Transcript EXCHANGE RATE VOLATILITY AND PRODUCTIVITY GROWTH: …

Academy of Economic Studies Bucharest
Doctoral School of Finance and Banking
DOFIN
Forward Premium Puzzle: Futures
Contracts Evidence and Speculation
Strategies
Supervisor: Professor Dr. Moisa Altar
MSc Student: ALINA PICIOREA
Bucharest, July 2007
Contents
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?
Motivation
• 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’.
Literature Review
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: s
under the null hypothesis α=0 and β=1
t 1     * f t  v t 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:
st 1     ( f t  st )  t 1
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.
Futures Contracts Evidence
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.
The Expectations Hypothesis and
Futures Data

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:
s t  s t  m  k     ( m , k )( f t t m  s t  m  k )   t  m
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 ftt−m−st−m. Then the conventional expectations
hypothesis regression, often denoted as the ‘Fama regression’, is as follows:
yt  m     ( m ,0) ptt m   t  m
where the slope coefficient is:
cov[ yttm , pttm ]
 (m,0) 
var[ pttm ]
Data
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.
Estimates
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.
3
2.5
2
1.5
1
0.5
0
-0.5 0
-1
-1.5
-2
BETA estimates for the pooled data
BETA(m,0)
MA(4)
5
10
15
20
25
30
35
40
45
50
55
60
the slope coefficient is decreasing with the length of maturity horizon m
 the 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.

Estimates
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.
Dependent Variable: BETAS
Method: Least Squares
Variable Coefficient
MAT
-0.0233
C
0.8172
R-squared
Std. Error
0.0050
0.1843
t-Statistic
-4.6836
4.4342
Prob.
0.0000
0.0000
Ramsey test
Prob.
0.2715
25.83%
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

Outside Regressions
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.
( st  st  m )  ( st  m  st  m  k )     ( m, k )[( f t t m  st  m )  ( st  m  st  m  k )]  t  m
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.
Inside Regressions
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.
( st  st  m  q )     (m, k )[( f t t m  st  m )  ( st  m  q  st  m )]  t  m
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.
Outside and Inside Regressions
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.
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.
Minimum, maximum and mean of BETA

Close to k=0 there is quite a wide
range of different slope values

2.5
Outside Regression
2.0
Inside Regression
1.5
1.0
0.5
0.0
-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
-0.5
-1.0
min
max
β(m,q) rapidly converges towards -1.5
zero as q gets larger.
R-squared is very low for the inside regression (k<0) and

becomes substantial, even close to 1 when k rises.
median
Looking Forward in the ‘Outside’..
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.
cov[ y tt m  k , p tt m  y ttmm k ]
 (m, k ) 

var[ p tt m  y ttmm k ]
k 2
 ( m ,0 ) 
 ( m ,0) var[ p tt m ]  cov[ y ttmm k , y tt m ]  cov[ y ttmm k , p tt m ]  k 2
var[ p tt m ]



t
2
t
t m
var[ p t  m ]  k  cov[ p t  m , y t  m  k ]
k 2
1
var[ p tt m ]
while var[ y ttmm k ]  k var[ y ttmm1 ]  k 2
t m
(constant volatility)
t m
and cov[ y t  m , y t  m  k ]  cov[ pt  m , y t  m  k ]  0 (weak form efficiency assumption holds if
the exchange rate innovations and premium from non-overlapping time intervals are
uncorrelated)
t

t
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.

