forward premium puzzle: futures contracts evidence and speculation strategies
DESCRIPTION
Supervisor: Professor Dr. Moisa Altar MSc Student: ALINA PICIOREA. Forward Premium Puzzle: Futures Contracts Evidence and Speculation Strategies. Academy of Economic Studies Bucharest Doctoral School of Finance and Banking DOFIN. Bucharest, July 2007. Contents. PART I - PowerPoint PPT PresentationTRANSCRIPT
Forward Premium Puzzle: Futures
Contracts Evidence and SpeculationStrategies
Forward Premium Puzzle: Futures
Contracts Evidence and SpeculationStrategies
Academy of Economic Studies BucharestAcademy of Economic Studies BucharestDoctoral School of Finance and BankingDoctoral School of Finance and Banking
DOFINDOFIN
Academy of Economic Studies BucharestAcademy of Economic Studies BucharestDoctoral School of Finance and BankingDoctoral School of Finance and Banking
DOFINDOFIN
Supervisor: Professor Dr. Moisa Altar
MSc Student: ALINA PICIOREA
Bucharest, July 2007
ContentsContents
PART I New evidence from futures contracts (instead of the forward contracts), in support of
the forward premium puzzle, and therefore filling the gap at the (multi-) day maturity level
Inside and outside regressions
PART II Two currency speculation strategies
– Carry trade: widely used by practitioners.
• Sell currencies that are at a forward premium.
• Buy currencies that are at a forward discount.
– BGT Strategy: Use a particular regression to forecast payoff to selling currencies forward: Backus, Gregory, and Telmer (1993)
Properties of the speculation payoffs
Does risk explain the high Sharpe Ratios?
PART I New evidence from futures contracts (instead of the forward contracts), in support of
the forward premium puzzle, and therefore filling the gap at the (multi-) day maturity level
Inside and outside regressions
PART II Two currency speculation strategies
– Carry trade: widely used by practitioners.
• Sell currencies that are at a forward premium.
• Buy currencies that are at a forward discount.
– BGT Strategy: Use a particular regression to forecast payoff to selling currencies forward: Backus, Gregory, and Telmer (1993)
Properties of the speculation payoffs
Does risk explain the high Sharpe Ratios?
• Uncovered interest rate parity (UIP) assumes that the expected change in the exchange rate compensates for the interest rate differential or, given that covered interest rate parity holds, equals the forward premium.
• UIP is a key feature of linearized open-economy models; it reflects the market’s expectations of exchange rate changes and it represents the starting point for any analysis which depends on future exchange rate values.
• Problem: UIP is overwhelmingly rejected by the data.
– `Forward premium-depreciation anomaly‘ is a particularly egregious deviation from UIP
– Currencies that are at a forward premium tend to depreciate.
Traditional Reponses to this Problem
• Ignore rejection of UIP and hope that UIP isn’t central to the predictions of the model.
• Add an UIP `risk premium shock’.
• Uncovered interest rate parity (UIP) assumes that the expected change in the exchange rate compensates for the interest rate differential or, given that covered interest rate parity holds, equals the forward premium.
• UIP is a key feature of linearized open-economy models; it reflects the market’s expectations of exchange rate changes and it represents the starting point for any analysis which depends on future exchange rate values.
• Problem: UIP is overwhelmingly rejected by the data.
– `Forward premium-depreciation anomaly‘ is a particularly egregious deviation from UIP
– Currencies that are at a forward premium tend to depreciate.
Traditional Reponses to this Problem
• Ignore rejection of UIP and hope that UIP isn’t central to the predictions of the model.
• Add an UIP `risk premium shock’.
MotivationMotivation
Forward Rate Unbiasedness Hypothesis stipulates that under the joint hypothesis of risk neutrality and rational expectations, the current forward rate is an unbiased predictor of the future spot rate
Early investigations of forward rate unbiasedness (e.g. Frenkel, 1976, 1981; and Levich, 1978) relied on: under the null hypothesis α=0 and β=1
The puzzle arises because β<>1.
Fama (1984) suggests that the expected change in the exchange rate is often inversely related to the forward premium
Following Meese and Singleton’s (1982) evidence that foreign exchange rates are nonstationary, it has been common (e.g. Longworth, 1981; Hodrick, 1987; McCallum, 1994) to test the unbiasedness by estimating:
Liu and Maddala (1992) and Barnhart, McNown and Wallace (1999), claims that the conventional Fama regression is invalidated, due to problems of endogeneity, which may result from the appearance of an unobserved risk premium.
Forward Rate Unbiasedness Hypothesis stipulates that under the joint hypothesis of risk neutrality and rational expectations, the current forward rate is an unbiased predictor of the future spot rate
Early investigations of forward rate unbiasedness (e.g. Frenkel, 1976, 1981; and Levich, 1978) relied on: under the null hypothesis α=0 and β=1
The puzzle arises because β<>1.
Fama (1984) suggests that the expected change in the exchange rate is often inversely related to the forward premium
Following Meese and Singleton’s (1982) evidence that foreign exchange rates are nonstationary, it has been common (e.g. Longworth, 1981; Hodrick, 1987; McCallum, 1994) to test the unbiasedness by estimating:
Liu and Maddala (1992) and Barnhart, McNown and Wallace (1999), claims that the conventional Fama regression is invalidated, due to problems of endogeneity, which may result from the appearance of an unobserved risk premium.
Literature ReviewLiterature Review
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Conventionally the expectations hypothesis is tested by using forward exchange rates.
But, the forward rates come only in maturities of one, two, three, six and twelve months. Thus, one is restricted to using monthly horizons and multiples thereof.
Futures contracts have a fixed maturity date, which is e.g. the third Wednesday of a month. Accordingly, the maturity length is determined by the date when the futures contract is traded and the maturity spectrum can be measured in daily units. Thus, futures data embody a much finer set of information.
m – time to maturity and run from one day up to three months, that is between 1 and 65 working days.
A necessary condition for the comparability of estimation results based on forward contract and futures contracts is that there is no significant difference between forward and futures prices. The general finding (e.g. Cornell and Reinganum, 1981; Polakoff and Grier, 1991; Chang and Chang, 1990 and Hull, 2006) is that the factors that might cause forward and futures prices to differ (e.g. differences in default risk or liquidity premium), can be ignored and that the two prices are the same.
Conventionally the expectations hypothesis is tested by using forward exchange rates.
But, the forward rates come only in maturities of one, two, three, six and twelve months. Thus, one is restricted to using monthly horizons and multiples thereof.
Futures contracts have a fixed maturity date, which is e.g. the third Wednesday of a month. Accordingly, the maturity length is determined by the date when the futures contract is traded and the maturity spectrum can be measured in daily units. Thus, futures data embody a much finer set of information.
m – time to maturity and run from one day up to three months, that is between 1 and 65 working days.
A necessary condition for the comparability of estimation results based on forward contract and futures contracts is that there is no significant difference between forward and futures prices. The general finding (e.g. Cornell and Reinganum, 1981; Polakoff and Grier, 1991; Chang and Chang, 1990 and Hull, 2006) is that the factors that might cause forward and futures prices to differ (e.g. differences in default risk or liquidity premium), can be ignored and that the two prices are the same.
