders the same variable in the

empirical equation. Since changes in positions of carry trade have a one-to-one effects

on the fund balance in equilibrium, αCarry is set to 1. We also assume that a new

carry trade positions are not accumulated at the trough of the exchange rate. This

assumption reflects that carry traders are opportunistic investors and at the trough,

their perceived risk is so great that they choose not to participate in carry trade. At

the peak, the net change in positions of carry trade is assumed to be zero or safely

ignorable in comparison with the unwinding position at the trough. This argument

is not far-fetched because carry trades are slowly built up while it unwinds suddenly.

By applying these assumptions, we have (2.12). Unfortunately, we cannot observe

how much funds were unwound at the trough. It is reasonable to postulate that the

unwinding position is proportional to the built-up position of carry trades prior to

the unwinding, which is shown in (2.13).

NFSi,trough − NFSi,peak = cNFS + αNFS (pi,trough − pi,peak)+

αCarry

(Unwindingi,trough − Unwindingi,peak

)+

αCarry

(BuildingUpi,trough − BuildingUpi,peak

)+ eNFS,i

(2.11)

NFSi,trough − NFSi,peak = cNFS + αNFS (pi,trough − pi,peak) + Unwindingi,trough + eNFS,i

(2.12)

Unwindingi,trough = βUn(Built-up position of carry trade) + eunwinding,i (2.13)


Still, data on built-up positions of carry trade is not available. Instead, we can

observe inflows of funds into the country of the investment currency. Since this

data—inflows of funds into the country—is an inaccurate measurement of what we

attempt to gauge, built-up position of carry trade, we introduce instruments to pin

down the build-up position of carry trade. The instruments are interest differentials

between the funding and investment currencies and the appreciation of the investment

currency prior to 2008. These two instruments well cover the profitability side of carry

trade. Even though the risk side of carry trade is not covered by the instruments, the

estimation is still valid. The argument on instrument variables is summarized in the

following equations.

(Inflows of Funds) = (Built-up position of carry trade) + einflow,i (2.14)

(Built-up position of carry trade) = cbuilt-up + βInt(Interest rate differential)+

βApp(Appreciation before 2008) + ebuilt-up,i(2.15)

In sum, net foreign supply equation is translated into a two-equation system due

to data availability:

(Decrease in Foreign Claims) = cNFS + βNFS(Max drop of exchange rate)+

βUn(Inflows of Funds) + ϵNFS,i, and

(Inflows of Funds) = cInflow + βInt(Interest rate differential)+

βApp(Appreciation before 2008) + ϵIN,i.

(2.16)

2.4 Results

The previous section translates the conceptual model with two equations into an em-

pirically estimable model with three equations, as shown in (2.10) and (2.16). Since

the system involves multiple equations and multiple endogenous variables in an equa-

tion, the method of three stage least squares is used in estimation. A pair of a funding

currency and an investment currency constitutes an observation and therefore, the


sample is cross-sectional. Since data values of each observation differ owing to hetero-

geneous sizes of economies and the degree of exposure to the international financial

market, normalization of the data is necessary. The data on decrease in foreign claims

and inflows of funds are normalized by the average foreign claims position between

2000 and 2008. Exports and imports are normalized by their values in 2007. Ex-

ports and imports are total values for the country of the investment currency rather

than bilateral values between the countries of the funding and investment currencies.

By taking total values rather than bilateral values, exports and imports data now

measure the degree of overall tightening in the local foreign exchange markets, not

against a particular funding currency. Since exchanges among funding currencies were

relatively unaffected by the unwinding of carry trades on a particular investment cur-

rency, the depreciation of the local currency should be affected by the overall tightness

of the local foreign exchange market.

The data for this study are taken from International Financial Statistics (IFS) and

the Bank for International Settlements (BIS) bank statistics. Exchange rate data are

taken from IFS and are observed on a monthly basis. The peak and trough are

designated, based upon monthly average values. The data for exports and imports

are also taken from there. Positions of foreign claims are taken from the BIS and

they are quarterly observations. There are four funding currencies in the data set.

In each equation, the dummy variables for each funding currency are added. As

investment currencies, 33 currencies are taken. Not all pairs of funding currencies

and investment currencies are included for estimation due to data availability and

the issues of outliers. Finally, the sample size is 113.

Table 2.2 shows the estimation result of the empirical model. βUn and βNDD are

significantly estimated. These two parameters measure the proportion of unwound

positions and net domestic demand’s price elasticity, respectively. For βNFS, net

foreign supply’s price elasticity, the null hypothesis that this parameter is zero is

not rejected. This suggests that the supply of the investment currency by foreign

banks was largely unaffected by the level of the exchange rate during unwinding of

carry trade. This result can be interpreted as (1) the true parameter value is zero,

i.e. the exchange rate does not affect the supply of the local currency by foreign


banks and/or (2) variations in the level of net domestic demand is not so strongly

pronounced by means of exchange rate variations in the sample that the estimation

procedure cannot pin down the estimate. The first argument seems reasonable, in

that the foreign supply of the investment currency or local currency did not depend

on the exchange rate during unwinding.

2.5 Discussions

This section provides analyses on the impact of unwinding carry trades on foreign

exchange markets in 2008, interpreting the estimation results of the previous section.

The foremost question is whether carry trades were the real cause behind the large

depreciations of peripheral currencies in 2008. The estimate on βUN implies that

the 20 percents of the previously built-up carry trade position is unwound during

the period of interest. The unwinding supplies investment currencies to the market,

shifting the net foreign supply to the right. The shift is shown in Figure 2.5, where

supply and demand are depicted in terms of the investment currency or the local

currency. A new equilibrium takes place at the point where the shifted net foreign

supply line meets with the net domestic demand line and it brings with outflows of

foreign funds and depreciation of the investment currency, which are consistent with

experiences of the peripheral currencies in 2008.

The next point regards the distinction among funding currencies. During the later

half of 2008, the four funding currencies appreciated against peripheral currencies in

different degrees. In the model, the appreciation is determined by the interaction of

credit crunch reflected in excess net foreign supply and responses of the investment

currencies, expressed in net domestic demand. The yen appreciated more than the

other funding currencies. The appreciation of the euro and the pound sterling were

moderate with respect to the dollar’s appreciation. The estimation on the dummy

variables (See Table 2.2) on each funding currency in net domestic demand suggests

that the euro and the pound sterling had stronger local supply than the dollar and

the yen had weaker local supplies. On the other hand, the estimation of currency

dummies in the equation of net foreign supply implies that the credit crunch for


Table 2.2: Estimation Results

Parameters Estimate Std Err t Value p Value

Net Domestic Demand

c 4.62 13.18 0.35 0.73

NDD 3.63 1.06 3.42 0.

Ex 0.46 0.25 1.85 0.07

Im 0.33 0.14 2.33 0.02

16.18 8.11 1.99 0.05

38.9 10.76 3.62 0.

32.21 8.19 3.93 0.

Net Foreign Supply

c 8.45 12.3 0.69 0.49

NFS 0.3 1.18 0.25 0.8

Un 0.2 0.05 3.87 0.

5.39 8.91 0.6 0.55

4.34 12.45 0.35 0.73

19.94 8.06 2.47 0.01

Inflows of funds

c 95.52 13.74 6.95 0.

Int 6.88 1.18 5.82 0.

App 10.05 1.81 5.56 0.

72.94 18.89 3.86 0.

84.25 19.71 4.27 0.

15.33 18.15 0.84 0.4

Note: This table reports the estimation result of the empirical model.


NFS2

$ inv. currency

Outflows of

Foreign Credits

NDD

NFS1

Figure 2.5: Unwinding Carry Trades

Note: The figure exhibits how unwinding in carry trade causes depreciation of the localcurrency.


NFS:$, ,

funding inv. currency

NDD:$NDD:

NFS1

NDD:

Figure 2.6: The Unwinding Scenario for the euro and pound sterling

Note: The figure shows how unwinding of major currencies such as the euro and the poundseterling was received by the market.

the yen is milder than the other investment currencies. Can these findings explain

differences across the investment currencies in 2008? Let us first investigate the case

of the euro and the pounds sterling. As shown in Figure 2.6, the net domestic demand

lines for the euro and the pound sterling are located to the right of the one for the

dollar, while the three currencies have similar shifts in the net foreign supply line.

This graphical analysis suggests that depreciations for the euro and the pound sterling

were less severe than that of the dollar, which is consistent with the observation.

The Japanese yen has quite a different story, which is shown in Figure 2.7 . The

shock in net foreign supply for the yen is less severe than the other funding currencies

and this can be interpreted that the credit crunch of the yen by foreign banks was less

acute than the other funding currencies. The culprit behind of the yen’s appreciation

in a larger scale lies in the limited supply of the yen by the domestic banks, which is


NFS:$, ,

funding inv. currency

NDD:$

NFS1

NDD:

NFS:

Figure 2.7: The Unwinding Scenario for the yen

Note: The figure shows how unwinding of the yen was received by the market.

expressed in the figure by placing the net domestic demand line to the left of those

for the other currencies. In sum, even though the credit crunch for the yen was

milder than the other three currencies, the limited supply of the yen forced the large

depreciation of the investment currencies against the yen.

