Chapter Objective:

This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity.

6Chapter Six

International Parity Relationships and Forecasting Foreign Exchange Rates

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Chapter Outline

Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates

Interest Rate Parity Covered Interest Arbitrage IRP and Exchange Rate Determination Reasons for Deviations from IRP

Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates

Interest Rate Parity Purchasing Power Parity

PPP Deviations and the Real Exchange Rate Evidence on Purchasing Power Parity

The Fisher Effects Forecasting Exchange Rates

Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates

Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates

Efficient Market Approach Fundamental Approach Technical Approach Performance of the Forecasters

Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates

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…almost all of the time!

Interest Rate Parity Defined

Idea: $1 (or any amount in $ or in any FC) invested in anywhere should yield the same $ return (or FC return) if the world investment market is perfect! Competitive returns! Otherwise?

IRP is an “no arbitrage” condition. If IRP did not hold, then it would be possible for an

astute trader to make unlimited amounts of money exploiting the arbitrage opportunity.

Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds.

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A Simple Interest Rate Arbitrage Example

BOA 4% vs Nations Bank 5% Identify L and H, Borrow Low & Invest (Deposit) High

Borrow say $1 from BOA and Deposit at NB Cash Flow at 0: +$1 from BOA -$1 to NB = $0 Cash Flow at1: +$1.05 from NB -$1.04 to BOA = $0.01 arbitrage

gain.

A few issues: 1) Bid-Asked? How about 3.99~3.01% vs 4.99~5.01% 2) Can it be sustained?

What is the equilibrium situation, then?

What about

4% in the US vs 5% in UK? Well, we need more info to determine the

arbitrage opportunity. Why? US interest rate, i$, is a $ interest rate and

the UK rate, iBP, is a BP interest rate. It is like comparing apples and organges.

What do you need? Exchange rates!

A Box Diagram to show $1 invested in the US => $1.04 $1 => 0.5 BPs at So = $2/BP, or (1/So) BPs Then 0.5 BPs => 0.5*(1.05) = 0.525 BPs, or (1/S0)*(1+iBP) BPs To convert BPs to $s, we need the future exchange rate. To have no

risks, we use a forward contract with the forward rate, say F=$2.01/BP. Then $ amount is $1.055, or $(1/S0)*(1+iBP)*F

$ interest rate investing in UK is 5.5% > 4% Why 5.5% > 5.0%? Investing in UK involves two transactions (or

investments)!

Borrow from the US and Invest in UK! Arbitrage strategy: Arbitrage profit = $0.015

In equilibrium with no arbitrage opportunity, 1+i$ = $(1/S0)*(1+iBP)*F. CIRP (why Covered?)

S$/£ ×F$/£ = (1 + i£)(1 + i$)

Interest Rate Parity Carefully Defined

Consider alternative one-year investments for $1:

1. Invest in the U.S. at i$. Future value = $ (1 + i$)

2. Trade your $ for £ at the spot rate, invest $(1/S$/£ ) in Britain at i£ while eliminating any exchange rate risk by selling the future value of the British investment forward.

S$/£

F$/£Future value = $(1 + i£) ×

S$/£

F$/£(1 + i£) × = (1 + i$)

Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist)

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IRP

Invest those pounds at i£

$1,000

S$/£

$1,000

Future Value =

Step 3: repatriate future value to the

U.S.A.

Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist

Alternative 1: invest $1,000 at i$ $1,000×(1 + i$)

Alternative 2:Send your $ on a round trip to Britain

Step 2:

$1,000

S$/£

(1+ i£) × F$/£

$1,000

S$/£

(1+ i£)

=

IRP

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Interest Rate Parity Defined

Formally,

IRP is sometimes approximated as

i$ – i¥ ≈S

F – S

1 + i$

1 + i¥ S$/¥

F$/¥=

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IRP and Covered Interest Arbitrage

If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example.

Consider the following set of foreign and domestic interest rates and spot and forward exchange rates.

Spot exchange rate S($/£) = $2.0000/£

360-day forward rate F360($/£) = $2.0100/£

U.S. discount rate i$ = 3.00%

British discount rate i£ = 2.49%

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IRP and Covered Interest Arbitrage

A trader with $1,000 could invest in the U.S. at 3.00%, in one year his investment will be worth

$1,030 = $1,000 (1+ i$) = $1,000 (1.03)

Alternatively, this trader could

1. Exchange $1,000 for £500 at the prevailing spot rate,

2. Invest £500 for one year at i£ = 2.49%; earn £512.45

3. Translate £512.45 back into dollars at the forward rate F360($/£) = $2.01/£, the £512.45 will be worth $1,030.

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Arbitrage I

Invest £500 at i£ = 2.49%

$1,000

£500

£500 = $1,000×$2.00

£1

In one year £500 will be worth

£512.45 = £500 (1+ i£)

$1,030 = £512.45 ×£1

F£(360)

Step 3: repatriate to the U.S.A. at

F360($/£) = $2.01/£ Alternative 1:

invest $1,000 at 3%FV = $1,030

Alternative 2:buy pounds

Step 2:

£512.45

$1,030

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Interest Rate Parity & Exchange Rate Determination

According to IRP only one 360-day forward rate, F360($/£), can exist. It must be the case that

F360($/£) = $2.01/£

Why?

