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

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1

1.52

2.5

3

0 5 10 15 20 25 30 35 40 45 50 55 60

BETA(m,0)

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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.

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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

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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’..

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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

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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

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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.

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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

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

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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