The story behind the yen’s appreciation evidences the real peril of a carry trade

strategy involving a funding currency with which the investment currency does not

have broad interactions. The strong local supply of the rest three investment cur-

rencies can be rationalized by the argument that local direct or indirect participants

in the foreign exchange market other than banks held significant positions in those

three currencies for various purposes such as still repatriated trade proceeds and they

converted these positions into the local currency at then favorable rate, thereby sup-

plementing the local supply of those three funding currencies. Since the Japanese yen


$

A

D

C B Fund

outflows

funding local

currency

NDD

NFS

Error in NFS

AB

C D

Large outflows

Mild depreciation

Moderate outflows

Severe depreciation

Large outflows

Severe depreciation

Moderate outflows

Mild depreciation

Error in NDD

Figure 2.8: The residual analysis of equations

Note: The figures shows the residual from the empirical model and the response of localcurrencies during the unwinding.

had extremely low yields prior to the credit crunch, it is unreasonable for the local

participants to hold liquid yen assets.

The final question that is answered from the estimation is whether or not an

investment currency reacted differently against each funding currency. An analysis

on residuals for an investment currency reveals that the reactions are different across

funding currencies. Based on residuals on the estimated equations, an observation

on a pair of a funding currency and an investment currency is placed on one of

four regions in the right panel of Figure 2.8 . The right panel of the figure reports

characteristics of an observation compared with the sample average. For instance,

an observation has a positive residual for the net domestic demand equation and a

negative residual for the foreign supply equation is located at the region D of the

figure and as a result, the currency pair will have moderate outflows of the funding

currency from the country of the investment currency and a mild depreciation of the

investment currency.

Figure 2.9 presents two cases for this analysis, Australia and Korea. Australia

experienced large outflow of the euro funds with mild depreciation against the euro

while the dollar funds exited from the country in a large scale, embarking the Aus-

tralian dollar’s large depreciation against the U.S. dollar. The euro credit crunch is


$

$Fund

outflows

funding local

currency

NDD

NFS

$

$Fund

outflows

funding local

currency

NDD

NFS

Australia Korea

Figure 2.9: The cases for Australia and Korea

Note: The figure applies the residual analysis to Anustralia and Korea.

met with strong local supply of the euro funds from Australia, resulting in large out-

flows of euro funds with mild depreciation. Note that this analysis compares a pair

of currencies with other currency pairs in the whole cross-sectional sample. A more

severe dollar credit withdrawal against Australia is met with a average local supply

of the dollar, forcing the Australia currency to suffer a large depreciation with a large

drain of the U.S. dollar funds from that country. Comparing the case of Australia

with Korea, the market for the euro and the pound sterling renders a similar outcome

between the two countries. But Korea has more moderate outflows of dollar and yen

funds than Australia.

2.6 Conclusion

This study investigates the cause of radical adjustments of nominal exchange rates

across countries in the later half of 2008. From the simultaneous equation analysis,

the cause of the deprecations is identified to be increased supply of the local cur-

rencies by foreign investors. The drastic increase of supply is in turn, attributable

to the preceding inflows of funds in the process of proliferating carry trades. Carry

trades are driven by gaps in interest rates between funding currencies and investment

currencies, an evidence of disparities in monetary policies across countries prior to the


crisis. Twenty percents of positions of funds that had been built up during the 2000-

2008 period was unwound, exacting radical depreciations of the peripheral currencies,

coupled with a huge withdrawal of credits from the peripheral countries. The turmoil

in the global financial markets is realized by the unwinding of carry trades, which

was brought about by credit crunches in major funding countries. This is simply a

realization of potential risk, which opportunistic investors engendered in the process

of carry trades. Their possibly destructive investment scheme is made profitable by

the large gap in interest rates across countries, or lax monetary policies of Japan and

United States.

Then, what is the impact of these movements in exchange rates on the global

economy? The increased uncertainty in exchange rates disrupts international trade,

exacerbating an additional harm of the credit crunch on the global economy. The

moral of this experience is that a prolonged large gaps in interest rates of two relatively

stable countries invite opportunistic investments, which will withdraw at any sign of

trouble with a disrupting ripple effect on the local as well as the global economy. The

traditional tri-lemma argument on promising the autonomy of the monetary policy at

the price of an floating exchange rate and open financial accounts should be revisited

under this new finding. A caveat should be placed on the autonomy to warn monetary

policy makers. If monetary policy of a country, specifically, its interest rate strays

too far from those of the funding countries, the country may inadvertently invite hot

money inflows from carry traders. The ebb and flow of hot money, accompanied by

a large swing of the exchange rate, is a real threat to achieving the monetary policy

goal—stabilizing the price level—especially, at the time of turbulence.

Chapter 3

The Economic Origin of Letters of

Credit

3.1 Introduction

The global economy is experiencing an unprecedented prosperity although there have

been momentary setbacks. This prosperity is on a global scale, and in no small part

international trade has been driving it. Although some economists are not totally

satisfied with the current level of trade, forcing themselves an endeavor to locate the

missing trade, their attentions have been rarely paid on the economic institution of in-

ternational trade in a transactional level, more specifically settlements of cross-border

commercial transactions. This component of transactions is important in interna-

tional trade because a transaction in international trade involves long distances and a

high level of uncertainty across parties of the transaction. Most macroeconomic mod-

els are silent on the matter of how agents in the model exchange goods and services,

assuming that impersonal exchange takes place without any frictions. Uncertainty in

settlement of commercial transactions is a considerable obstacle to Pareto-improving

exchanges. Any commercial transaction in which the exchange of goods or services

and the payment is not coincidental engenders the issue of trade credit. One of the

recent research on trade credit is Burkart and Ellingsen (2004) in which one mode of

trade credit, suppliers giving credit to buyers, is studied in the context of domestic

77

CHAPTER 3. LETTERS OF CREDIT 78

transactions. In the context of international trade, trade credit is not a choice but

a necessity. Whether it is buyers’ credit or sellers’ credit, one party of a transaction

is exposed to risk. Antras and Foley (2011) address this issue for international trade

using the data from a U.S. exporter. They show that the exporter’s choice of the

settlement condition, cash-in-advance, open account, collection or a letter of credit,

depends on the perceived contract enforcement of the trading countries. They treat

letters of credit as the importer’s credit toward the exporter.

A letter of credit is a guarantee forwarded by the importer’s bank toward the

exporter. It promises that the exporter will be paid if the exporter satisfies the terms

of the letter 1. Letters of credit usually specify documents such as bills of lading as a

condition of payment. A typical transaction involving a letter of credit is carried out

in the following steps:

i. The exporter and importer agree upon the terms and conditions of their trans-

action.

ii. In her local bank, the importer opens a credit line payable to the exporter,

pursuant to documentary requirements.

iii. The importer’s bank notifies the credit line to the exporter through his bank.

iv. The exporter ships the goods and prepares the documents specified in the letter

of credit.

v. The exporter submits the documents to his bank.

vi. If the exporter’s bank deems that the submitted documents satisfy the conditions

specified in the letter of credit, the exporter’s bank pays the specified amount to

the exporter and sends the documents to the importer’s bank.

vii. The importer’s bank checks the documents. If the documents satisfy the condi-

tions of the letter of credit, it pays the exporter’s bank and notifies the importer.

1For the modern legal definition, see Houtte (2002). Studies on the legal nature of this instrumentwere active in the early 20th century. For those studies, see Hershey (1918), McCurdy (1922), Mead(1922), Llewellyn (1929), Epps and Chappell (1952), Kozolchyk (1965) and Kozolchyk (1966).


viii. The importer pays her bank and receives the shipping documents, which include

the title to the shipped goods

Examples of letter of credit are found in McCurdy (1922) and Mead (1922). Many

studies on letters of credit by legal scholars in the early 20th century emphasize the

theoretical role of the new instrument within the system of the common law. A

consensus seems to be reached by treating a letter of credit as a mercantile specialty.

The historical origin of the letter of credit is unclear. Kozolchyk (1965) finds a

primitive form of the letter of credit at Malynes’s Lex Mercatoria which was published

in 1629, but the modern usage of this instrument in trade took place by the early to

the mid 19th century in England (Banks (1999)).2 As an economic institution, the

enforcing organization of the institution is as important as the rules of the institution.

Therefore, it can be argued that the letter of credit as an institution is developed by

merchant bankers in London by forming an organization of bankers issuing letters of

credit.

This essay broadens the previous discussions on institutional developments in

early modern Europe. North (1991) provides insightful observations from a historical

viewpoint. He discusses the issues of long-distance trade in the historical context,

which entails the agent problem and, contract negotiation and enforcement. He argues

that new institutions developed from the 11th to the 16th centuries reduced the cost

of exchange over long distances. He argues that innovations in the institution reduced

transaction cost by (1) increasing the mobility of capital (2) lowering information costs

and (3) spreading risk. Although the elements of this trichotomy are not exclusive of

one another, they are useful in understanding the contributions of a new institution.