Futures Contracts EvidenceFutures Contracts Evidence
st denote the log of the spot exchange rate at time t
ftt−m be the log of the futures exchange rate at time t−m with delivery for time t
and maturity m.
Following the expectations hypothesis, a futures rate is regarded as an efficient predictor of the spot exchange rate at the maturity date of the futures contract, t.
To test this hypothesis, realized spot rates are regressed on futures.
If the expectations hypothesis holds, then:
with the null hypothesis for efficiency is H0: α = 0 and β(m,k) = 1.
First we take the lag lenght k=0. Let ytt−m be short notation for the exchange rate
innovation st−st−m and ptt−m for the forward premium ft
t−m−st−m. Then the
conventional expectations hypothesis regression, often denoted as the ‘Fama regression’, is as follows:
where the slope coefficient is:
st denote the log of the spot exchange rate at time t
ftt−m be the log of the futures exchange rate at time t−m with delivery for time t
and maturity m.
Following the expectations hypothesis, a futures rate is regarded as an efficient predictor of the spot exchange rate at the maturity date of the futures contract, t.
To test this hypothesis, realized spot rates are regressed on futures.
If the expectations hypothesis holds, then:
with the null hypothesis for efficiency is H0: α = 0 and β(m,k) = 1.
First we take the lag lenght k=0. Let ytt−m be short notation for the exchange rate
innovation st−st−m and ptt−m for the forward premium ft
t−m−st−m. Then the
conventional expectations hypothesis regression, often denoted as the ‘Fama regression’, is as follows:
where the slope coefficient is:
The Expectations Hypothesis and Futures Data
The Expectations Hypothesis and Futures Data
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We observe :
68 different GBP/US$ futures contracts, with delivery between March 1990 and March 2007
38 different EUR/US$ futures contracts, with delivery between June 1998 and March 2007
68 different CHF/US$ futures contracts, with delivery between March 1990 and March 2007
We also pool the data set, which consists of 174 observations into one data set in order to increase the number of observations.
Dickey-Fuller tests show that the futures premium and the change of exchange rates satisfy the stationarity condition.
We use Seemingly Unrelated Regressions (SUR) to correct for the likely correlation of the error term across currencies. Such a correlation is almost inevitable when using bilateral exchange rates. For example, a strong dollar or a contagious currency crisis in a particular month would likely show up across many of the bilateral dollar exchange rates.
We observe :
68 different GBP/US$ futures contracts, with delivery between March 1990 and March 2007
38 different EUR/US$ futures contracts, with delivery between June 1998 and March 2007
68 different CHF/US$ futures contracts, with delivery between March 1990 and March 2007
We also pool the data set, which consists of 174 observations into one data set in order to increase the number of observations.
Dickey-Fuller tests show that the futures premium and the change of exchange rates satisfy the stationarity condition.
We use Seemingly Unrelated Regressions (SUR) to correct for the likely correlation of the error term across currencies. Such a correlation is almost inevitable when using bilateral exchange rates. For example, a strong dollar or a contagious currency crisis in a particular month would likely show up across many of the bilateral dollar exchange rates.
DataData
The estimates for the slope coefficient β(m,0) and its moving average are plotted with respect to the maturity length m in days.
We highlight the slope coefficients for the maturity horizons available for forward exchange rates covered by our observed forecast period, i.e. for m = {22, 43, 65}, by encircling these particular estimates. This highlights the extra information provided by the futures data.
the slope coefficient is decreasing with the length of maturity horizon mthe expectations hypothesis holds for shorter (less than 1 month) but not for
longer maturities we mostly confirm the forward premium puzzle of a negative slope coefficient.
The estimates for the slope coefficient β(m,0) and its moving average are plotted with respect to the maturity length m in days.
We highlight the slope coefficients for the maturity horizons available for forward exchange rates covered by our observed forecast period, i.e. for m = {22, 43, 65}, by encircling these particular estimates. This highlights the extra information provided by the futures data.
the slope coefficient is decreasing with the length of maturity horizon mthe expectations hypothesis holds for shorter (less than 1 month) but not for
longer maturities we mostly confirm the forward premium puzzle of a negative slope coefficient.
EstimatesEstimates
BETA estimates for the pooled data
-2
-1.5
-1-0.5
0
0.5
1
1.52
2.5
3
0 5 10 15 20 25 30 35 40 45 50 55 60
BETA(m,0)
MA(4)
To summarize the information which is in the futures data at the daily level, we fit a line through the slope coefficients when plotted against the maturity horizon in days.
The estimated constant is highly significant and positive. The Wald test shows that
this constant is not significantly different from the value of one. This suggests that we
would indeed not reject the expectations hypothesis for futures rates with a very short
maturity.
We confirm that there exists a significant negative relationship between the maturity horizon of the futures contract and the estimated value for β(m,0).
If the time to maturity increases by one (working) day, the estimated slope coefficient decreases by a value of around 0.023
This implies that the futures premium puzzle only shows up for maturity horizons longer than 1 month
To summarize the information which is in the futures data at the daily level, we fit a line through the slope coefficients when plotted against the maturity horizon in days.
The estimated constant is highly significant and positive. The Wald test shows that
this constant is not significantly different from the value of one. This suggests that we
would indeed not reject the expectations hypothesis for futures rates with a very short
maturity.
We confirm that there exists a significant negative relationship between the maturity horizon of the futures contract and the estimated value for β(m,0).
If the time to maturity increases by one (working) day, the estimated slope coefficient decreases by a value of around 0.023
This implies that the futures premium puzzle only shows up for maturity horizons longer than 1 month
EstimatesEstimates
Dependent Variable: BETASMethod: Least Squares
Ramsey testVariable Coefficient Std. Error t-Statistic Prob. Prob.
MAT -0.0233 0.0050 -4.6836 0.0000 0.2715C 0.8172 0.1843 4.4342 0.0000
25.83%R-squared
By estimating the ‘outside regression’ (k>0) we investigate, whether the forward
rate at time t−m is able to predict the change of exchange rates between the
maturity date t and a date that lies k time periods to the past of the pricing date of
that forward rate, t−m−k. Thus, the futures market at t−m incorporates the past
innovations of the exchange rate.
By estimating the ‘outside regression’ (k>0) we investigate, whether the forward
rate at time t−m is able to predict the change of exchange rates between the
maturity date t and a date that lies k time periods to the past of the pricing date of
that forward rate, t−m−k. Thus, the futures market at t−m incorporates the past
innovations of the exchange rate.
Outside RegressionsOutside Regressions
Thus, the ‘outside regression’ differs from the conventional ‘Fama regression’ (k = 0) in the way that we subtract from both sides of the regression the realized spot exchange rate return between t−m and t−m−k.
To the time t − m, when the futures rate is priced, this exchange rate return is already common knowledge. This is the ‘news part’ in the outside regression.
