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These correlations cannot be attributed to the expected spot price change
component of the currency futures basis, thus establishing the presence of a timevarying risk premium component in the currency futures basis.
I. Introduction
The presence of a timevarying risk premium (TVRP) was confirmed in a variety of futures markets
for commodities by
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Bailey and Chan (1993),
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who found that a small number of macroeconomic
risk factors from equities and bond markets are meaningfully related to futures basis movements.
Hodrick and Srivastava (1987), Bessembinder and Chan (1992), and McCurdy and Morgan (1992)
have established the presence of risk premia in currency futures pricing, while Hsieh (1993) found
evidence to the contrary.
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1261
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Introduction
The presence of a timevarying risk premium (TVRP) was confirmed in a variety of futures markets
for commodities by Bailey and Chan (1993), who found that a small number of macroeconomic
risk factors from equities and bond markets are meaningfully related to futures basis movements.
 Exact

Hodrick and Srivastava (1987), Bessembinder and Chan (1992), and McCurdy and Morgan (1992)
 Suffix

have established the presence of risk premia in currency futures pricing, while Hsieh (1993) found
evidence to the contrary. Contributing to this literature, this paper follows the approach of Bailey and
Chan and investigates the presence of risk premia in the currency futures basis in two steps.
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1430
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in a variety of futures markets
for commodities by Bailey and Chan (1993), who found that a small number of macroeconomic
risk factors from equities and bond markets are meaningfully related to futures basis movements.
Hodrick and Srivastava (1987), Bessembinder and Chan (1992), and McCurdy and Morgan (1992) have established the presence of risk premia in currency futures pricing, while
 Exact