North (1991) gives examples for the three channels. Bills of exchange is argued to

increase the mobility of capital especially under the usury law, and Munro (2003)

explains the usefulness of bills of exchange as a countermeasure of merchants against

the usury law and later against bullionism. A more detailed analysis on bills of

exchange in relations to letters of credit is offered in the next section. North (1991)

also mentions printing of prices of commodities and manuals, and marine insurance

as examples of the second and third channel of innovations.

2For developments in the 20th century, see Chapter 2 of Rooy (1984).


Letters of credit as an institution have impacts on all three channels. It increases

the mobility of capital by making accounts receivables liquid. Making account receiv-

able fungible has been possible since bills of exchange became negotiable. A seller can

draw a bill of exchange on his buyer or buyer’s bank, which is payable to the order

of the payee. If the bill is drawn on the bank, it is not the bank’s obligation until it

is accepted by the bank. Once the bill is accepted by the bank, becoming bankers’

acceptance, any holder in due course has a right to be paid by the bank. This means

that the bill can be traded without any concern on the underlying commercial trans-

action between the buyer and the seller. There was a secondary market for bankers’

acceptances in London to which exporters could sell bankers’ acceptances thereby

obtaining liquidity. However, the seller of the commercial transaction, or the initial

holder of the bill, cannot sell the bill prior to the acceptance of the drawee, the bank.

With the letter of credit, the buyer can sell the credit against the bank once he satis-

fies the condition of the letter. He is no longer concerned about the contingency that

the bank refuses to accept the bill. Letters of credit permit the seller to transform his

accounts receivables into marketable securities, thereby reducing the required level of

working capital.

Letters of credit contribute in international trade more significantly in the second

and third channels in innovation. The major concern of exporters in shipping mer-

chandise is whether the importer will fulfill her part of the deal. Letters of credit

relieve exporters from uncertainty on the payment, while exporters taking bills of

exchange are still exposed to the credit risk of their trading partners before trade

drafts are accepted by importers’ banks. The provision of this instrument also has a

signaling effect. Credit-worthy importers are willing to use letters of credit at least

for the initial transaction with a new exporter. Thus, exporters can weed out the

opportunistic importers from the pool of potential buyers by asking them to apply

for letters of credit, reducing costs in gathering information on their buyers.

The last point in the innovative aspects of letters of credit regards spreading risk

or managing risk. This innovation actually took place within the institution of bills

of exchange. Initially, sellers drew bills of exchange, or drafts on their buyers. Even

after a buyer accepts her draft, there is significant credit risk to the seller. There are


multiple elements in this credit risk. A sudden deterioration of business situation can

force the buyer to fail to pay the seller. Or, the buyer may be an outright opportunist

who believes that the seller does not have recourses to his nonperformance. These

elements of the risk can be removed by drawing the bill on knowingly solvent banks.

Once the bank accepts the bill, managing credit risk of the buyer is the responsibility

of the bank, which is better equipped in managing the risk because the bank is likely to

have a long-term relationship and other deals with the buyer. This simple apparatus,

just changing the name in the draft, brought a significant change in trade finance,

paving a road to specialization of trade finance and provided established merchant

houses with opportunities to play an intermediary role in trade, becoming merchant

banks. Credit risk itself is reduced by using bills of exchange drawn upon banks

owing to a low degree of information asymmetry and better recourses available to

banks than to exporters. After the acceptance of a trade draft, an exporter’s credit

risk against his importer is reduced to credit risk against the accepting bank. By the

action of the bank as an intermediary, the total credit risk is reduced and it is more

efficiently managed.

Appearance of merchant banks brought a tremendous change into international

trade as well as domestic trade. Although commodities were traded in a one-to-one

basis between exporters and importers, the accompanying financial part of transac-

tions was now executed in a hub and spoke mode. As a hub of financial transactions,

merchant banks monitored their clients, especially, importers—and other merchant

banks in items of credit risk. This model of trade also increased efficiency in settle-

ment. In the hub and spoke mode, merchant banks settled accounts with their clients

and with other banks. An exporter who obtained a bill of exchange drawn upon a

foreign bank sold the bill to his bank and the exporter’s bank settled with the foreign

bank. This process seems innocuous but it would have been impossible if the foreign

bank had refused to pay to the exporter’s bank because the foreign bank might have

argued that its creditor was the exporter, not his bank. This issue is solved by nego-

tiation. Once the bill is endorsed to the exporter’s bank, the exporter’s bank has an

equal right—technically a better right— over the drawee, the foreign bank. A private

financial obligation between the debtor and the creditor becomes a public one, which


a third party can use against the debtor in settling his account against the debtor

once the third party obtains the bill from the creditor by endorsement.3

A similar development as negotiation is found in the history of derivatives trading.

Kroszner (1999) documents the history of the Chicago Board of Trade. The first

forward contract of grain exchanged warehouse receipts, which were titles of grain

stored in a specific lot of a warehouse. The board adopted a standard on quality

of grain and after that, forward contracts were made upon quality of grain, not the

ownership of physical lots of warehouses. The efficiency in trading forward contracts

was further improved when groups of traders took each other’s contract as a tender in

settling contracts. As merchants disregarded the underlying mercantile transactions

in bills of exchange, the forward traders disregarded in physical locations of grain in

warehouses. By characterizing traded objects with crucial but succinct features—the

debtor and maturity for bills of exchange, and the quality and delivery for forward

contracts—transactors of these instruments achieved higher efficiency. Even the two

stories converge in establishing clearing houses later on.

The negotiable feature of bills of exchange made international trade efficient by

allowing large merchant houses to specialize in dealing the bills. Once merchant banks

were well-established in the trading community, the institution of letters of credit was

in some sense an extension from previous developments. The room for improvement

from bills of exchange lies in the fact that there was no protection for exporters

before acceptance of bills. Letters of credit close the hole in protection by providing

exporters guarantees for payment. Letters of credit differ from another mode of

settlement, cash-in-advance, in that the payment is contingent on the performance of

exporters, evidenced by shipping documents, while the cash-in-advance method just

shifts the bearer of credit risk from exporters to importers.

The rest of this essay is organized in the following way. Section 3.2 compares

bills of exchange and letters of credit. Section 3.3 provides a game theoretic model

3Negotiation is studied extensively by legal scholars owing to its conflict with the common lawconceptualization of contract. Lack of consideration in a relationship between the initial debtor andholders in due course—those who obtain the bill by endorsement by endorsement—was an issue.The legal issue is rested by presuming consideration in bills of exchange. Many technical details innegotiability are not discussed here because they lacks economic relevance. See Holdsworth (1977),Holden (1955) and Rooy (1984) for the legal discussion on the matter.


which analyzes the introduction of letters of credit by merchant banks. This model

follows the tradition of Milgrom, North, and Weingast (1990), Greif (1993) and Greif,

Milgrom, and Weingast (1994) in complementing historical narratives with a rigorous

game theory model. Section 3.4 discusses the various issues about this institution

and implications of this study in the context of institutional economics. Section 3.5

concludes.

3.2 Letters of Credit and Bills of Exchange

A bill of exchange is a financial instrument which involves three parties: a drawer, a

drawee and a payee. Suppose that in a commercial transaction, a buyer pledges to

pay her seller by means of a bill of exchange. There are multiple modes in using a bill

of exchange in international trade.4 If the buyer’s agent is in the same locale with the

seller for negotiation and inspection of merchandise, the agent draws a bill upon his

principal, who is the payor of the bill, while the seller is the payee. In another mode,

the seller draws upon the buyer in the importing country, designating himself as the

payee. If the buyer had an account with a renowned merchant and the seller agrees to

draw upon the merchant, the seller draws upon the merchant. The last usage became

popular as it gave a better protection to the seller and it is the efficient for the buyer.

Figure 3.1 shows the issue and acceptance of a bill of exchange. In the figure,

activities of the participants are expressed in a rounded box and outcomes of activities

are marked with hexagons. After shipping merchandise, the exporter obtains shipping

documents from his shipper and prepares a bill of exchange. The exporter sends the

bill and shipping documents to the importer’s bank. After receiving the bill and

shipping documents, the bank decides whether to accept the bill. For this decision,

the bank considers credit-worthiness of the importer and the importer’s consent to

pay back. After accepting the bill, the bank releases the shipping document to the

importer, who claims the merchandise. As shown in Figure 3.2, after obtaining the

bank’s acceptance or accepted bill, the exporter can wait until the maturity of the

4A bill of exchange is also used as a countermeasure to usury laws in so-called "dry exchanges."For discussion on this usage of bills of exchange, see Munro (2003).


bill or negotiate it to his bank, which was likely to have an account in the importer’s

bank. The payment at the maturity was usually executed by adjustments in balances

of accounts.

The most salient feature of the institution of bills of exchange is negotiability.

