Lecture 23:
Forward Market Bias & the Carry Trade
Motivations:
• Efficient markets hypothesis
• Does rational expectations hold?
• Does the forward rate reveal all public information?
• Does Uncovered Interest Parity hold? Or is there a risk premium?
• The carry trade: Does “borrow at low i & lend at high i* ” make money?
Outline of lecture
1. Specification of the test of unbiasedness.
2. Answer: F is biased.
3. How should we interpret the bias?
●
Risk premium: Introduction to the portfolio balance model.
API-120 - Macroeconomic Policy Analysis I, Professor Jeffrey Frankel, Kennedy School of Government, Harvard University
Sample
page of
spot and
forward
exchange
rates,
Spot rate
|
Forward rates
local per $
(but $/₤ and $/€).
Financial Times
Jan. 30, 2009
API-120 - Macroeconomic Policy Analysis I
Professor Jeffrey Frankel, Kennedy School of Government, Harvard University
Tests of Unbiasedness in the Forward Exchange Market
OVERVIEW OF CONCEPTS
H0: Et ( St+1 ) = Ft .
• Specification of unbiasedness equation
H0:
st 1  fdt   t 1
t+1 ≡ prediction error
Et ( t+1 ) = 0 .
Would unbiasedness H0 => accurate forecasts?
No.
<= ( t+1  0).
API-120 - Macroeconomic Policy Analysis I: Prof. J.Frankel, Harvard University
Et st 1  f t
Et st 1  st  f t  st
We proceed in logs.
(See appendix on Siegal Paradox.)
Et st 1  fdt
st  1     ( fdt )   t  1
Most popular test:
Unbiasedness of the fx market:
H0 :   1
No time-varying risk premium: s e t  fdt  
+
}
s e t  Et st 1  st 1   t 1 ,
Rational expectations:
where Et εt+1 =0
=>
conditional on info at time t.
H0:
st 1    fdt   t 1
But usual finding: β<<1, e.g., ≈ 0.
• Does EMH => Et st+1 = fd t ?
Not necessarily. <= Could be rp  0.
• UIP version of unbiasedness st 1    (i  i*)t   t 1
.
Finding: rejection of H0 .
One can make money, on average, betting against the
forward discount or, equivalently, doing the carry trade.
How to interpret?
(i) exchange risk premium, or
(ii) expectations biased in-sample
Tests of forward market bias extended to emerging markets:
A majority of currencies show a rejection of unbiasedness
and an inability to reject a coefficient of zero (same as advanced countries).
Statistical significance levels
†
‡
† probability that rejection of β=0 (random walk) is just chance.
‡ probability that rejection of β=1 (unbiasedness) is just chance.
Brian Lucey & Grace Loring, 2013, “Forward Exchange Rate Biasedness Across Developed and Developing Country Currencies:
Do Observed Patterns Persist Out of Sample?” Emerging Markets Review, vol.17, pp. 14-28.
Applications of the forward discount
bias (or interest differential bias) strategy
• The Convergence Play in the European Monetary System
(1990-92): Go short in DM;
long in £, Swedish kronor, Italian lira, Finnish markka & Portuguese escudo.
• The Carry Trade
– (1991-94) Go short in $,
– (1995-98) Go short in ¥;
long in Mexican pesos, etc.
long in $ assets, in Asia or US
– (2002-07) Go short $, ¥, SFr; long in Australia, Brazil, Iceland, India,
Indonesia, Mexico, New Zealand, Russia, S. Africa, & Turkey.
• New convergence play (2007):
– Go short in €;
long in Hungary, Baltics, other EMU candidates.
• New carry trade (2009-12): Go short in $.
API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University
Carry trade: A strategy of going short in the (low-interest rate) ¥
and long in the (high interest rate) A$ made a little money every
month 2001-08: the 5% interest differential was not offset
by any depreciation of the A$ during these years.
}
interest differential = 500 basis points
”How to trade the carry trade,” Futures Magazine, www.futuresmag.com, Sept. 2011
Suddenly in 2008, the strategy of going short in ¥ and
long in A$ lost a lot of money, as risk concerns rose sharply,
the carry trade “unwound,” and the A$ plunged against the ¥.
Unwinding of
the carry trade
”How to trade the carry trade,” Futures Magazine, www.futuresmag.com, Sept. 2011
Unanswered question:
Is the systematic component of  -- the fd bias -- due to:
« a risk premium rp? or
« a failure of Rational Expectations?
Three possible approaches:
1) Find a measure of ∆se.
(See Appendix 4 on survey data.)