Looking Forward in the ‘Inside’..
cov[ y tt m  y ttmm  q , p tt m  y ttmm  q ]
 (m, q) 

var[ p tt m  y ttmm  q ]
 ( m ,0) var[ ptt m ]  cov[ y ttmm  q , y tt m ]  cov[ y ttmm  q , p tt m ]  var[ y ttmm  q ]

var[ p tt m ]  q 2  2 cov[ p tt m , y ttmm  q ]
cov[ y ttmm  q , p tt m ]
 ( m ,0) 
var[ p tt m ]


2 cov[ p tt m , y ttmm  q ]
q 2
1

t
var[ p t  m ]
var[ p tt m ]

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 q 2 / var[ ptt m ]

the extra term cov[ ptt m , y ttmm  q ]
in the numerator and denominator shows that for small
values of q this slope estimate provides extra information

UIP Testing - Conclusion

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.
Currency Speculation Strategies
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.
Statistical Tests of UIP
UIP Regressions, 1990-2007
1 Month Regression
alfa
We test Fama regression in prices terms (not log):
Great Britain
Japan
• 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
Switzerland
Euro
Poland
Hungary
( S t 1  S t ) / S t     ( Ft  S t ) / S t   t 1
Romania
beta R-squared
-0.0033
-3.8948
[0.2418]
[0.0521]
-0.0072
-2.1708
[0.0505]
[0.0571]
-0.0042
-2.0186
[0.1277]
[0.0948]
0.0015
-2.7082
[0.4738]
[0.0542]
-0.0075
1.0004
[0.1019]
[0.0547]
-0.0071
1.1886
[0.2019]
[0.0919]
0.0010
-2.5981
[0.9006]
[0.0499]
2.983%
1.798%
1.543%
2.241%
2.898%
2.256%
11.839%
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:
( S t 1  S t ) / S t     ( Ft  S t ) / S t   t 1
– Sell dollars forward when Ft>St.
– Buy dollars forward when Ft<St.
 0 if Ft  S t ,
xt  
 0 if Ft  S t ,
x-no of $ sold fwd
This strategy is equivalent to:
– Borrow low interest rate currency;
– Lend high interest rate currency;
– Do not hedge the exchange rate risk.
 0 if R t  Rt* ,
yt  
*

0
if
R

R
,
t
t

y-no of $ borrowed
This strategy is also equivalent to using the current spot to forecast the future exchange rate.
2. BGT Strategy
( Ft  S t 1 ) / S t 1  a  b( Ft  S t ) / S t   t 1
– Suggested by Backus, Gregory and Telmer (1993)
– Use the above regression to predict the returns to selling currency forward
Carry 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,
  1 if Ft  S t ,
xt  
  1 if Ft  S t ,
and obtain the payoff:
Carry Trade with Bid-Ask Spreads
Agents adopt the decision rule:
and obtain the payoff:
Ft
z t  xt (
 1)
S t 1
  1 if Ftb /S at  1