Negotiability improved total welfare and some parties enjoyed gains of this new cus-

tom. Suppose that there is a merchant who has extensive commercial relationships

with many other traders. By pledging that he will honor a draft drawn upon him

although the draft is transferred to a third party once the draft is accepted by him,

he enjoys many benefits. First, settlements of drafts become efficient. This benefit is

contingent on whether other bankers also take their drafts negotiable. His financial

obligations to individuals or banks can be offset by his financial rights against them.

Second, the negotiable drafts are more liquid than nonnegotiable ones. A holder of a

negotiable draft can use the draft as a tender in other commercial transactions if their

sellers accept the draft. Provided that the drawee is sufficiently credible, the unilat-

eral pledge of negotiability will make drafts drawn upon him attractive to those who

use bills of exchange as a payment tool, opening an opportunity of banking business

to the drawee.

The greatest impact of bills of exchange on international trade is that the in-

stitution made possible trade across countries with very little usage of the common

currency, gold at that time. One example is trade between the U.S. and England

in 18th century. Four parties were involved in the articulate exchanges that made

the transportation of gold obsolete. They are U.S. exporters, usually, producers of

plantation crops such as cotton, U.S. importers such as factory owners who needed

to buy machines and parts from England producers with advanced technology. The

English textile industry imported cotton from U.S. plantations. Payments to U.S.

exporters were paid in bills of exchange drawn on banks in Manchester or London,

and U.S. importers bought these bills to pay for their imports from England through

their banks. By using bills of exchange in settlements in the transatlantic trade,

transportation of species was not necessary. (Kirkaldy and McLeod (1924), Banks

(1999), and Chapman (1988))

Bills of exchange were also broadly used in domestic trade within England, referred


Exporter Importer’s Bank Importer

Draw

Consider

Acceptance

Claim

Merchandise

Release

DocumentsNegotiate

Draft

Documents

Acceptance Rejected

Ready

Money

Claimed

Merchandise

Figure 3.1: Issue and Acceptance of Bills of Exchange

Note: The figure shows the business process of issuing and accepting bills of exchange.Activities are marked by round boxes and outcomes are expressed in hexagons.


Exporter’s Bank Importer’s Bank Importer

Adjust

Accounts

Send

Draft

Receive

Draft

Account

Credited

Account

Debited

Figure 3.2: Settlement of Bills of Exchange

Note: The figure shows the business process of settling bills of exchange.


to as inland bills. These bills were traded in the London money market once they were

accepted by the drawn bank. Usual buyers were banks in rural areas, who needed

safe and short-term investment opportunities and through the market, they provided

the drawn banks liquidity necessary in commercial transactions. Nishimura (1971)

systematically investigates the decline of these bills traded in the London market.

One aspect worthy of discussion is the money creation effect of negotiability. By

allowing negotiability, the private debt became a public one, represented by accepted

bills which were used as de facto money. When there was no concern on future liq-

uidity of accepting banks, bills accepted by them were equivalent to money, relieving

the monetary constraint imposed by the gold standard. In the quantity equation of

money, MV = PY , where M is money, V is velocity, P is the price level and Y is

output, the left hand side increases by adding a new class of money. Accordingly, the

right hand side quantities, the price level or output increases. Without negotiability

of bills, the growing economy of Europe in the 18th century would have experienced

a severe deflation owing to the monetary constraint.

Taking bills in place of cash for settlement has money creation effect. Like money,

holders in due course of the instrument have rights independent of the commercial

transaction that engendered the instrument in the first place. The left hand side of

the quantity equation of money now depends on perceived creditworthiness on the

other party of commercial transactions. If business cycles are monetary phenomena

as argued by monetarists, the essential element of the monetary phenomena is the

expansion and contraction of private credits (Bergman, Bordo, and Jonung (1998),

Basu and Taylor (1999)). If this explanation of the business cycle is correct, the

modern business cycle is a price to pay for prosperity owing to financial revolutions,

which have arrived differently across countries (Sylla (2002)).

A further development from bills of exchange with respect to acceptance is letters

of credit. The greatest concern of exporters in international transaction with bills

of exchange is whether the importer’s bank will accept the bill. Before the bank

accepting the bill, the exporter only relies upon credibility of the importer. This

concern is relieved by a pledge of the bank that the bill will be accepted if certain

verifiable conditions are met, rather than subject to criteria such as the importer’s


Exporter’s Bank Importer’s Bank Importer

L/C

Issued

Application

Rejected

Evaluate Apply

Inform

Exporter

L/C

Notified

Figure 3.3: Issuing a Letter of Credit

Note: The figure shows the business process of issuing a letter of credit.

satisfaction. In order to minimize any possible issue on the compliance of the exporter

to the condition of the letter, the standard of strict compliance is used in practice.

This means that the test whether the exporter satisfies the condition of a letter is

determined by nothing but literal match between conditions specified in the letter

and documents provided by the exporter (Rooy (1984)).

Figure 3.3 shows the process of issuing of a letter of credit. The formal procedure

is initiated by the importer by applying a credit line for the exporter at her bank.

Then the importer’s bank sends a letter to an exporter that she will pay the promised

amount to the exporter if the exporter submits the shipping documents to the bank.

This letter is usually relayed through the exporter’s bank who later negotiates, or


pays the exporter for the documents. By negotiating the shipping documents to his

bank, the exporter can be paid right after shipping the merchandise, relieving the

credit risk against his importer. The negotiating bank’s job is to verify whether the

documents comply the condition of the letter. With the verification, the negotiating

bank has a right for the payment against the importer’s bank. By sending the shipping

documents, the negotiating bank requests the payment to the importer’s bank. The

importer’s bank, referred to as issuing bank in the context of letters of credit, first

checks whether the documents match the conditions of the documentary credit and

then informs the importer the arrival of shipping documents, asking the payment from

the importer. The importer claims the shipping documents after paying to her bank.

Figure 3.4 depicts the processes that are executed from notification to negotiation .

3.3 A Theoretic Model of Letters of Credit

3.3.1 A Game Model

The choice of a settlement method in commercial transactions depends on the fi-

nancing cost in settlement. The financing cost depends on the degree of information

asymmetry. Those who give credit ask for a premium in the price which is expressed

in a discount or a surcharge in the price. This is equivalent to the interest rate

charged to borrowers by lending banks. For example, for open account transactions

by which exporters ship merchandise before payments without any protection but

their importer’s word of honor, exporters ask a higher price than a cash-in-advance

transaction with which exporters are paid prior to shipments. The higher price in-

corporates a pure financing cost for the exporter and a risk premium for the deferred

payment from his buyer. The latter part is proportional to uncertainty on the fu-

ture payment. Each settlement method places exporters and importers in different

positions in the financial aspect of transactions.

In this section, a game theoretical model is considered in which an exporter and

importer decide the settlement method for a transaction. Five settlement methods


Exporter Exporter’s Bank Importer’s Bank

Ship

Merchandise

L/C

Notified

Ship

Merchandise

Prepare

documents

PresentCheck

documents

No

Discrepancy

Discrepancies

Found

Pay

Send

Documents

Consider

Payment

Release

Documents

Payment

Received

Figure 3.4: Negotiation of a Letter of Credit

Note: The figure shows the business process of negotiating a letter of credit.


are considered. They are open account (OC), cash-in-advance (CIA), bills of exchange

drawn upon banks (BEB), bills of exchange drawn upon importers (BEM) and finally,

letters of credit (LC). In each method of settlement, the exporter sets the prices to

compensate for his risk in the transaction, and the importer evaluates the prices and

decides the settlement method.

The structure of the game is as follows. There are two players in the game:

the exporter and the importer. There are two types for each player: fraudulent and

genuine. Each player does not have information on the type of the other player. First,

nature chooses the types of all players. Given his type, the exporter offers the prices

of the five settlement methods. Then, the importer chooses one of the methods. She

may reject all the methods. Once they agree upon the payment method, the exporter

decides to ship the merchandise before the payment for all methods but CIA and then

the importer decides whether or not to pay. Although the importer’s bank is involved

in some methods, its role is assumed to be mechanical in the sense that it acts by the

rule of the settlement method. For the CIA condition, the importer decides whether

or not to pay and then the exporter decides whether or not to ship after observing

the importer’s decision. Figure 3.5 shows the structure of the game.

In the figure, information sets are not described to clearly show the strategies of

the game. The letter E stands for the exporter and M does for the importer. Since

there are infinitely many possible offers from the exporter, there are infinitely many

nodes after the exporter’s initial node. Every node of the importer is a member of an

information set of two nodes, which reflects the fact that the importer does not know

the other player’s type.

Although the idea of the model is simple, a full description of the model in an

extensive form would be too complicated to offer any valuable insight of the model.

Instead, payoffs in every contingency are listed in Table 3.1.

After Nature chooses the types of two players, the exporter offers five prices for

five settlement methods, PCIA, POC, PBEM, PBEB, and PLC. Letter w is the working

capital used by the exporter at the point of the shipment. The letter R is the revenue

from the merchandise at the point of the payment, or at the end of the grace period

for all settlement conditions but CIA. It is assumed that the importer recovers all


X

M MM

M

X

Prices

Settlement Method

Pay Do Not Pay

Ship Do Not Ship

CIA LC

E

M

Ship Do Not Ship

Pay Do Not Pay

... ...