Thus, the ‘outside regression’ differs from the conventional ‘Fama regression’ (k = 0) in the way that we subtract from both sides of the regression the realized spot exchange rate return between t−m and t−m−k.
To the time t − m, when the futures rate is priced, this exchange rate return is already common knowledge. This is the ‘news part’ in the outside regression.
The lag length k can be seen as the ’news advantage’ of the forward rate at t−m relative to the spot rate at t−m−k.
The lag length k can be seen as the ’news advantage’ of the forward rate at t−m relative to the spot rate at t−m−k.
mtkmtmtmttmtkmtmtmtt sssfkmssss )]())[(,()()(
The futures data also allow us to do the opposite and move inside the
maturity horizon, by taking the lag length k<0. Thus, we also consider a
regression of st − st−m+q on ftt−m − st−m+q for q=−k > 0 and m>q>0.
The futures data also allow us to do the opposite and move inside the
maturity horizon, by taking the lag length k<0. Thus, we also consider a
regression of st − st−m+q on ftt−m − st−m+q for q=−k > 0 and m>q>0.
Inside RegressionsInside Regressions
This regression generates some interesting information since it asks whether forex returns during the later part of the maturity horizon are moving as predicted by the futures contract signed much earlier.
This regression generates some interesting information since it asks whether forex returns during the later part of the maturity horizon are moving as predicted by the futures contract signed much earlier.
Thus we can potentially deduce whether the futures contract has more to say regarding the earlier or the later day-to-day forex returns over the maturity period.
Thus we can potentially deduce whether the futures contract has more to say regarding the earlier or the later day-to-day forex returns over the maturity period.
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We run regression (1) for m=1, . . . , 65, k=−65, . . . , 65 (m+k>0) for each pair
and for the pooled data set.
Thus, we end up with 65 estimated slope coefficients for every value of k>0 and
with m−q slope coefficients for every k=−q, since q<m.
We run regression (1) for m=1, . . . , 65, k=−65, . . . , 65 (m+k>0) for each pair
and for the pooled data set.
Thus, we end up with 65 estimated slope coefficients for every value of k>0 and
with m−q slope coefficients for every k=−q, since q<m.
Outside and Inside Regressions
Outside and Inside Regressions
The slope coefficient rapidly increases towards 1 when the news advantage (k>0) increases. With a news advantage of only three days, the mean of the slope coefficients turns to a significantly positive value and converges to the value of one.
Close to k=0 there is quite a wide range of different slope values
β(m,q) rapidly converges towards zero as q gets larger.
The slope coefficient rapidly increases towards 1 when the news advantage (k>0) increases. With a news advantage of only three days, the mean of the slope coefficients turns to a significantly positive value and converges to the value of one.
Close to k=0 there is quite a wide range of different slope values
β(m,q) rapidly converges towards zero as q gets larger.
Minimum, maximum and mean of BETA
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-64 -59 -54 -49 -44 -39 -34 -29 -24 -19 -14 -9 -4 2 7 12 17 22 27 32 37 42 47 52 57 62
min max median
Outside Regression
Inside Regression
R-squared is very low for the inside regression (k<0) and becomes substantial, even close to 1 when k rises.
β(m,k) is close to unity if the market has a news advantage beyond the horizon of a fortnight
>> this cannot be taken as evidence that the forward premium puzzle has disappeared.
β(m,k) is close to unity if the market has a news advantage beyond the horizon of a fortnight
>> this cannot be taken as evidence that the forward premium puzzle has disappeared.
Looking Forward in the ‘Outside’..
Looking Forward in the ‘Outside’..
while (constant volatility)
and (weak form efficiency assumption holds if the exchange rate innovations and premium from non-overlapping time intervals are uncorrelated)
When the lag length k>>, β(m,k)1
But, this is not incompatible with β(m,0)<0, so that the premium puzzle is still present in the background.
while (constant volatility)
and (weak form efficiency assumption holds if the exchange rate innovations and premium from non-overlapping time intervals are uncorrelated)
When the lag length k>>, β(m,k)1
But, this is not incompatible with β(m,0)<0, so that the premium puzzle is still present in the background.
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Looking Forward in the ‘Inside’..
Looking Forward in the ‘Inside’..
When q>>, β(m,k)0
As is the case for the outside regression, this effect depends on the magnitude of the news dominance feature
the extra term in the numerator and denominator shows that for small values of q this slope estimate provides extra information
When q>>, β(m,k)0
As is the case for the outside regression, this effect depends on the magnitude of the news dominance feature
the extra term in the numerator and denominator shows that for small values of q this slope estimate provides extra information
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Our estimation results confirm negative slope coefficients when testing the
expectations hypothesis for maturity horizons usually covered by forward exchange
rate contracts at the monthly frequency.
However, we find that there exists a significant negative relationship between
the slope coefficients and the maturity horizon of the futures contracts.
If the time to maturity m is small, the rejection of the expectations hypothesis is
less decisive and slope coefficients hover around the predicted value of one.
For very long maturities the evidence reported in other research is also in line
with the expectations hypothesis. Thus it appears that the market in the beginning
follows the predictions of the expectations hypothesis, but reverses itself, only to
come back to this once again after a period of years. This leads us to conclude that
the typical form of the premium correlation when plotted against the maturity horizon
is V-shaped.
Our estimation results confirm negative slope coefficients when testing the
expectations hypothesis for maturity horizons usually covered by forward exchange
rate contracts at the monthly frequency.
However, we find that there exists a significant negative relationship between
the slope coefficients and the maturity horizon of the futures contracts.
If the time to maturity m is small, the rejection of the expectations hypothesis is
less decisive and slope coefficients hover around the predicted value of one.
For very long maturities the evidence reported in other research is also in line
with the expectations hypothesis. Thus it appears that the market in the beginning
follows the predictions of the expectations hypothesis, but reverses itself, only to
come back to this once again after a period of years. This leads us to conclude that
the typical form of the premium correlation when plotted against the maturity horizon
is V-shaped.
UIP Testing - ConclusionUIP Testing - Conclusion
Since our objective in this paper is not to explain the failure of UIP, we proceed next with measuring the economic significance of this failure. Our metric for significance is the amount of money that can be made by exploiting deviations from UIP
DATA
Bid and ask interbank spot exchange rate (St) and 1-month forward exchange rate (Ft)
for:
- Developed economies: GBPUSD, EURUSD, USDCHF, USDJPY (smpl Sept 1990-May 2007)
- Emerging economies: USDPLN, USDHUF, USDRON (smpl Jul 1996-May 2007)
All quotes are in FCY/US Dollar.
Frequency: Daily converted into non-overlapping monthly observations by sampling in the second working day of every month (to exclude the possibility of creating a moving average error process)
Source: Reuters, Ecowin
The quotes are indicative quotes for small trade sizes.
Since our objective in this paper is not to explain the failure of UIP, we proceed next with measuring the economic significance of this failure. Our metric for significance is the amount of money that can be made by exploiting deviations from UIP
DATA
Bid and ask interbank spot exchange rate (St) and 1-month forward exchange rate (Ft)
for:
- Developed economies: GBPUSD, EURUSD, USDCHF, USDJPY (smpl Sept 1990-May 2007)
- Emerging economies: USDPLN, USDHUF, USDRON (smpl Jul 1996-May 2007)
All quotes are in FCY/US Dollar.