If F360($/£) $2.01/£, an astute trader could make money with one of the following strategies:

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Arbitrage Strategy I

If F360($/£) > $2.01/£

i. Borrow $1,000 at t = 0 at i$ = 3%.

ii. Exchange $1,000 for £500 at the prevailing spot rate, (note that £500 = $1,000 ÷ $2/£) invest £500 at 2.49% (i£) for one year to achieve £512.45

iii. Translate £512.45 back into dollars, if

F360($/£) > $2.01/£, then £512.45 will be more than enough to repay your debt of $1,030.

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Arbitrage Strategy II

If F360($/£) < $2.01/£

i. Borrow £500 at t = 0 at i£= 2.49% .

ii. Exchange £500 for $1,000 at the prevailing spot rate, invest $1,000 at 3% for one year to achieve $1,030.

iii. Translate $1,030 back into pounds, if

F360($/£) < $2.01/£, then $1,030 will be more than enough to repay your debt of £512.45.

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Reasons for Deviations from CIRP Transactions Costs

There may be bid-ask spreads to overcome

Capital Controls Governments sometimes restrict import and export of

money through taxes or outright bans.

Different risks

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Transactions Costs Example Will an arbitrageur facing the following prices be

able to make money?

  Borrowing Lending

$ 5.0% 4.50%

€ 5.5% 5.0%  Bid Ask

Spot $1.42 = €1.00 $1.45 = €1,00

Forward $1.415 = €1.00 $1.445 = €1.00

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Purchasing Power Parity

Purchasing Power Parity and Exchange Rate Determination

PPP Deviations and the Real Exchange Rate Evidence on PPP

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Purchasing Power Parity and Exchange Rate Determination

The exchange rate between two currencies should equal the ratio of the countries’ price levels (Absolute PPP): So = P$/P£

Alternatively, P$ = So*P£, Price level in each country determined in the same currency ($) should be the same in both countries. What you can buy with $100 should be the same anywhere in the world. => Living costs are the same!

Relative PPP If Absolute PPP holds at each point in time, say at t=0 and t=1,

then We can show that %chg in the exchange rate (=(S1-So)/So, FC

appreciation rate relative to $) is equal to the difference between the %chg in the US price level (=US inflation rate) and the %chg in the UK price level (=UK inflation rate), E(e) = E(π$) – E(π£)

If the inflation rate in the U.S. is expected to be 5% in the next year and 3% in the euro zone,

Then the expected change in the exchange rate in one year should be 5 - 3=2%, euro is expected to be 2% stronger against $

Make sense?

Fisher Equations

Domestic (Closed) i$ = ρ$ + E(π$), 1+i$ = (1+$)*(1+E($)) to be exact International (Open)

Assuming that ρ$ = ρ£ ,

i$ - i£ = E(π$) – E(π£) Relative PPP + International Fisher E(e) = E(π$) – E(π£) = i$ - i£

Evidence on PPP

PPP probably doesn’t hold precisely in the real world for a variety of reasons. Non-tradable goods like services, perishable products Transactions & Transportation costs including tariffs,

etc. Different consumption baskets

PPP-determined exchange rates still provide a valuable benchmark.

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Forward Parity

F = E(S1) (F – So)/So = (E(S1) – So)/So = E(e)

Approximate Equilibrium Exchange Rate Relationships

E($ – £)

≈ CIRP≈ Rel PPP

≈ Int Fisher

≈ Fwd Parity

S

F – S

E(e)

(i$ – i¥)

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Forecasting Exchange Rates

Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters

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Efficient Markets Approach

Financial Markets are efficient if prices reflect all available and relevant information.

If this is so, exchange rates will only change when new information arrives, thus:

St = E[St+1| It]and/or

Ft = E[St+1| It] Predicting exchange rates using the efficient

markets approach is affordable and is hard to beat.

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Fundamental Approach Involves econometrics to develop models that use a

variety of explanatory variables. This involves three steps: step 1: Estimate the structural model. step 2: Estimate future parameter values. step 3: Use the model to develop forecasts.

The downside is that fundamental models do not work any better than the forward rate model or the random walk model.

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Technical Approach

Technical analysis looks for patterns in the past behavior of exchange rates.

Clearly it is based upon the premise that history repeats itself.

Thus it is at odds with the EMH

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Performance of the Forecasters

Forecasting is difficult, especially with regard to the future.

As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate.

The founder of Forbes Magazine once said:

“You can make more money selling financial advice than following it.”

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