Figure 3.5: The Structure of the Game

Note: The figure shows the structure of the game given that nature chooses the types of theexporter(X) and the importer(M). Given the exporter’s offer on settlement conditions, whichis one of the infinitely many possible offers, the importer chooses the settlement condition.Information sets are not expressed for clarity.


Table 3.1: Payoffs of the Game

Settlement Method ContingencyStrategy Payoff

On the equilibrium pathShipping Payment Exporter Importer

CIA All Yes Yes PCIA w R FV PCIA Yes

No w R

No Yes PCIA VX FV PCIA

No 0 0

OC Normal Yes Yes PV POC w R POC Yes

No w R VM

No Yes PV POC POC

No 0 0

Bankcrupcy M Yes Yes w R POC Yes

No w R VM

No Yes 0 POC

No 0 0

Business Change Yes Yes PV POC w R POC

No w R Yes

No Yes PV POC POC

No 0 0

BEM Normal Yes Yes PV PBEM w R PBEM Yes

No w R PBEM

No Yes PV PBEM PBEM

No 0 0

Bankruptcy M Yes Yes w R PBEM Yes

No w R PBEM

No Yes 0 PBEM

No 0 0

BEB Normal Yes Yes PV PBEB w R PBEB Yes

No w R PBEB

No Yes PV PBEB PBEB

No 0 0

Bankruptcy M Yes Yes w R PBEB Yes

No w R PBEB

No Yes 0 PBEB

No 0 0

Bankruptcy B Yes Yes w R PBEB Yes

No w R PBEB

No Yes 0 PBEB

No 0 0

LC Normal Yes Yes PV PLC w R PLC Yes

No w R PLC

No Yes PV PLC PLC

No 0 0

Bankruptcy M Yes Yes w R PLC Yes

No w R PLC

No Yes 0 PLC

No 0 0

Note: This table reports payoffs for each contingency. After agreeing on the settlementcondition, the exporter’s strategy is whether or not to ship and the importer’s strategy iswhether or not to pay, as shown in the third and fourth columns. There are two types ofbankruptcies considered in the model. They are bankruptcy of the importer, as marked byletter M and bankruptcy of the bank, expressed with letter B. End nodes of the equilibriumpath are shown in the last column


the proceeds from the merchandise at the end of the period. I refer to the end of the

grace period as the payment since the payment is made all but the CIA condition.

PV discounts cash flows at the payment to cash flows at the point of the shipment.

FV transforms cash flows at the shipment into a future cash flow at the payment.

VX is the value to the exporter in maintaining the relationship with the importer.

The value is greater than working capital w for the genuine exporter and is zero

for a fraudulent exporter. VM is the continuing value to the importer and the value

is greater than the revenue R for the genuine exporter and is zero for a fraudulent

importer. α is the fraction of the payment that the importer is forced to make in

the case that she refuses to pay although she is obliged to pay owing to a financial

contract such as a bill of exchange and a letter of credit. α is assumed to be one for

a genuine importer and 0 for a fraudulent importer.

If the importer’s bank or importer herself goes bankrupt, the exporter loses the

opportunity to be paid. Bankruptcies that matter are those that happen between

the shipment and the payment. Bankruptcy is modeled as a exogenous event of

which arrival time is distributed as a exponential distribution. The exporter recovers

nothing from his bankrupt buyer. The importer pays the owed amount even in the

case of bankruptcy although the amount is not relayed to the exporter. This is a valid

assumption if a single transaction is so small that the importer does not go bankrupt

not to pay for a single transaction. Another event in which the exporter fails to

recover the payment is business change of the importer. In this case, the importer’s

continuing value of the relationship with the exporter drops to zero and the importer

accordingly chooses not to pay. This event is meaningful only for the open account

settlement and is assumed to arrive in an exponential distribution.

Finally, it is assumed that there are many identical exporters in the market. This

drives a price competition and exporters set the price as low as to barely recovery

their working capital.


3.3.2 Equilibrium

Since the exporter faces an competitive market and aims to recover the working

capital w through the transaction, the prices set by the exporter for each settlement

method is rather straightforward. For an open account transaction, the exporter sets

the price so that

E[MPOC

]= w, (3.1)

where M is the stochastic discount factor of the exporter and POC is an uncertain

future cash flow from the importer. If the importer pays for the merchandise, it is

equal to POC but otherwise it is zero. The payment is made to the exporter if all of

the three events happens. They are (1) the importer is not fraudulent, (2) the import

does not go bankrupt until the payment and (3) no business change occurs. The

three events are independent and their probabilities are e−µM , e−TSPλM , and e−TSPλXC ,

respectively with e−µM being the probability that the importer is not fraudulent,

e−TSPλM being the probability that the bankruptcy does not happen during the period

between the shipment and the payment, TSP and e−TSPλXC being the probability that

the business change does not happen in the same period. λM and λXC are rates by

which bankruptcy and business change happen. Therefore,

E[POC

]= POCe

−µM e−TSP(λM+λXC ). (3.2)

Assuming that the payment by the importer is not correlated with the stochastic

discount factor, or Cov[M, POC

]= 0,

E[MPOC

]= Cov

[M, POC

]+E[M ]E

[POC

]= e−rXf TSPPOCe

−µM e−TSP(λM+λXC ), (3.3)

since E[M ] = e−rXf TSP with rXf being a risk-free rate at which the exporter can borrow.

The price set by the exporter POC is

POC = weµM eTSP(rXf +λM+λXC ). (3.4)

For CIA transactions, the price is just w because the payment is made at the


point of the shipment,

PCIA = w (3.5)

For a bill of exchange drawn upon the importer, the price is

PBEM = weµM eTSP(rXf +λM), (3.6)

since the importer pays even when business change happens.

For a bill of exchange drawn upon the importer’s bank, the exporter is paid

if (1) the importer is not fraudulent, (2) the import does not go bankrupt until the

acceptance by the bank and (3) the bank does not go bankrupt between the acceptance

and the payment. The expected value of the payment is,

E[PBEB

]= PBEBe

−µM e−TSAλM e−TAPλB , (3.7)

where TSA is the time between the shipment and the acceptance by the bank and TAP

is the time between the acceptance and the payment. λB is the rate by which the

bankruptcy of the bank happens. Accordingly, the price is

PBEB = weµM eTSA(rXf +λM)eTAP(rXf +λB). (3.8)

For the letter of credit transaction, the only concern of the exporter is bankruptcy

of the importer’s bank. Since the importer is guaranteed by the bank, the exporter

does not charge a risk premium for the fraud risk. The price for letters of credit

transaction is

PLC = weTSP(rXf +λB). (3.9)

In this essay, a perfect Bayesian equilibrium (PBE), in particular, a semi-pooling

one is sought. A fraudulent exporter offers the same deal as a genuine exporter so

that the importer cannot distinguish between the two types of exporters. Given five

prices offered by the exporter, the importer decides the settlement method. The

importer’s decision depends on the type of her. If she is fraudulent, she chooses one

of OC, BEB or BEM settlements and does not pay later. If the exporter is fraudulent,


he hopes that the importer chooses CIA so that he can earn the payment w by not

shipping the merchandise after receiving the payment. A genuine importer chooses a

settlement method to maximize the return on the transaction because she can scale

up or down the transaction. For the actions taken in the equilibrium, see the last

column of Table 3.1.

A fraudulent exporter cannot attract the importer to accept the CIA condition

by lowering the price of the CIA price because the importer has the belief that a

lower price is a sign of the fraudulent seller. A genuine exporter cannot filter out

the fraudulent importer by increasing the prices of OC, BEB and BEM conditions

because he will lose the business to other exporters, and he also cannot decrease prices

for CIA and LC settlement because he will not be able to recover the working capital.

For the five settlement conditions, the importer’s payoffs are as follows. The im-

porter earn R from the merchandise right before the payment. For the OC condition,

the importer does not pay if business change takes place between the shipment and

the payment. The importer does not pay with the probability Exp[−(TSPλ

MC

)],

where λMC is the rate by which business change arrives. Note that λM

C is the arrival

rate in the viewpoint of the importer and λXC is the same quantity in the viewpoint

of the exporter. The importer’s value at the point of the payment is

UM [OC] = R− POCExp[−(TSPλ

MC

)]. (3.10)

For the CIA condition, the import obtains the merchandise and earns the revenue R if

the exporter is not fraudulent, which is the case with the probability Exp [−µX ]. The

importer’s payment at the shipment is adjusted to reflect the time value of money

with the importer’s financing cost rM , which is equal to rMf + λM . rMf is the risk free

rate of the importer. Putting together these adjustments, the importer’s expected

value at the payment is

UM [CIA] = RExp [−µX ]−PCIAExp [TSPrM ] = RExp [−µX ]−PCIAExp[TSP

(rMf + λM

)].