Frequency: Daily converted into non-overlapping monthly observations by sampling in the second working day of every month (to exclude the possibility of creating a moving average error process)
Source: Reuters, Ecowin
The quotes are indicative quotes for small trade sizes.
Currency Speculation Strategies
Currency Speculation Strategies
Statistical Tests of UIPStatistical Tests of UIP
alfa beta R-squared
-0.0033 -3.8948 2.983%[0.2418] [0.0521]
-0.0072 -2.1708 1.798%[0.0505] [0.0571]
-0.0042 -2.0186 1.543%[0.1277] [0.0948]
0.0015 -2.7082 2.241%[0.4738] [0.0542]
-0.0075 1.0004 2.898%[0.1019] [0.0547]
-0.0071 1.1886 2.256%[0.2019] [0.0919]
0.0010 -2.5981 11.839%
[0.9006] [0.0499]
Poland
Hungary
Romania
UIP Regressions, 1990-20071 Month Regression
Great Britain
Japan
Switzerland
Euro
We test Fama regression in prices terms (not log):
• For developed countries and Romania, β < 0.
• For Poland and Hungary, there is evidence that investors find it easier to forecast the direction of movement of these currencies
We test Fama regression in prices terms (not log):
• For developed countries and Romania, β < 0.
• For Poland and Hungary, there is evidence that investors find it easier to forecast the direction of movement of these currencies
11 /)(/)( ttttttt SSFSSS
Two Currency Speculation Strategies
Two Currency Speculation Strategies
1. Carry Trade – Sell forward currencies that are at a forward premium and buy currencies that are at a forward discount.
• β<<0 suggests:
– Sell dollars forward when Ft>St. x-no of $ sold fwd
– Buy dollars forward when Ft<St.
This strategy is equivalent to:
– Borrow low interest rate currency; y-no of $ borrowed
– Lend high interest rate currency;
– Do not hedge the exchange rate risk.
This strategy is also equivalent to using the current spot to forecast the future exchange rate.
2. BGT Strategy
– Suggested by Backus, Gregory and Telmer (1993)
– Use the above regression to predict the returns to selling currency forward
1. Carry Trade – Sell forward currencies that are at a forward premium and buy currencies that are at a forward discount.
• β<<0 suggests:
– Sell dollars forward when Ft>St. x-no of $ sold fwd
– Buy dollars forward when Ft<St.
This strategy is equivalent to:
– Borrow low interest rate currency; y-no of $ borrowed
– Lend high interest rate currency;
– Do not hedge the exchange rate risk.
This strategy is also equivalent to using the current spot to forecast the future exchange rate.
2. BGT Strategy
– Suggested by Backus, Gregory and Telmer (1993)
– Use the above regression to predict the returns to selling currency forward
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Carry TradeCarry Trade
Carry Trade without Bid-Ask Spreads
Agents follow the rule: Sell 1 Dollar forward when the Dollar is at a forward premium, Ft>St,
and obtain the payoff:
Carry Trade with Bid-Ask Spreads
Agents adopt the decision rule:
and obtain the payoff:
Symbol Definition Applies toSa/Fa Spot/Fwd Ask Foreign Currency/Dollar Exchange Rate Buying Dollars spot/forwardSb/Fb Spot/Fwd Bid Foreign Currency/Dollar Exchange Rate Selling Dollars spot/forward
Carry Trade without Bid-Ask Spreads
Agents follow the rule: Sell 1 Dollar forward when the Dollar is at a forward premium, Ft>St,
and obtain the payoff:
Carry Trade with Bid-Ask Spreads
Agents adopt the decision rule:
and obtain the payoff:
Symbol Definition Applies to
Sa/Fa Spot/Fwd Ask Foreign Currency/Dollar Exchange Rate Buying Dollars spot/forwardSb/Fb Spot/Fwd Bid Foreign Currency/Dollar Exchange Rate Selling Dollars spot/forward
otherwise 0
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BGT StrategyBGT Strategy• Use the BGT regression to forecast the excess returns from selling dollars forward, Ft-St+1:
Sell dollars forward when:
Buy dollars forward when:
where ât and b[ t are the time t recursive estimates of a
and b.
Equivalence
Suppose 1/S\t is a martingale.
Then BGT regression is roughly equivalent to:
Can re-arrange this equation to show that a=-α and
b=1-β in standard UIP regression.
>> β close to 2 implies b close to 3.
• Use the BGT regression to forecast the excess returns from selling dollars forward, Ft-St+1:
Sell dollars forward when:
Buy dollars forward when:
where ât and b[ t are the time t recursive estimates of a
and b.
Equivalence
Suppose 1/S\t is a martingale.
Then BGT regression is roughly equivalent to:
Can re-arrange this equation to show that a=-α and
b=1-β in standard UIP regression.
>> β close to 2 implies b close to 3.
111 /)(/)( ttttttt SSFbaSSF
a b R-squared
0.0025 3.9659 3.103%[0.3816] [0.0476]
0.0070 3.1072 3.634%[0.0552] [0.0066]
0.0026 2.3741 2.324%[0.2855] [0.0299]
-0.0005 2.2855 2.369%[0.8169] [0.0438]
0.0063 0.4050 0.427%[0.1886] [0.4838]
-0.0033 2.1244 2.999%[0.6530] [0.0898]
0.0062 1.0979 4.421%[0.4349] [0.1607]
Romania
Switzerland
Euro
Poland
Hungary
BGT Regressions, 1990-20071 Month Regression
Great Britain
Japan
0)(ˆˆ tt SFba
0)(ˆˆ tt SFba
11 /)(/)( ttttttt SSFbaSSF
Currency Speculation andExchange Rate ForecastsCurrency Speculation andExchange Rate Forecasts
Both currency speculation strategies rely implicitly on forecasts of future exchange rates.
• Carry trade (‘random walk’ forecasts):
• BGT:
Both currency speculation strategies rely implicitly on forecasts of future exchange rates.