x t    1 if Fta /S bt  1
0
otherwise

 x t (Ftb /S at 1  1) if x t  0

z t 1   x t (Fta /S bt 1  1) if x t  0
0
if x t  0

Symbol Definition
Sa/Fa Spot/Fwd Ask Foreign Currency/Dollar Exchange Rate
Sb/Fb Spot/Fwd Bid Foreign Currency/Dollar Exchange Rate
Applies to
Buying Dollars spot/forward
Selling Dollars spot/forward
BGT Strategy
• Use the BGT regression to forecast the excess returns from selling dollars forward, Ft-St+1:
( Ft  S t 1 ) / S t 1  a  b( Ft  S t ) / S t   t 1
BGT Regressions, 1990-2007
Sell dollars forward when: aˆ  bˆ ( Ft  S t )  0
Buy dollars forward when: aˆ  bˆ ( Ft  S t )  0
where ât and b̂t are the time t recursive estimates of a
and b.
Equivalence
Suppose 1/S̄t is a martingale.
Then BGT regression is roughly equivalent to:
( F t  S t 1 ) / S t  a  b( F t  S t ) / S t   t 1
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.
1 Month Regression
Great Britain
Japan
Switzerland
Euro
Poland
Hungary
Romania
a
0.0025
b
R-squared
3.9659
3.103%
[0.3816]
[0.0476]
0.0070
3.1072
[0.0552]
[0.0066]
0.0026
2.3741
[0.2855]
[0.0299]
-0.0005
2.2855
[0.8169]
[0.0438]
0.0063
0.4050
[0.1886]
[0.4838]
-0.0033
2.1244
[0.6530]
[0.0898]
0.0062
1.0979
[0.4349]
[0.1607]
3.634%
2.324%
2.369%
0.427%
2.999%
4.421%
Currency Speculation and
Exchange Rate Forecasts
Both currency speculation strategies rely implicitly on forecasts of
future exchange rates.
• Carry trade (‘random walk’ forecasts):
• BGT:
E t ( S t 1 )  S t
E t (1 / S t 1 )  [1  a  b( Ft  S t ) / S t ]Ft 1 
E t ( S t 1 )  (1  b)Ft  (b  a ) S t
Returns to the Carry Trade
Strategies
Returns to Carry Trade Strategies 1990-2007
• 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
No Transaction Costs
Mean
Std. Dev. Sharpe Ratio
With Transactions Costs
Mean
Std. Dev. Sharpe Ratio
Great Britain
Japan
Switzerland
Euro
0.0018
0.0027
-0.0019
0.0036
0.0275
0.0264
0.0300
0.0265
0.0656
0.1008
-0.0637
0.1362
0.0012
0.0023
-0.0023
0.0251
0.0262
0.0265
0.0300
0.0633
0.0442
0.0856
-0.0783
0.0038
Developed
countries portfolio
0.0031
0.0138
0.2244
0.0023
0.0137
0.1668
Poland
Hungary
Romania
0.0056
0.0060
0.0171
0.0312
0.0302
0.0323
0.1782
0.1997
0.5304
0.0044
0.0032
0.0101
0.0280
0.0279
0.0301
0.1558
0.1134
0.3347
Emerging countries
portfolio
0.0105
0.0268
0.3901
0.0064
0.0245
0.2613
0.0050
0.0043
0.0292
0.0105
0.1639
0.4111
0.0063
0.0033
0.0331
0.0101
0.0942
0.3239
0.0088
0.0373
0.0438
0.0767
0.1997
0.4863
All Average
Equally-weighted
portfolio - all
S&P 500
BSE BET
Returns to the BGT Strategies
Returns to BGT Strategies 1990-2007
• 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
No Transaction Costs
With Transactions Costs
Mean Std. Dev. Sharpe Ratio
Mean Std. Dev. Sharpe Ratio
0.0034
0.0068
0.0019
0.0038
0.0273
0.0256
0.0300
0.0265
0.1234
0.2657
0.0637
0.1446
0.0029
0.0064
0.0015
0.0035
0.0274
0.0256
0.0300
0.0265
0.1054
0.2503
0.0511
0.1330
Developed countries
0.0056
portfolio
0.0175
0.3201
0.0052
0.0175
0.2955
Great Britain
Japan
Switzerland
Euro
Poland
Hungary
Romania
0.0105
0.0069
0.0202
0.0299
0.0300
0.0305
0.3511
0.2314
0.6636
0.0083
0.0050
0.0173
0.0301
0.0300
0.0306
0.2751
0.1666
0.5664
Emerging countries
portfolio
0.0133
0.0281
0.4739
0.0109
0.0281
0.3859
All Average