Hsieh (1993)
 Suffix

found
evidence to the contrary. Contributing to this literature, this paper follows the approach of Bailey and
Chan and investigates the presence of risk premia in the currency futures basis in two steps.
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4727
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When major foreign currencies are considered, the covered interest parity (CIP) relation is presumed
to hold so as to preclude riskless arbitrage opportunities. The CIP relationship is reasonably well
supported by the data
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(Frenkel and Levich (1975, 1977), Taylor (1987, 1989), Frankel (1991)).
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Under the CIP condition, the foreign currency futures basis is necessarily determined by the relative
interest rates in domestic and foreign markets, with observed discrepancies attributed to transactions
costs and errors in measurement.1 The CIP condition may be stated as
Ft−St=Rt−Rt*,(1)
where tF is the log of the futures price for delivery at time t+1, as observed at time t, tS is the log
of th
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The decomposition in (2) is then applied to determine to what
degree the observed relationship reflects the influence of expectational errors versus that of risk
premia.
The identification of common factors which might be expected to influence the workings of
currency markets is based on recent findings by
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Bailey and Chan (1993),
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who associated
macroeconomic risks common to all asset markets to variations in the basis of twentytwo physical
commodities. They found that after accounting for the effect of interest rates, common basis
variations were correlated with observed proxies for systematic risk in the stock and bond markets.
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Their bond market variables
are two termstructure factors, a default premium and a term premium. The rationale for including
the above variables in the futures basis equation derives from the studies by
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Keim and Stambaugh (1986), Fama and French (1988a,
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b, 1993) and Chen (1991) which have shown that the variables in
question possess significant forecast power for equity and bond returns. More specifically, these
variables are negatively related to business conditions and positively related to expected returns in the
equity and bond markets.
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Their bond market variables
are two termstructure factors, a default premium and a term premium. The rationale for including
the above variables in the futures basis equation derives from the studies by Keim and Stambaugh (1986), Fama and French (1988a, b, 1993) and
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Chen (1991)
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which have shown that the variables in
question possess significant forecast power for equity and bond returns. More specifically, these
variables are negatively related to business conditions and positively related to expected returns in the
equity and bond markets.
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Figure 2 plots the correlograms for up
to fortyeighth order serial correlation in the currency futures basis and indicates that the
autocorrelation function is very similar across currency futures basis. Formal evidence of serial
dependence in the basis series is presented in Table II. The BoxPierce test, adjusted for the presence
of conditional heteroscedasticity
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(Diebold, 1986),
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indicates substantial serial correlation in all basis
series. Also, there is evidence of nonlinear dependence in the data as manifested by the significant
test statistics for Engle's (1982) test for autoregressive conditional heteroscedasticity (ARCH).
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Lowfrequency properties
of the currency basis series are rigorously investigated since the regression methods used later
assume stationarity of the data. Two unit root tests are utilized: the PhillipsPerron test (PP)
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(Phillips (1987),
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Phillips and Perron (1986)), and the KwiatkowskiPhillipsSchmidtShinn test
(KPSS) (Kwiatkowski et al. (1992)). In contrast to the PP test (as well as other standard unit root
tests) in which the null hypothesis is nonstationarity (existence of a unit root), the KPSS test
assumes stationarity under the null.
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Lowfrequency properties
of the currency basis series are rigorously investigated since the regression methods used later
assume stationarity of the data. Two unit root tests are utilized: the PhillipsPerron test (PP)
(Phillips (1987), Phillips and Perron (1986)), and the KwiatkowskiPhillipsSchmidtShinn test
(KPSS)
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(Kwiatkowski et al. (1992)).
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In contrast to the PP test (as well as other standard unit root
tests) in which the null hypothesis is nonstationarity (existence of a unit root), the KPSS test
assumes stationarity under the null.
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It must be
noted, however, that the PP test has low power against the alternative of integration order slightly
less than one especially in small samples as is the case here. Although it is difficult to make reliable
inferences about the stationarity of the stock market variable, it is assumed stationary for purposes of
analysis.
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Keim and Stambaugh (1986)
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assumed stationarity for DY for the same reasons. Finally,
the bond market variables DEF and TERM appear to be stationary since the PP test strongly rejects
the unitroot null while the KPSS test fails to reject the null hypothesis of stationarity.
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The stock market variable is the dividend yield, DY, and the bond market variables are the
bond default spread, DEF, and term spread, TERM. The argument for including risk proxies for
only the U.S. economy is based on evidence by
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Harvey and Huang (1991) and Bollerslev and Engle (1993)
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that U.S. macroeconomic news dominates the effects of news in European markets for U.S.European rates.
The following ARMAXGARCH(1, 1) model is estimated for the futures basis for each
currency:
100⋅
i,t
F−
i,t
S
Si,t=i0α+t−1i1αDY+i2αt−1DEF+i3αt−1TERM+i,tε
εi,t=βiL()i,tε+γiL()i,tu, βiL()=ilβ
l=1
p
∑lL,γiL()=ilγ
l=1
q
∑lL(6)
Vari,tutΩ()≡i,t2σ=iω+iiδi,t−12u+iiςi,t−12σ
where L is
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The specific source of risk (stock versus
bond market) matters, with the relationship being positive (negative) for the stock (bond) market risk
factors. This differential response of currency futures basis to stock and bond market risk factors
awaits explanation. These results contrast with those in
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Bailey and Chan (1993),
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which suggest a
uniformly positive association of futures basis for commodities to stock and bond market risk
factors. However, the results resemble those in Bessembinder and Chan (1992), who found that
currency futures returns were related positively to the dividend yield and negatively to the bond
spread (except for the JY).
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These results contrast with those in Bailey and Chan (1993), which suggest a
uniformly positive association of futures basis for commodities to stock and bond market risk
factors. However, the results resemble those in
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Bessembinder and Chan (1992),
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who found that
currency futures returns were related positively to the dividend yield and negatively to the bond
spread (except for the JY).
The estimated models for the futures basis across currencies appear to be properly specified
on the basis of residual diagnostic tests.
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Given the presence of IGARCH in the spot
and futures currency rates established in previous studies, this result indicates that the spot and
futures rates for these four currencies are copersistent, in the sense of
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Bollerslev and Engle (1993),
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with copersistence vector (1, 1).8 For the futures basis for these currencies shocks to volatility have
a finite duration and the unconditional variance is finite.
Risk Premia versus Spot Forecast Error
Does the importance of equity and bond market factors in explaining common variation in
currency futures basis necessarily substantiate the presence of a timevarying risk premium?
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The factors in question relate to the currency futures basis through
the expected timevarying risk premium component of the basis as opposed to the expected spot
forecast error component. These results on the currency futures basis are thus consistent with the
evidence provided by
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Hodrick and Srivastava (1987), Bessembinder and Chan (1992), and McCurdy and Morgan (1992)
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regarding the presence of risk premia in currency futures pricing.
V. Conclusions
This paper establishes the existence of timevarying risk premia in the currency futures basis
and demonstrates that these risk premia may be forecast using three common variables (dividend
yield, default spread, and term spread) that have previously been shown to possess forecast power
for returns in equity and bon
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