• Carry trade (‘random walk’ forecasts):
• BGT:
ttt SSE )( 1
tttt SabFbSE )()1()( 1
11 ]/)(1[)/1( tttttt FSSFbaSE
Returns to the Carry Trade Strategies
Returns to the Carry Trade Strategies
Mean Std. Dev. Sharpe Ratio Mean Std. Dev. Sharpe Ratio
0.0018 0.0275 0.0656 0.0012 0.0262 0.04420.0027 0.0264 0.1008 0.0023 0.0265 0.0856-0.0019 0.0300 -0.0637 -0.0023 0.0300 -0.07830.0036 0.0265 0.1362 0.0251 0.0633 0.0038
0.0056 0.0312 0.1782 0.0044 0.0280 0.15580.0060 0.0302 0.1997 0.0032 0.0279 0.11340.0171 0.0323 0.5304 0.0101 0.0301 0.3347
0.0050 0.0292 0.1639 0.0063 0.0331 0.09420.0043 0.0105 0.4111 0.0033 0.0101 0.3239
0.0088 0.0438 0.19970.0373 0.0767 0.4863
S&P 500BSE BET
0.0064 0.0245 0.26130.0105 0.0268 0.3901
0.0023 0.0137 0.16680.0031 0.0138 0.2244
Romania
All AverageEqually-weighted
portfolio - all
Developed countries portfolio
Emerging countries portfolio
SwitzerlandEuro
PolandHungary
Returns to Carry Trade Strategies 1990-2007
With Transactions CostsNo Transaction Costs
Great BritainJapan
• We use Sharpe Ratio as a measurement of the return-risk ratio. • There are large diversification gains from combining country strategies• The Sharpe Ratios are considerably higher for the strategies in the emerging markets compared to the ones in the developed economies
• We use Sharpe Ratio as a measurement of the return-risk ratio. • There are large diversification gains from combining country strategies• The Sharpe Ratios are considerably higher for the strategies in the emerging markets compared to the ones in the developed economies
Returns to the BGT StrategiesReturns to the BGT Strategies
Mean Std. Dev. Sharpe Ratio Mean Std. Dev. Sharpe Ratio
0.0034 0.0273 0.1234 0.0029 0.0274 0.10540.0068 0.0256 0.2657 0.0064 0.0256 0.25030.0019 0.0300 0.0637 0.0015 0.0300 0.05110.0038 0.0265 0.1446 0.0035 0.0265 0.1330
0.0105 0.0299 0.3511 0.0083 0.0301 0.27510.0069 0.0300 0.2314 0.0050 0.0300 0.16660.0202 0.0305 0.6636 0.0173 0.0306 0.5664
0.0077 0.0286 0.2633 0.0064 0.0286 0.22110.0063 0.0178 0.3564 0.0053 0.0178 0.2987
0.0088 0.0438 0.19970.0373 0.0767 0.4863
S&P 500BSE BET
Returns to BGT Strategies 1990-2007
No Transaction Costs With Transactions Costs
Great BritainJapan
SwitzerlandEuro
Developed countries portfolio
Poland
0.0056 0.0175 0.3201
Equally-weighted portfolio - all
0.0281 0.4739Emerging countries
portfolio0.0133 0.0281 0.3859
All Average
0.0109
HungaryRomania
0.0052 0.0175 0.2955
• The BGT strategy yields smaller returns than the Carry Trade for the equally-weighted portfolio, but greater returns in the individual cases. • There are some diversification gains from combining country strategies, but mostly close to the average.• Romania yields again the highest Sharpe Ratio
• The BGT strategy yields smaller returns than the Carry Trade for the equally-weighted portfolio, but greater returns in the individual cases. • There are some diversification gains from combining country strategies, but mostly close to the average.• Romania yields again the highest Sharpe Ratio
Bid-Ask Spreads Have LargeImpact on Excess Returns
Bid-Ask Spreads Have LargeImpact on Excess Returns
• Bid-ask spreads have a sizable impact on the profitability of currency speculation• Bid-ask spreads are smaller in developed countries than in emerging ones– If agent buys and sells one pound against the U.S. dollar in the spot market he loses onaverage Sb-Sa=0.0008 dollars.
• Bid-ask spreads have a sizable impact on the profitability of currency speculation• Bid-ask spreads are smaller in developed countries than in emerging ones– If agent buys and sells one pound against the U.S. dollar in the spot market he loses onaverage Sb-Sa=0.0008 dollars.
Mean Std. Dev. Sharpe Ratio Mean Std. Dev. Sharpe Ratio
0.0043 0.0105 0.4111 0.0063 0.0178 0.3564
0.0033 0.0101 0.3239 0.0064 0.0286 0.2211BGT
Equally weighted
portfolio
Average of Bid - Ask With Bid - Ask Spread
Carry Trade
Since the spreads are of the same order of magnitude as the expected payoff associated with our two currency-speculation strategies, in the remainder of this presentation, we only consider strategies and payoffs that take bid-ask spreads into account
Since the spreads are of the same order of magnitude as the expected payoff associated with our two currency-speculation strategies, in the remainder of this presentation, we only consider strategies and payoffs that take bid-ask spreads into account
Spot 1 Month Spot 1 Month
8 9 0.05 0.054 5 0.04 0.044 5 0.04 0.042 3 0.03 0.0367 80 0.18 0.2139 48 0.17 0.2258 113 0.19 0.38
pips % of bid
Great BritainJapan
SwitzerlandEuro
PolandHungaryRomania
Bid - Ask Spreads
Realized Returns to Currency Speculation
Realized Returns to Currency Speculation
Realized Sharpe Ratio: 1 Year Rolling Window
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Carry trade BGT
Realized Returns to Carry Trade and BGT With Costs - equally weighted
portfolio
-0.05
-0.03
-0.01
0.01
0.03
0.05
0.07
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
BGT Carry trade
58,105.30 23,709.05 36,809.68 12,989.95
- 54,307.43
51,853.67 28,589.31 19,131.01 10,068.54 26,349.70 16,690.28 8,262.86 4,815.14 USDRON
Monthly bets ('000) in speculation
strategies to obtain $ 1 mio/year
Carry Trade BGT
USDCHF
USDEURUSDPLNUSDHUF
USDGBPUSDJPY
BGT strategies yields higher returns than the Carry Trades. Even though Sharpe ratios including transactions costs are high, the average payoffs to currency-speculation strategies are rather low. So to generate substantial profits speculators must wager very large sums of money.
BGT strategies yields higher returns than the Carry Trades. Even though Sharpe ratios including transactions costs are high, the average payoffs to currency-speculation strategies are rather low. So to generate substantial profits speculators must wager very large sums of money.
Realized Returns to Currency Speculation
Realized Returns to Currency Speculation
Portfolio Cumulative Realized Nominal Returns to
Currency Speculation (Sep96=1)
0.7
1.2
1.7
2.2
2.7
3.2
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
CARRY TRADELIBOR payoffS&P payoffBGT
We use the realized payoffs to compute the cumulative realized return measured in U.S. dollars to committing one dollar in the beginning of the sample to various currency-speculation strategies and reinvesting the proceeds at each point in time.
The agent starts with one U.S. dollar in his bank account and bets that dollar in the currency strategy. From that point forward the agent bets the balance of his bank account on the currency strategy. Currency strategy payoffs are deposited or withdrawn from the agent’s account.
Since the currency strategy is a zero-cost investment, the agent’s net balances stay in the bank and accumulate interest at the bid Libor rate published by the Federal Reserve. It turns out that the bank account balance never becomes negative in our sample. This result reflects the fact that strategy payoffs are small in absolute value.
For Romania, the stock market’s index BET out-performs all strategies (BET SR=0.4863)
We use the realized payoffs to compute the cumulative realized return measured in U.S. dollars to committing one dollar in the beginning of the sample to various currency-speculation strategies and reinvesting the proceeds at each point in time.