0.0077
0.0286
0.0064
0.0286
Equally-weighted 0.0063
portfolio - all
S&P 500
0.0088
BSE BET
0.0373
0.0178
0.2633
0.3564
0.0053
0.0178
0.2211
0.2987
0.0438
0.0767
0.1997
0.4863
Bid-Ask Spreads Have Large
Impact on Excess Returns
Equally weighted
Average of Bid - Ask
With Bid - Ask Spread
portfolio
Mean
Std. Dev. Sharpe Ratio
Mean Std. Dev. Sharpe Ratio
Carry Trade
0.0043
0.0105
0.4111
0.0063
0.0178
0.3564
BGT
0.0033
0.0101
0.3239
0.0064
0.0286
0.2211
• 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 on
average Sb-Sa=0.0008 dollars.
Bid - Ask Spreads
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
pips
Great Britain
Japan
Switzerland
Euro
Poland
Hungary
Romania
Spot 1 Month
8
9
4
5
4
5
2
3
67
80
39
48
58
113
% of bid
Spot
0.05
0.04
0.04
0.03
0.18
0.17
0.19
1 Month
0.05
0.04
0.04
0.03
0.21
0.22
0.38
Realized Returns to Currency
Speculation
Realized Returns to Carry Trade and BGT With Costs - equally weighted
0.07
portfolio
1.4
0.05
1.2
0.03
1
0.01
0.8
-0.011996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Carry trade
BGT
0.6
0.4
-0.03
-0.05
Realized Sharpe Ratio: 1 Year Rolling Window
BGT
Carry trade
0.2
0
-0.21997 1998 1999 2000 2001 2002
2003 2004 2005 2006 2007
-0.4
Monthly bets ('000) in speculation
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.
strategies to obtain $ 1 mio/year
USDGBP
USDJPY
USDCHF
USDEUR
USDPLN
USDHUF
USDRON
Carry Trade
BGT
58,105.30
36,809.68
51,853.67
19,131.01
26,349.70
8,262.86
23,709.05
12,989.95
54,307.43
28,589.31
10,068.54
16,690.28
4,815.14
Realized Returns to Currency
Speculation
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)
Portfolio Cumulative Realized Nominal Returns to
USDRON Cumulative Realized Nominal Returns to
Currency Speculation (Sep96=1)
Currency Speculation (Jul03=1)
3.2
2.7
2.2
CARRY TRADE
LIBOR payoff
S&P payoff
BGT
1.7
4.7
4.2
3.7
CARRY TRADE
BUBID payoff
BET
BGT
3.2
2.7
2.2
1.2
1.7
1.2
0.7
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
0.7
2003 2003 2004 2004 2004 2005 2005 2005 2006 2006 2006 2007
Why is the Sharpe Ratio so high?
• Risk
• Fat tails
• Price pressure (Burnside,
2006)
Returns to Carry Trade, Equally-Weighted Portfolio Returns to BGT Strategy, Equally-Weighted Portfolio
Risk & Macro Factors Correlations
Intercept
Fama Mkt-Rf
Intercept
0.0246
[0.0011]
[0.2345]
0.0026
0.0005
[0.0061]
[0.0571]
1.120%
4.557%
0.0003
Fama HML
S&P500
Fama Mkt-Rf
0.0055
-0.0115
[0.0010]
[0.7523]
0.0046
0.0003
[0.0067]
[0.4896]
Fama SMB
Retail Sales
0.0028
0.0019
[0.0219]
[0.5903]
0.0043
-0.0054
[0.0000]
[0.0266]
0.0035
-0.0770
[0.0003]
[0.3660]
Fama HML
M1
M2
M3
MZM
0.0054
2.998%
0.0010
[0.0850]
0.230%
Term Premium
3.872% Consumption Growth
0.649%
Retail Sales
Macro Factors
Fed Fund Rate
0.079%
0.0001
[0.0565]
Consumption Growth
R-squared
[0.9087]
0.0006
Term Premium
Slope
Risk Factors
0.0031
[0.1762]
Inflation
Fama-French factors,
consumption growth and M1
growth enter significantly into
Carry Trade returns regression.
R-squared
Risk Factors
S&P500
Fama SMB
Are Excess Returns
Correlated with Risk
Factors?
• We regress the payoffs on
several risk factors and on
macro variables (monetary
policy can generate timevarying risk premium).
Slope
0.0066
-0.0054