(3.11)

For the bill of exchange drawn upon the importer, no adjustment is necessary


since the importer is assumed to be responsible for the payment even in the case of

bankruptcy.

UM [BEM] = R− PBEM (3.12)

If the bill is drawn upon the bank, the bank pays the bill at the maturity but the

credit is extended to the importer between the point of acceptance and the payment.

This structure of financing is equivalent to the situation that the importer borrows

PBEBe−TAPrB at the point of the acceptance and pays PBEB back to the bank at the

point of the payment or the maturity of the bill, with rB being the deposit rate of

the bank, or the bank’s borrowing rate. Therefore, the cost of merchandise at the

point of the payment is PBEBeTAP(rBM−rB) where rBM is the bank’s lending rate on the

importer. The importer has the value

UM [BEB] = R− PBEBeTAP(rBM−rB) = R− PBEBe

TAP(λBM−λB) (3.13)

with the bill of exchange drawn upon the bank, where rBM = rMf + λBM and rB =

rMf +λB. λBM is the rate at which the importer defaults on the loan by the bank and

λB is the rate at which the bank go bankrupt. A transaction with a letter of credit

gives a similar value with a bill of exchange drawn upon the bank. Since a letter of

credit provides a credit line to the importer from the point of the shipment, the value

of the transaction to the importer is

UM [LC] = R− PLCeTSP(λBM−λB). (3.14)

Since the transaction can be scaled, the criteria for the genuine importer is the

return on the transaction. By plugging price formulas in (3.4),(3.5),(3.6),(3.8) and

(3.9) into the corresponding payoff formulas above, I obtain payoffs of the importer

in terms of parameters. For example, the payoff from the OC is

UM [OC] =(R− POCExp

[−(TSPλ

MC

)])=(R− weµM eTSP(rXf +λM+λX

C )Exp[−(TSPλ

MC

)]),

(3.15)


accordingly, the gross return from the OC transaction is

RM [OC] = Exp[v − µM − TSP

(rXf + λM

)+ TSP

(λMC − λX

C

)], (3.16)

where R is expressed as wExp[v]. Similarly, returns for other settlement conditions

are

RM [CIA] = Exp[v − µX − TSPr

Mf − TSPλM

)], (3.17)

RM [BEM] = Exp[v − µM − TSPr

Xf − TSPλM

], (3.18)

RM [BEB] = Exp[v − µM − TSPr

Xf − TSAλM − TAPλBM

], and (3.19)

RM [LC] = Exp[v − TSPr

Xf − TSPλBM

]. (3.20)

The importer chooses the settlement condition which maximizes the return from

the transaction. The theoretical model in Antras and Foley (2011) can be understood

in the context of this model. In their model, the exporter is assumed to give a

take-or-leave offer to the importer and the settlement method is determined by the

unilateral problem of profit maximization. This study is different from theirs in a few

aspects. First, they focus on the expected return of trade finance which depends on

the institutional maturity of the trading countries, while this model clearly identifies

the cause of nonperformance such as business change or bankruptcy and links this

risk to the required returns.

Second, Antras and Foley (2011) only cover cash-in-advance, post shipment, which

covers open account and documentary collection in a single category and finally, letters

of credit. This study provides more careful distinctions among settlement conditions

and risk associated with them. In this study, trading partners decide the settlement

condition to maximize returns on the transaction.

Among five settlement conditions, the method that maximizes the importer’s ex-

pected return is chosen by the interaction of the exporter and the importer, for there

are many exporters and the importer can adjust the scale of the transaction. From

now on, the discussion assumes that λM > λBM and µM > 0. The first inequality

states that the risk of the importer is greater for the exporter residing on the foreign


soil than for her bank. This assumption makes sense that the importer’s bank has

a better monitoring capability and is equipped with superior recourses against her

client in the case of nonperformance than the exporter. By the second inequality, the

importer is a fraud with positive probability.

Under the above assumptions, a bill of exchange drawn upon the importer has a

lower return than a bill of exchange drawn upon the bank. In turn, a bill of exchange

drawn upon the bank has a lower return than a letter of credit. The open account

condition may be chosen if the importer so much more strongly expects a business

change than the exporter that the likelihood of nonpayment compensates for the

high financing cost. The cash-in-advance condition may be chosen if the importer’s

financing cost is much lower than the exporter’s financing cost. This finding implies

that the importer could increase the return on the transaction by drawing the bill

upon her bank rather than herself. Moreover, letters of credit offers a better deal to

the importer by removing the fraud risk.

Players’ beliefs are required to be consistent with Bayes’ rule in the PBE. The

exporter believes that the importer is not a fraud if she chooses CIA or LC. If the im-

porter chooses other settlement methods, the exporter maintains the prior probability

on the importer’s type.

This analysis assumes no financial friction. For example, the model assumes that

the exporter can negotiate the bill drawn upon the foreign bank without any friction.

Practically, it takes a considerable time to sell foreign bills, and exporters have to

provide credit between the acquirement of a bill and the sales of it. If this friction

is sufficiently burdensome, exporters are more likely to prefer letters of credit to bills

of exchange because bills of exchange become marketable after acceptances while

an exporter with letters of credit acquires an marketable financial instrument after

shipping documents are ready.

This model also assumes that there is no risk associated with letter of credit

itself. Theoretically, exporters with a letter of credit and shipping documents are

entitled to the payment specified in the letter, but the bank may refuse to pay,

citing insufficiency or noncompliance of the documents with the letter. The standard

in this kind of dispute is strict compliance. Under this standard, the exporter or


any negotiating parties from him deem to satisfy the condition of the letter if the

accompanying documents literally meet the condition of the letter. The gap between

the strict compliance and actual compliance is a risk which may fall upon both parties

in the transaction.

If the risk factors on the importer are not consistent with the general case as

assumed above, open account settlements and bills of exchange drawn upon importers

may be used. For example, open account settlements are widely used in trade between

firms and their overseas subsidiaries.

Another benefit of drafts drawn upon banks over drafts drawn upon importers

is that drafter upon banks are more marketable than the others. In the model, the

exporter is assumed to hold drafts to the maturity. If the exporter can negotiate

accepted drafts upon banks, or banker’s acceptances, at the acceptance and at the

shipment for the letter of credit, the returns on these settlement methods are higher

than described above. Negotiation replaces the exporter’s risk-free rate with the nego-

tiating bank’s risk free rate for the period between the negotiation and the maturities

of the negotiated drafts. This seems insignificant in theory but in practice, exporters

may not have an access to financial markets owing to immaturity of the local financial

market or destruction of financial networks. The latter is especially true after the war.

The rapid recovery of Western Europe and Japan after the Second World War can

be attributed to export-driven activities, which provided liquidity in the local market

as well as jobs and income. This was made possible by efficient trade finance such as

letters of credit, which removed the burden of financing from exporters in order to

sell abroad, while providing a guarantee of shipment.

Until now, the role of the opening bank has been largely ignored and the profit

of the bank is set to be zero. However, in reality, banks earn significant profits from

trade finance. Banks can charge on importers as much as the difference between

the optimal returns of letters of credit and the second best settlement method. The

profit comes from efficiency gain in the new institution of letters of credit. This is an

incentive for the banks to initiate and maintain this institution.


3.4 Discussions

The model in the previous section shows that letters of credit improved the efficiency

by reducing the degree of asymmetry of information from bills of exchange. The new

institution was not born in a vacuum. The custom of drawing bills upon banks had

existed prior to letters of credit. This custom reinforced monitoring among banks

and firmly established negotiation of bills. Another development of bills of exchange

drawn upon banks was that they separated the financial element of transactions from

the mercantile element. This development concentrated the financial element of most

international trade into a group of banks or acceptance houses which met twice per

week at the Royal Exchange to determine rate for bills of exchange and to deal among

themselves (Banks (1999))

This process of concentrating transactions within a group of trustable parties

seems a general phenomenon. Kroszner (1999) documents the development of the

derivatives clearing house. Prior to the clearing house by the Chicago Board of Trade,

traders formed "rings" within which they offset positions against other members in

the ring. This is a process of positive feedbacks. Once big merchants established

a large volume among them, the transaction cost among them was drastically re-

duced and then other peripheral merchants found it efficient to take advantage of

the channel between the big merchants, which later specialized in banking business,

thereby becoming merchant banks. Eventually, London became a clearinghouse of

global trade prior to the First World War (Banks (1999))

Although modern economic institutions to some degree depend on legal enforce-

ments by political entities, the development of bills of exchange and letters of credit

as an institution took place in the absence of legal enforcements. Legal scholars at-

tribute the origin of these financial instruments to rules of the self-organized merchant

congregation, Lex Mercatoria. The rules in these instruments are not in line with the

common law and it took a considerable time and efforts to adopt the rules as a part of

the law in England. During that process, decisions in the court were not completely

consistent with commercial practice.