The agent starts with one U.S. dollar in his bank account and bets that dollar in the currency strategy. From that point forward the agent bets the balance of his bank account on the currency strategy. Currency strategy payoffs are deposited or withdrawn from the agent’s account.
Since the currency strategy is a zero-cost investment, the agent’s net balances stay in the bank and accumulate interest at the bid Libor rate published by the Federal Reserve. It turns out that the bank account balance never becomes negative in our sample. This result reflects the fact that strategy payoffs are small in absolute value.
For Romania, the stock market’s index BET out-performs all strategies (BET SR=0.4863)
USDRON Cumulative Realized Nominal Returns to
Currency Speculation (Jul03=1)
0.7
1.2
1.7
2.2
2.7
3.2
3.7
4.2
4.7
2003 2003 2004 2004 2004 2005 2005 2005 2006 2006 2006 2007
CARRY TRADE BUBID payoff
BET BGT
Why is the Sharpe Ratio so high?
Why is the Sharpe Ratio so high?
• Risk• Fat tails• Price pressure (Burnside, 2006)
Are Excess Returns Correlated with Risk Factors?• We regress the payoffs on several risk factors and on macro variables (monetary policy can generate time-varying risk premium).
Fama-French factors, consumption growth and M1 growth enter significantly into Carry Trade returns regression.
• Risk• Fat tails• Price pressure (Burnside, 2006)
Are Excess Returns Correlated with Risk Factors?• We regress the payoffs on several risk factors and on macro variables (monetary policy can generate time-varying risk premium).
Fama-French factors, consumption growth and M1 growth enter significantly into Carry Trade returns regression.
Intercept Slope R-squared Intercept Slope R-squared
0.0031 0.0246 1.120% 0.0055 -0.0115 0.079%[0.0011] [0.2345] [0.0010] [0.7523]
0.0026 0.0005 4.557% 0.0046 0.0003 2.998%[0.0061] [0.0571] [0.0067] [0.4896]
0.0003 0.0001[0.1762] [0.9087]
0.0006 0.0010
[0.0565] [0.0850]
0.0028 0.0019 0.230% 0.0066 -0.0054 0.642%[0.0219] [0.5903] [0.0023] [0.3688]
0.0043 -0.0054 3.872% 0.0072 -0.0039 1.021%[0.0000] [0.0266] [0.0021] [0.2584]
0.0035 -0.0770 0.649% 0.0055 -0.0563 0.112%
[0.0003] [0.3660] [0.0010] [0.7073]
0.0054 -0.0054 1.031% 0.0078 -0.0006 0.421%[0.0100] [0.2541] [0.0357] [0.4669]
0.0168 -0.0001 1.272% 0.0072 0.0000 0.008%[0.1169] [0.2050] [0.7009] [0.9205]
-0.1604 0.1634 4.970% -0.1285 0.1336 1.079%[0.0131] [0.0114] [0.2627] [0.2434]
-0.1982 0.2004 1.458% -0.0986 0.1034 0.126%[0.1816] [0.1745] [0.7061] [0.6910]
0.0251 -0.0209 0.304% 0.0722 -0.0659 0.872%[0.4901] [0.5605] [0.2858] [0.3231]
-0.1762 0.1783 2.067% -0.0416 0.0467 0.005%[0.1119] [0.1054] [0.8316] [0.8103]
M1
Fama SMB
Fama HML
Term Premium
Consumption Growth
Returns to BGT Strategy, Equally-Weighted Portfolio
Risk Factors
M2
M3
MZM
Retail Sales
Macro Factors
Fed Fund Rate
Inflation
S&P500
Fama Mkt-Rf
Risk & Macro Factors Correlations Returns to Carry Trade, Equally-Weighted Portfolio
Risk Factors
S&P500
Fama Mkt-Rf
Macro Factors
Fed Fund Rate
MZM
Inflation
M1
M2
M3
Fama SMB
Fama HML
Term Premium
Retail Sales
Consumption Growth
…and in the case of RON?…and in the case of RON?
inflation and NBR’s key policy rate entering significantly and with a positive sign in the carry-trade payoffs regression, but n ot the same for the BGT Strategy
How might a tightening in monetary policy influence Carry Trades returns?
it leads to an immediate rise in short-term interest rates, and therefore to a widening interest-rate spreads leads to an immediate appreciation of the high-yield market's currency
it leads to a decline in actual and expected inflation the ccy's value gains further (a decline in inflation expectations boost the real return on assets)
it leads to a to more stable domestic GDP growth, investors should gradually demand less compensation in the form of a risk premium
inflation and NBR’s key policy rate entering significantly and with a positive sign in the carry-trade payoffs regression, but n ot the same for the BGT Strategy
How might a tightening in monetary policy influence Carry Trades returns?
it leads to an immediate rise in short-term interest rates, and therefore to a widening interest-rate spreads leads to an immediate appreciation of the high-yield market's currency
it leads to a decline in actual and expected inflation the ccy's value gains further (a decline in inflation expectations boost the real return on assets)
it leads to a to more stable domestic GDP growth, investors should gradually demand less compensation in the form of a risk premium
Intercept Slope R-squared Intercept Slope R-squared
0.0075 0.0007 3.605% 0.0180 0.0002 0.382%[0.1369] [0.2116] [0.0007] [0.6868]
0.0244 -0.5306 0.429% 0.0612 -1.5841 3.946%[0.4656] [0.6656] [0.0621] [0.1857]
0.2173 -0.0297 2.658% 0.1591 -0.0201 1.261%[0.2567] [0.2790] [0.4006] [0.4574]
-0.0041 0.0214 12.487% 0.0104 0.0124 4.315%[0.5620] [0.0160] [0.1589] [0.1660]
-0.0099 0.1509 8.284% 0.0111 0.0569 1.219%[0.3698] [0.0524] [0.3252] [0.4651]
Returns to Carry Trade, USDRON Returns to BGT Strategy, USDRONRisk & Macro Factors Correlations
Risk Factors Risk Factors
BET BET
GDP growth GDP growth
NBR Policy Rate NBR Policy Rate
GDP per capita
Inflation
GDP per capita
Inflation
Fat TailsFat Tails
Fat Tails
• Payoffs to speculation in individual currencies have fat tails (except BGT for USDCHF, USDEUR and USDHUF).
• These fat tails are reduced once currencies are combined into equally-weighted portfolio (for the Carry trade we cannot reject the normal distribution hypothesis).
Fat Tails
• Payoffs to speculation in individual currencies have fat tails (except BGT for USDCHF, USDEUR and USDHUF).
• These fat tails are reduced once currencies are combined into equally-weighted portfolio (for the Carry trade we cannot reject the normal distribution hypothesis).