[0.0023]
[0.3688]
0.0072
-0.0039
[0.0021]
[0.2584]
0.0055
-0.0563
[0.0010]
[0.7073]
0.642%
1.021%
0.112%
Macro Factors
-0.0054
[0.0100]
[0.2541]
0.0168
-0.0001
[0.1169]
[0.2050]
-0.1604
0.1634
[0.0131]
[0.0114]
-0.1982
0.2004
[0.1816]
[0.1745]
0.0251
-0.0209
[0.4901]
[0.5605]
-0.1762
0.1783
[0.1119]
[0.1054]
1.031%
Fed Fund Rate
1.272%
Inflation
4.970%
M1
1.458%
M2
0.304%
M3
2.067%
MZM
0.0078
-0.0006
[0.0357]
[0.4669]
0.0072
0.0000
[0.7009]
[0.9205]
-0.1285
0.1336
[0.2627]
[0.2434]
-0.0986
0.1034
[0.7061]
[0.6910]
0.0722
-0.0659
[0.2858]
[0.3231]
-0.0416
0.0467
[0.8316]
[0.8103]
0.421%
0.008%
1.079%
0.126%
0.872%
0.005%
…and in the case of RON?
Returns to Carry Trade, USDRON
Returns to BGT Strategy, USDRON
Risk & Macro Factors Correlations
Intercept
Slope
R-squared
Intercept
Risk Factors
BET
GDP growth
GDP per capita
Inflation
NBR Policy Rate
Slope
R-squared
Risk Factors
0.0075
0.0007
[0.1369]
[0.2116]
0.0244
-0.5306
[0.4656]
[0.6656]
0.2173
-0.0297
[0.2567]
[0.2790]
-0.0041
0.0214
[0.5620]
[0.0160]
-0.0099
0.1509
[0.3698]
[0.0524]
3.605%
0.429%
2.658%
12.487%
8.284%
BET
GDP growth
GDP per capita
Inflation
NBR Policy Rate
0.0180
0.0002
[0.0007]
[0.6868]
0.0612
-1.5841
[0.0621]
[0.1857]
0.1591
-0.0201
[0.4006]
[0.4574]
0.0104
0.0124
[0.1589]
[0.1660]
0.0111
0.0569
[0.3252]
[0.4651]
0.382%
3.946%
1.261%
4.315%
1.219%
 inflation and NBR’s key policy rate entering significantly and with a positive sign in the carrytrade payoffs regression, but not 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 interestrate 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
Fat Tails
Fat Tails
Skewness, Kurtosis and Normality Test
Returns to Carry Trade
Returns to BGT Strategy
Skewness Kurtosis Jarque-Bera
Skewness Kurtosis Jarque-Bera
Great Britain
Japan
Switzerland
Euro
Poland
-1.2171
-1.0812
-0.2194
-0.4205
-1.0179
8.6559
7.4259
3.9248
3.5463
5.3549
452.1820
205.2424
8.8617
8.5076
52.0824
-1.3062
-0.9331
0.2183
-0.2494
-1.0812
9.8289
6.9105
2.9501
3.3430
5.9779
320.7043
158.8025
1.6336
3.1001
72.8003
Hungary
Romania
0.4721
1.1640
4.1613
5.0732
12.0406
18.6254
0.1567
0.6012
3.5775
4.1265
2.3024
5.2033
Average
Equally-weighted
-0.3314
5.4489
-0.3705
5.2449
-0.3380
3.6246
0.4671
4.0909
portfolio
4.5185
• 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 equallyweighted portfolio (for the Carry trade
we cannot reject the normal
distribution hypothesis).
11.0007
24
20
Series: Returns to Carry Trade
Series: The Returns To BGT
20
16
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
12
8
4
0.003261
0.004230
0.028499
-0.026788
0.010067
-0.338028
3.624630
Jarque-Bera 4.518479
Probability 0.104430
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
16
12
8
4
Jarque-Bera 11.00070
Probability 0.004085
0
0
-0.0250
-0.0125
-0.0000
0.0125
0.0250
0.005307
0.004158
0.069500
-0.047377
0.017763
0.467074
4.090871
-0.04
-0.02
-0.00
0.02
0.04
0.06
Conclusions
• 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?
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Appendix: Sharpe Ratio
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
SHARPE RATIO 
Average Excess Return
STDEV of Excess Returns
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.