Under the situation that legal enforcement by state was absent, economic institu-

tions relied upon the organization to which transactors belong. Greif (1998) stresses

the identification of the enforcing organization in the framework of historical and com-

parative institutional analysis. This issues of enforcing organizations are discussed

in many studies such as Greif (1993), Greif (2006) and Milgrom, North, and Wein-

gast (1990). In their studies, institutions are enforced through peer monitoring, the

community and jurists, respectively. There are two layers in the institution of trade

finance. The outer layer governs the relationship between trading parties and the

intervening merchant banks. The inner layer consists of the merchant banks. Given

a transaction, opportunistic behavior of a merchant bank against another merchant

bank was not likely because the gain from a single transaction was so little compared

to the total gain from the whole volume of transactions among major players. The

outer layer was enforced by the long-term relationship between the exporters or im-

porters and their merchant banks. Since merchant banks had an account of their

clients, deviations by their clients were curbed. Deviations of merchant banks against

their clients were more or less an issue of reputation.

Consider the trade between an exporter and importer. Without instruments of

trade finance, their trade is enforced by their mutual trust, the organization to which

both belong if any. With bills of exchange and letters of credit, the financial portion

of the trade is enforced by banks, in essence, middlemen. While previous studies

mentioned above identify non-economic organizations to enforce the economic insti-

tutions, the institution of this study is enforced by middlemen who act on their own

interests. These middlemen made viable transactions which would have been too

costly without their interventions.

Merchant banks as middlemen in international settlements drove a new institution

for profit. The profit originated from the gain in efficiency in transactions. There are

two drivers behind this improvement: concentration and projection. Concentration

refers to the process by which transactions are channeled through major players in

the market who hold a high level of trust among themselves and by market partici-

pants. This process happened in the case of trade finance through merchant banks.

The members of the Chicago Board of Trade were another example. Concentration


improves efficiency in transactions by reducing information asymmetry and netting

positions among major players.

A more subtle aspect of this process is projection. Projection is a concept named

here to describe the situation in which market participants evaluate traded objects

in terms of minimally crucial characteristics. For example, in the forward market of

farming goods, the goods are evaluated by quality determined by the inspector and

delivery dates, ignoring other characteristics such as the producer or the location in

the warehouse (Kroszner (1999)). Another example is negotiation of bills. Market

participants in the money market only consider the maturity and drawee-debtor of

the bill, ignoring the original payee or the commercial transaction that engenders

the bill. By disregarding nonessential or residual characteristics of traded objects,

market participants do not need to gather information on such characteristics thereby

increasing efficiency in trade. It is possible that one market participant gets an object,

which has a lower value than he pays for because the object has a unfavorable residual

characteristic. Therefore, this approach is untenable if the transaction volume is not

sufficiently large.

If the transaction volume of a market participant is large enough, the impact

of individual residual characteristics is averaged out. This is why this approach

is referred to as projection. The whole characteristics of the marketed object are

projected onto a few variables and the value of the object is decided by the minimally

crucial variables. Projection is driven by the interest of major players in the market

to improve the efficiency in transactions, while making the market deeper. This

approach focuses on the ex-ante aggregate outcome of transactions rather than the

ex-post individual outcomes of transactions. This transformation of the market is

made possible by the concentration of transactions and the law of large numbers.

The key element of the institution of letters of credit is strict compliance. Shipping

documents are compared with conditions in a letter of credit. A very clear and

objective standard—literal match—is employed. Therefore, it is possible that the

merchandise may differ from what is intended in the underlying commercial contract

although the shipping documents literally satisfy the condition. Strict compliance

is an example of projection, for the value of shipping documents depends only on


its consistency with the letter and nothing else. By strict compliance, bankers are

exempt for hassles to check the consistency between shipping documents and what

is intended in the contract, or more extremely, between the shipping documents and

merchandise on the ship.

Through projection, some institutions achieve ex-ante aggregate efficiency. Previ-

ous studies on institutions are largely silent on how institutions improve welfare of the

economy. The institution of trade finance improves ex-ante aggregate efficiency. Some

participants in transactions suffer from the negative impact of residual characteris-

tics but they refrain themselves from opportunistic actions because of the aggregate

benefit of the institution. This is how a good institutions improve the efficiency of

the economy.

3.5 Conclusions

This study traces the economic origin of letters of credit to the profit-seeking activ-

ity of merchant banks. By providing a reliable channel of international settlements,

they improved the efficiency in international trade, increasing returns of trade or

making trade viable. This shows that institutions matter in international trade es-

pecially because information asymmetry is more severe than domestic transactions.

The literature in international trade has been trying to explain the international trade

pattern with abstract exporter-importer relations. Belloc (2006) offers a new view

on this issue by trying to find a possible cause of trade pattern in institutions. But

her approach is limited in that she tries to find the cause from domestic institutions.

Nunn (2007) analyzes the relationship between the pattern of trade and contract

enforcement.

The model in this paper shows that the outcome of international trade depends on

the institution surrounding international transactions. One of the important roles of

institutions in economic transactions is to manage asymmetry of information so that

two strangers can execute a welfare improving transaction. In international trade, at

least in its earlier period, the network of merchant banks was instrumental in reducing

asymmetry of information. Therefore, the issue of the missing trade can be resolved


by a missing network or channel between rich countries and poor countries.

The key contribution of this work is singling out two drivers, concentration and

projection, in improving efficiency in a transactional level. This improvement would

have been impossible without institutions, more specifically, the enforcing organiza-

tions of institutions. Institutions studies here reduced harmful effects of asymmetry of

information by routing transactions through an efficient channel. Key players in the

route built a high way for commerce by adopting strategy of concentration and pro-

jection. They processed a large volume of transactions (concentration) and focused

on the crucial characteristics (projection) and obtained an improvement in aggregate

and ex-ante efficiency.

Appendix A

Appendix to Chapter 1

A.1 Details on data

A.1.1 U.S. durables

There are two data sources for the stocks of consumer durable goods: (1) Annual

consumer durable goods from: http://www.bea.gov/national/FA2004/Details/

Index.html and (2) Table 2.3.3 Real Personal Consumption Expenditures by Ma-

jor Type of Product, Quantity Indexes of National Income and Product Accounts

(NIPA). The first data set is annual and the second set is quarterly. For each year, I

distributed the total annual investment into quarters by the ratio from the quarterly

data and solve a single depreciation rate for each year so that the year-end stock is

equal to the reported value in the annual stock. Therefore, depreciation rates are dif-

ferent by year. Using these depreciation rates, the quarterly stocks of durable goods

are constructed.

A.1.2 U.S. nondurables

The price and quantity data of nondurable consumption and service consumption are

used to construct a Fisher quantity index. The quantity data are from NIPA Table

2.3.3. Real Personal Consumption Expenditures by Major Type of Product, Quantity

Indexes of NIPA and the price data are from Table 2.3.4. Price Indexes for Personal

107

APPENDIX A. APPENDIX TO CHAPTER 1 108

Consumption Expenditures by Major Type of Product.

A.1.3 U.S. Market returns

This data is obtained from Kenneth French’s data library at http://mba.tuck.

dartmouth.edu/pages/faculty/ken.french/data_library.html.

A.1.4 U.S. population

The population data are obtained from NIPA Table 2.1 at http://www.bea.gov/

national/.

A.1.5 Japanese durables

Like the U.S., the data for the consumption durable stock are available in an annual

basis from the website (http://www.esri.cao.go.jp) of the Economic and Social

Research Institute (ESRI) of the Japanese government. The quarterly consumption

data on durables, nondurables and semi-durables are available. Japanese durables

are taken as investments on durable goods. The same procedure as with the U.S.

data is used to derive quarterly stock data.

A.1.6 Japanese nondurables

Quarterly data for nondurable, semi-durable and service consumption are aggregated

to obtain nondurable consumption data.

A.1.7 Japanese Market returns

The Nikkei index taken from Global Financial Data is used.

A.1.8 Japanese population

The population data of International Financial Statistics are used. The 2009 estima-

tion is from the Economic Intelligence Unit.


A.1.9 Business Cycles

The reference dates from the NBER and the ESRI are used.

A.2 Derivation of Fundamental Open Interest Par-

ity

From (1.10),

St+1

St

=

(NJP,C

t+1 +∆N JPt+1

)NUS

t+1

.

Multiply both side byE[NUS

t+1]E[NJP,C

t+1 ],

St+1

St

E[NUS

t+1

]E[NJP,C

t+1

] =

(NJP,C

t+1 +∆N JPt+1

)/E[NJP,C

t+1

]NUS

t+1/E[NUS

t+1

] .

Superscript C is suppressed from now on. Let IUS,ft+1 be the U.S. risk free nominal

gross return with maturity t+1. Take log on both sides and using Log[E[NUS

t+1

]]=

−Log[IUS,ft+1

]≈ −i$t+1 and use a similar formula for Japan,

∆st+1 + it+1 − i$t+1 =(Log

[(NJP,C

t+1 +∆N JPt+1

)]− Log

[E[NJP,C

t+1

]])−(Log

[NUS

t+1

]− Log

[E[NUS

t+1

]]).