0
4
8
12
16
20
-0.0250 -0.0125 -0.0000 0.0125 0.0250
Series: Returns to Carry Trade
Mean 0.003261Median 0.004230Maximum 0.028499Minimum -0.026788Std. Dev. 0.010067Skewness -0.338028Kurtosis 3.624630
Jarque-Bera 4.518479Probability 0.104430
0
4
8
12
16
20
24
-0.04 -0.02 -0.00 0.02 0.04 0.06
Series: The Returns To BGT
Mean 0.005307Median 0.004158Maximum 0.069500Minimum -0.047377Std. Dev. 0.017763Skewness 0.467074Kurtosis 4.090871
Jarque-Bera 11.00070Probability 0.004085
Skewness Kurtosis Jarque-Bera SkewnessKurtosis Jarque-Bera
-1.2171 8.6559 452.1820 -1.3062 9.8289 320.7043-1.0812 7.4259 205.2424 -0.9331 6.9105 158.8025-0.2194 3.9248 8.8617 0.2183 2.9501 1.6336-0.4205 3.5463 8.5076 -0.2494 3.3430 3.1001-1.0179 5.3549 52.0824 -1.0812 5.9779 72.8003
0.4721 4.1613 12.0406 0.1567 3.5775 2.30241.1640 5.0732 18.6254 0.6012 4.1265 5.2033
-0.3314 5.4489 -0.3705 5.2449
0.4671 4.0909 11.0007
AverageEqually-weighted
portfolio -0.3380 3.6246 4.5185
HungaryRomania
Poland
JapanSwitzerland
Euro
Skewness, Kurtosis and Normality Test
Returns to Carry Trade Returns to BGT Strategy
Great Britain
ConclusionsConclusions• We bring new evidence in support of the forward premium puzzle by using the futures contracts instead of the forward ones and then we quantify the economical significance of UIP failure
• Our results confirm negative slope coefficients when testing the expectations hypothesis for standard maturity horizons.
• We find a significant negative relationship between the slope coefficients and the maturity horizon of the futures contracts. If the time to maturity m is small, the rejection of the expectations hypothesis is less decisive and slope coefficients hover around the predicted value of one.
• We figured that the typical form of the premium correlation when plotted against the maturity horizon is V-shaped.
• We document that appropriate currency-speculation strategies, like Carry trades and BGT generate very large Sharpe ratios.
• In addition, the excess returns to these strategies are uncorrelated with standard risk factors.
• While the statistical failure of UIP is very sharp, the amount of money that can be made from this failure with our currency-speculation strategies seems relatively small
• Why don’t agents massively invest in these strategies and eliminate the high Sharpe ratios?
• We bring new evidence in support of the forward premium puzzle by using the futures contracts instead of the forward ones and then we quantify the economical significance of UIP failure
• Our results confirm negative slope coefficients when testing the expectations hypothesis for standard maturity horizons.
• We find a significant negative relationship between the slope coefficients and the maturity horizon of the futures contracts. If the time to maturity m is small, the rejection of the expectations hypothesis is less decisive and slope coefficients hover around the predicted value of one.
• We figured that the typical form of the premium correlation when plotted against the maturity horizon is V-shaped.
• We document that appropriate currency-speculation strategies, like Carry trades and BGT generate very large Sharpe ratios.
• In addition, the excess returns to these strategies are uncorrelated with standard risk factors.
• While the statistical failure of UIP is very sharp, the amount of money that can be made from this failure with our currency-speculation strategies seems relatively small
• Why don’t agents massively invest in these strategies and eliminate the high Sharpe ratios?
ReferencesReferences
[1]Alexius, A.(2001). ”Uncovered Interest Parity Revisited”, Review of International Economics 9, 505-517.[2]Baillie, R.T. and Bollerslev, T. (1989). ”Common Stochastic Trends in a System of Exchange Rates”, Journal of Finance
44, 167-181.[3]Baillie, R.T. and Bollerslev, T. (2000). ”The Forward Premium Anomaly is not as bad as you think”, Journal of
International Money and Finance 19, 471-488.[4]Bekaert, G. and Hodrick, R.J. (1993). ”On Biases in the Measurement of Foreign Exchange Risk Premiums”, Journal of
International Money and Finance 12, 115-138.[5]Bilson, J.F.O. (1981). ”The ’Speculative Efficiency’ Hypothesis”, Journal of Business 54, 435-451.[6]Burnside, Craig, Martin Eichenbaum, Isaac Kleshchelski, and Sergio Rebelo. (2006) “The Returns to Currency
Speculation in Emerging Markets”,.National Bureau of Economic Research Working Paper 12489.[7]Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2006a) “Currency Speculation: The Gains from
Diversification,” mimeo, Northwestern University.[8]Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2006b) “Understanding the Forward Premium Puzzle: A
Microstructure Approach,” mimeo, Northwestern University.[9]Chaboud, A.P. and Wright, J.H. (2005). ”Uncovered Interest Parity, it works, but not for long”, Journal of International
Economics 66(2), 349-362.[10]Chang, C.W. and J.S.K. (1990). ”Forward and future prices: Evidence from the foreign exchange markets”, Journal of
Finance 45, 1333-35.[11]Chinn, M.D. (2006). ”The (partial) Rehabilitation of the Interest Parity in the Floating Rate Era: Longer Horizons,
Alternative Expectations, and Emerging Markets”, Journal of International Money and Finance 25, 7-21.[12]Chinn, D.C. and Meredith, G. (2004). ”Monetary Policy and Long Horizon Uncovered Interest Parity”, IMF Staff Papers
51(3), 409-430. [13]Clarida, R.H. and Taylor, M.P. (1997). ”The Term Structure of Forward Exchange Premiums and the Forecastability of
Spot Exchange Rates: Correcting the Errors”, The Review of Economics and Statistics 79, 353-361.[14]Engel, C. (1996). ”The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence”, Journal of
Empirical Finance 3, 123-192.[15]Evans, M.D.D. and Lewis, K. (1995). ”Do Long-Term Swings in the Dollar Affect Estimates of the Risk Premium?”,
The Review of Financial Studies 8, 709-742.[16]Fama, E. (1970). ”Efficient Capital Markets: A Review of Theory and Empirical Work”, Journal of Finance 25, 383-
417.