2) Model rp theoretically. See if prediction errors
depend systematically on variables rp should depend on.
―> Subject of Lecture 23: Optimal portfolio diversification.
3) Cast a wider net, with respect to countries or horizons.
API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University
Introduction to the portfolio-balance model:
Each investor at time t allocates shares
of his or her portfolio to a menu of assets,
as a function of expected return, risk,
& perhaps other factors (tax treatment, liquidity...):
xi, t = βi (Et rt+1 , risk) .
Sum across investors i to get the aggregate demand
for assets, which must equal supply in the market.
We will invert the function to determine
what Et rt+1 must be, for supplies xt to be willingly held.
xt = A + B rpt .
Now invert:
rp t = B-1 x t - B-1 A .
We see that asset supplies are a determinant of the risk premium.
Special case : | B-1 | = 0 ,
• perfect substitutability ( |B|=∞ ),
• no risk premium (rpt = 0),
and so
• no effect from sterilized forex intervention.
How the supply of debt x determines the risk premium rp
in the portfolio balance model
A large x forces up the expected return
that portfolio holders must be paid.
API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Government, Harvard University
Appendix 1:
TESTS OF UNBIASEDNESS IN THE
FORWARD EXCHANGE MARKET, OVERVIEW OF CONCEPTS (continued)

Definition: Random Walk
(∆s t+1 = ε t+1 ).
Does unbiasedness => RW?
No.
<=
(fdt  0), so Et ∆s t+1  0.
Def.: Rational Expectations  Set = Et (St+1)
Def.: Efficient Markets Hypothesis  F reveals all info
Does RE => EMH ?
Not necessarily.
<= There could be transactions costs, capital controls, missing markets...
Appendix 2:
Technical econometrics regarding error term:
• Overlapping observations => MA error process
• “Peso problem:”
small probability of big devaluation
=> error term not ~ iid normal.
• The Siegal paradox:
Is H0 Ft = Et(St+1)? or 1/Ft = Et(1/St+1)?
API-120 - Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard University
Appendix, cont.:
The Siegal Paradox
-- an annoying technicality–
an instance of “Jensen’s inequality.”
One would think that if
the forward rate is unbiased
when one currency is defined
to be the domestic currency,
it would also be unbiased
when the other is.
Unfortunately this is not the case,
unless spot & forward
rates are defined in logs.
(A justification for using logs
-- a Siegal paradox resolution –
is available as an Addendum to this lecture.)
API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Harvard University
Appendix 3:
Tests of unbiasedness
in the forward discount
for individual countries
Results reported in
Engel survey are typical:
On average, not only
does S fail to move in
the direction indicated by
the forward discount,
but it tends, if anything,
to move opposite.
Pooling slope
estimates across
all emerging
countries, the
sign > 0 =>
much less bias
than the
estimates for
rich countries.
Even so, β<<1 =>
unbiasedness
still rejected.
(See below for results
on individual countries.)
Source: J.Frankel & Jumana Poonawala, 2010, “Are Forward Exchange Rates
Biased Indicators of Spot Exchange Rates in Emerging Market Economies?” JIMF.
For each industrialized country,
the slope β is negative.
Source: Frankel & Poonawalla, JIMF, 2010
For emerging markets,
some currencies have
negative slopes, but some
have positive slopes.
Source: Frankel & Poonawalla, 2010
The estimates for the
emerging countries
show less bias than
the estimates for rich
countries.
Source: J.Frankel & Jumana Poonawala,
“Are Forward Exchange Rates Biased Indicators of Spot
Exchange Rates in Emerging Market Economies?” 2010 .
API-120 - Macroeconomic Policy Analysis I
Professor Jeffrey Frankel, Kennedy School of Government, Harvard University
Lucey & Loring, “Forward Exchange Rate Biasedness Across Developed and Developing Country Currencies:
Do Observed Patterns Observed Patterns Persist Out of Sample? “ Emerging Markets Review, 2013.
Appendix 4
Survey data to measure expectations:
sˆ t  s t  u
t
e
e
Test for risk premium:
sˆe t   2   2 ( fd )  u
t
t
H 0 :  2  1,
no time-varying risk premium.
Finding: Failure to reject H0 .
(Allows for a constant risk premium α2.)
API-120 - Macroeconomic Policy Analysis I ; Professor Jeffrey Frankel, Harvard University
Coefficient
on fd (β2) is
insignificantly
different from 1.
=>
time-variation in
fd is variation in
∆se, not in rp.
API-120 - Macroeconomic Policy Analysis I; Professor Jeffrey Frankel, Kennedy School of Government, Harvard University