Using the formula Log[NJP

t+1 +∆NJPt+1

]≈ Log

[NJP,C

t+1

]+ IJP,ft+1 ∆NJP

t+1, which is proved

at the end of this appendix,

∆st+1 + it+1 − i$t+1 =(Log

[NJP,C

t+1

]− Log

[E[NJP,C

t+1

]])−(Log

[NUS

t+1

]− Log

[E[NUS

t+1

]])+ IJP,ft+1 ∆NJP

t+1.


Use Log[NUS

t+1

]− Log

[E[NUS

t+1

]]= Log

[Mt+1

E[Mt+1]

]− ∆qUS

t+1 + cUS = mUSt+1 − ∆qUS

t+1 +

cUS,where

cUS = Log [E [Mt+1]]−Log

[E

[Mt+1

(QUS

t+1

QUSt

)−1]]

.

Note that Nt+1 = Mt+1

(QUS

t+1

QUSt

)−1

. Apply the same formula for Japan,

∆st+1 + it+1 − i$t+1 =(cJP − cUS

)+(mJP

t+1 −mUSt+1

)+(∆qUS

t+1 −∆qJPt+1

)+ IJP,ft+1 ∆NJP

t+1,

where ηt+1 in (1.11) is IJP,ft+1 ∆NJPt+1. The constant cUS can be expressed by

cUS = −Log

Cov Mt+1

E [Mt+1],

(QUS

t+1

QUSt

)−1

E[(

QUSt+1

QUSt

)−1]+ 1

− Log

[E

[(QUS

t+1

QUSt

)−1]]

.

The constants cJP and cUS are small if the real SDFs and inflation rates are not

correlated and inflations are mild. Or, the two countries are similar in those aspects,

the constant term can be safely ignored.

Now, it is shown that

Log[NJP

t+1 +∆NJPt+1

]≈ Log

[NJP

t+1

]+ IJP,ft+1 ∆NJP

t+1.

Log[N + ϵ] = Log [en + ϵ]

By using Taylor approximation around n = Log[E[N]] and ϵ = 0,

Log [en + ϵ] =Log[E[N ]]+

(en

en + ϵ

)(LogE[N ],0)

(n−LogE[N ])+

(1

en + ϵ

)(LogE[N ],0)

ϵ=n+1

E[N ]ϵ.

Substitute N with NJPt+1, and ϵ with ∆NJP

t+1,

Log[NJP

t+1 +∆NJPt+1

]= Log

[NJP

t+1

]+

1

E[NJP

t+1

]∆NJPt+1


Since there is the nominal risk free gross return IJP,ft+1 , which is equal to 1

E[NJPt+1]

,

Log[NJP

t+1 +∆NJPt+1

]= Log

[NJP

t+1

]+ IJP,ft+1 ∆NJP

t+1.

A.3 Preference behind the Linear Factor Model

Yogo (2006) proposes a general functional form of preference in a recursive form

Ut ={(1− β)u (Ct, Dt)

1−1/σ + β(Et

[U1−γt+1

])1/(1−γ)/(1−1/σ)}1/(1−1/σ)

,

where intraperiod utility of households is defined by the constant elasticity of substi-

tution (CES) function

u[C,D] =((1− α)C1−1/ρ + αD1−1/ρ

)1/(1−1/ρ).

Ct and Dt are consumption of durable goods and nondurable goods by households

at period t respectively, and Ut+1 is the time t+1 utility. σ,γ, and ρ are parameters

explained below. This seemingly complicated preference can be decomposed into

three aggregations by the CES aggregator,

A [{x1, x2....} , {α1, α2, ..} , η] =(∑

αix1−1/ηi

)1/(1−1/η)

.

Here, η is the elasticity of substitution and αi stands for the weight on good xi.

For example, the intraperiod utility can be expressed by

u[C,D] = A [{Ct, Dt} , {1− α, α}, ρ] .

The parameter η ≥ 0 measures the degree of substitution. For a large value of η,

goods are readily substitutable and if η = ∞, goods are perfectly substitutable and

the preference has a linear indifference curve. For a small value of η, goods are

complementary and if η = 0, good are perfectly complementary and it has a Leontief

indifferent curve. If η = 1, the utility function is Cobb-Douglas or equivalently a


logarithmic form. By successively applying the CES aggregator, the intertemporal

utility in the first equation of this appendix can be expressed by

Ut = A [A [{Ct, Dt} , {1− α, α}, ρ] , A [{Ut+1 [st+1]} , {πt [st+1]} , 1/γ] , {(1− β), β}, σ] .

The lower level aggregation happens between today’s durable consumption and non-

durable consumption. At the same level, the future utility is aggregated by

Et

[U1−γt+1

]1/(1−γ)=

∑s∈St+1

πt[s]U1−γt+1

1/(1−γ)

= A [{Ut+1 [st+1]} , {πt [st+1]} , 1/γ] ,

where πt [st+1] is the conditional probability at time t for the state st+1. Here, 1/γ

works as the elasticity of substitution across states and γ is also known as the co-

efficient of relative risk aversion. The upper level aggregation takes place between

the aggregation of today’s consumption (A [{Ct, Dt} , {1− α, α}, ρ]) and another ag-

gregation on future consumptions (A [{Ut+1 [st+1]} ,{πt [st+1]} , 1/γ]), employing the

elasticity of intertemporal substitution σ:

Ut = A[utility from today’s consumption, utility from future consumption, {(1− β), β}, σ]

= A [A [{Ct, Dt} , {1− α, α}, ρ] , A [{Ut+1 [st+1]} , {πt [st+1]} , 1/γ] , {(1− β), β}, σ] .

This preference incorporates three different elasticities of substitution, ρ, σ, and 1/γ.

Studies prior to Yogo (2006) have restricted functional forms such that two elasticities

of substitution are set to be the same. For example, Epstein and Zin (1991) set the

elasticity of intertemporal substitution (σ) equal to the elasticity of substitutions

between two consumption goods (ρ). The preference of popular expected utility

has a single parameter for both the elasticity of intertemporal substitution and the

elasticity of substitution across different states (1/γ), or the inverse of relative risk

aversion.

Yogo (2006) reports estimations for the three parameters. The estimates on ρ, σ,

and 1/γ are such that ρ > σ > 1/γ and the tests of σ = ρ and σ = 1/γ are both

rejected. Lustig and Verdelhan (2007) also report a similar result without explicitly


performing the tests. This finding suggests that durable goods and nondurable goods

are more readily substitutable than consumption today and consumption tomorrow,

which intuitively makes sense. A more controversial substitution is the one across

different future states. Yogo (2006)’s estimation shows that σ > 1/γ and this finding

is consistent with Epstein and Zin (1991), who, however, set ρ equal to σ. This finding

implies that substitutions among future states are more painful than a substitution

between today and future. Households care more about the bad state tomorrow than

the average consumption tomorrow. A practical interpretation is that households are

less responsive to changes in insurance premium than changes in interest rates. Both

Yogo (2006) and Lustig and Verdelhan (2007) report very high value of γ between

100 and 200, or very low value of 1/γ and refer this estimation to the still unresolved

equity premium puzzle. This high estimate of γ may be inconsistent with estimations

from other literature such as the real business cycle theory (King and Rebelo (1999))

but any value of 1/γ less than σ is internally consistent as long as households are less

responsive to changes in insurance premium than the interest rate.

The high estimated value of risk averseness can be rationalized by a measurement

issue. Even though the consumption-based asset pricing models can be thought as a

part of a general equilibrium model, what the estimation procedure does, is measuring

the stochastic discount factor of an agent who has the same consumption pattern

with the overall economy and more importantly, actively participating in financial

markets. First, someone who is more risk averse is likely to save for the future and

has resources to engage in financial investments if there is a realistic borrowing limit.

Second, among agents with financial resources, those who are more risk averse, are

more likely to actively manage risks through financial transactions. These two factors

seem to create a chasm in measurements of risk averseness between macroeconomic

models and models of financial markets. Representative agents for the real business

cycle model and their counterparts for the consumption-based capital pricing models

are likely to come from different walks of life although they may be pulled from the

same population. Yogo (2006) also mentions his belief that the representative agent

model cannot resolve this puzzle.

From the problem on consumption and portfolio allocation of households, Yogo


(2006) derives the stochastic discount factor Mt+1, as a function of consumption in

durable goods D and nondurable goods C and the return on wealth from the market

portfolio Rw,t+1(see Appendix B of Yogo (2006)),

Mt+1 =

(β

(Ct+1

Ct

)−1/σ (v [Dt+1/Ct+1]

v [Dt/Ct]

)(1/ρ−1/σ)

R1−κw,t+1

)κ

,

where v[x] =(1− α+ αx1−1/ρ

)1/(1−1/ρ)and κ = (1 − γ)/(1 − 1/σ). The above SDF

is loglinearized into:

−mt ≈ −k + b1∆ct + b2∆dt + b3rw,t,

where b’s are the functions of preference parameters such as ρ, σ, and 1/γ.

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