[1]Alexius, A.(2001). ”Uncovered Interest Parity Revisited”, Review of International Economics 9, 505-517.[2]Baillie, R.T. and Bollerslev, T. (1989). ”Common Stochastic Trends in a System of Exchange Rates”, Journal of Finance
44, 167-181.[3]Baillie, R.T. and Bollerslev, T. (2000). ”The Forward Premium Anomaly is not as bad as you think”, Journal of
International Money and Finance 19, 471-488.[4]Bekaert, G. and Hodrick, R.J. (1993). ”On Biases in the Measurement of Foreign Exchange Risk Premiums”, Journal of
International Money and Finance 12, 115-138.[5]Bilson, J.F.O. (1981). ”The ’Speculative Efficiency’ Hypothesis”, Journal of Business 54, 435-451.[6]Burnside, Craig, Martin Eichenbaum, Isaac Kleshchelski, and Sergio Rebelo. (2006) “The Returns to Currency
Speculation in Emerging Markets”,.National Bureau of Economic Research Working Paper 12489.[7]Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2006a) “Currency Speculation: The Gains from
Diversification,” mimeo, Northwestern University.[8]Burnside, Craig, Martin Eichenbaum and Sergio Rebelo (2006b) “Understanding the Forward Premium Puzzle: A
Microstructure Approach,” mimeo, Northwestern University.[9]Chaboud, A.P. and Wright, J.H. (2005). ”Uncovered Interest Parity, it works, but not for long”, Journal of International
Economics 66(2), 349-362.[10]Chang, C.W. and J.S.K. (1990). ”Forward and future prices: Evidence from the foreign exchange markets”, Journal of
Finance 45, 1333-35.[11]Chinn, M.D. (2006). ”The (partial) Rehabilitation of the Interest Parity in the Floating Rate Era: Longer Horizons,
Alternative Expectations, and Emerging Markets”, Journal of International Money and Finance 25, 7-21.[12]Chinn, D.C. and Meredith, G. (2004). ”Monetary Policy and Long Horizon Uncovered Interest Parity”, IMF Staff Papers
51(3), 409-430. [13]Clarida, R.H. and Taylor, M.P. (1997). ”The Term Structure of Forward Exchange Premiums and the Forecastability of
Spot Exchange Rates: Correcting the Errors”, The Review of Economics and Statistics 79, 353-361.[14]Engel, C. (1996). ”The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence”, Journal of
Empirical Finance 3, 123-192.[15]Evans, M.D.D. and Lewis, K. (1995). ”Do Long-Term Swings in the Dollar Affect Estimates of the Risk Premium?”,
The Review of Financial Studies 8, 709-742.[16]Fama, E. (1970). ”Efficient Capital Markets: A Review of Theory and Empirical Work”, Journal of Finance 25, 383-
417.
ReferencesReferences[17]Fama, F.E. (1984). ”Forward and Spot Exchange Rates”, Journal of Monetary Economics 14, 319-338.[18]Fama, F.E. (2006). ”The Behavior of Interest Rates”, Review of Financial Studies 19, 359-379.[19]Fama, F.E. and Bliss, R.R. (1987). ”The Information in Long-Maturity Forward Rates”, American Economic Review 77,
680-92.[20]Frankel, J., Chinn, M. (1993). ”Exchange Rate Expectations and the Risk Premium: Test for a Cross Section of 17
Currencies”, Review of International Economics 1, 136-144.[21]Frenkel, J.A. (1977). ”The Forward Exchange Rate, Expectations and the Demand for Money: the German
Hyperinflation”, American Economic Review 67, 653-670.[22]Froot, K.A. and Frankel, A. (1989). ”Forward Discount Bias: Is it an Exchange Risk Premium?”, The Quarterly Journal
of Economics 104, 139-161.[23]Froot, K.A. and Frankel, A. (1990). ”Anomalies: Foreign Exchange”, Journal of Economic Perspectives 4, 179-92.[24]Hodrick, R.J. and Srivastava, S. (1986). ”The Covariation of Risk Premiums and Expected Future Spot Exchange
Rates”, Journal of International Finance 5, 5-21.[25]Hsieh, D.A. (1984). ”Tests of Rational Expectations and no Risk Premium in Forward Exchange Markets”, Journal of
International Economics 17, 173-84.[28]Hull, J. C. (2006). Options, Futures, and other Derivatives. Pearson Prentice Hall.[29]Lewis, K.K. (1995). ”Puzzles in International Financial Markets”, in Handbook of International Economics, Vol.III,
edited by G. Grossman and K. Rogoff, 1913- 1971.[30]Mark, N.C. (1985). ”On Time Varying Risk Premia in the Foreig Exchange Market”, Journal of Monetary Economics
16, 3-18.[31]Mark, N.C., Wu, Y. and Hai, W. (1997). ”Understanding Spot and Forward Exchange Rate Regressions”, Journal of
Applied Econometrics 12, 715-734.[32]Mark, N.C., Wu, Y. (1998). ”Rethinking Deviations from Uncovered Interest Parity: The Role of Covariance Risk and
Noise”, The Economic Journal 108. [33]McCallum, B.T. (1994). ”A Reconsideration of the Uncovered Interest Parity Relationship”, Journal of Monetary
Economics 33, 105-132. [34]Meese, R. A. and K. Rogoff (1983). ”Empirical exchange rate models of the seventies: Do they fit out-of-sample?”,
Journal of International Economics 14, 324.[35]Meese, R., Singleton, K.J. (1982). ”On Unit Roots and the Empirical Modeling of Exchange Rates”, Journal of Finance
37, 1029-1035.[36]Pope, P.F. and Peel, D. (1991). ”Forward Foreign Exchange Rates and Risk Premia-A Reappraisal”, Journal of
International Money and Finance 10, 443-456.
[17]Fama, F.E. (1984). ”Forward and Spot Exchange Rates”, Journal of Monetary Economics 14, 319-338.[18]Fama, F.E. (2006). ”The Behavior of Interest Rates”, Review of Financial Studies 19, 359-379.[19]Fama, F.E. and Bliss, R.R. (1987). ”The Information in Long-Maturity Forward Rates”, American Economic Review 77,
680-92.[20]Frankel, J., Chinn, M. (1993). ”Exchange Rate Expectations and the Risk Premium: Test for a Cross Section of 17
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We use the Sharpe ratio as a statistic which aims to sum up the desirability of our risky investment strategies by dividing the average period excess return by the standard deviation of the return generating process
Formulated in 1966 by Nobel Laureate Bill Sharpe to measure risk-adjusted performance for mutual funds, it undoubtedly has some value as a measure of strategy “quality”, but it also has several crucial limitations:
while return is a definite and an “observable” quantity, risk is not. Standard deviation can be calculated from any time series of return data, but its “meaning” will not be the same for all time series. In order to be a meaningful statistic at all the return time series must be generated from a process that is both stationary and parametric.
SR can have some perverse attributes the standard deviation takes into account the distance of each return from the mean, positive or negative large positive returns increase the perception of risk and are penalized
An improvement would be considering only the negative semi-standard deviation a measure known as the Sortino ratio (Frank A. Sortino) differentiate between harmful volatility from volatility in general and shows how much down-side risk is taken to earn the returns.
We use the Sharpe ratio as a statistic which aims to sum up the desirability of our risky investment strategies by dividing the average period excess return by the standard deviation of the return generating process
Formulated in 1966 by Nobel Laureate Bill Sharpe to measure risk-adjusted performance for mutual funds, it undoubtedly has some value as a measure of strategy “quality”, but it also has several crucial limitations:
while return is a definite and an “observable” quantity, risk is not. Standard deviation can be calculated from any time series of return data, but its “meaning” will not be the same for all time series. In order to be a meaningful statistic at all the return time series must be generated from a process that is both stationary and parametric.
SR can have some perverse attributes the standard deviation takes into account the distance of each return from the mean, positive or negative large positive returns increase the perception of risk and are penalized
An improvement would be considering only the negative semi-standard deviation a measure known as the Sortino ratio (Frank A. Sortino) differentiate between harmful volatility from volatility in general and shows how much down-side risk is taken to earn the returns.
Appendix: Sharpe RatioAppendix: Sharpe Ratio
Returns Excess ofSTDEV
Return Excess AverageRATIO SHARPE