Page 166 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

International Trade and Finance

Notes ij ij  ) 
E r
F – S t = ( i,t1 ) + E (∆ i,t1 )  − E r + ) + E (∆ i,t1 

+
+
+  
( j,t1
t
 E r ) – E r   ( V ) – E V ) 
= ( i,t1 ( j,t1 ) + E ln i,t1 ( ln j,t1 

+
+

+
+

− ln V it − ln V jt   ... (8)

ij
With complete PPP, s = V/V , that is, the spot exchange rate is the ratio of the price levels in the
it
jt
t
two countries, and (11) reduces to
( )

 E r
F t ij = ( i,t +1 ) – E r +1 ) + E S ij ... (9)
( j,t


t+1
In words, with the Fisher equation, interest rate parity and purchasing power parity, the premium
P t in the forward rate expression (1) is just the difference between the expected real returns on the
nominal bonds of the two countries. Thus, the variables that determine the difference between the
expected real returns on the nominal bonds (for example, differential purchasing power risks of their
nominal payoffs) also explain the premium in the forward rate. This interpretation applies to any
model of international capital market equilibrium characterized by IRP, PPP, and the Fisher equation
for nominal interest rates. Examples are the international version of the Sharpe (1964) and Lintner
(1965) model discussed by Fama and Farber (1979) or the version of the Lucas (1978) model discussed
by Hodrick and Srivastava (1984).
The lock between the premium in the forward exchange rate and the interest rates on the nominal
bonds of two countries is the direct consequence of the interest rate parity condition (7) of an open
international bond market. For example, using IRP and an international version of the Breeden (1979)
model, Stulz (1981) derives an expression for the forward rate similar to (1) or (9), but for a world in
which (a) complete PPP does not hold, and (b) differential tastes for consumption goods combine
with uncertainty about relative prices to strip the Fisher equation of its meaning.
Data and summary statistics
Spot exchange rates and thirty-day forward rates for nine major currencies are taken from the Harris
Bank Data Base supported by the Center for Studies in International Finance of the University of
Chicago. The rates are Friday closes sampled at four-week intervals. There are 122 observations
covering the period August 31, 1973, to December 10,1982. All rates are U.S. dollars per unit of foreign
currency.
Table 1 shows means, standard deviations, and autocorrelations of S + t1 − S (the four-week change
t
F – S
in the spot rate), t + t 1 (the thirty-day forward rate minus the spot rate observed four weeks later),
F – S
and t t (the forward rate minus the current spot rate). Since the forward and spot rates are in
logs and the differences are multiplied by 100, the three variables are on a percent per month basis.
The standard deviations of F – S + t 1 in table 1 are larger than the standard deviations of S + t1 − S .
t
t
Thus, in terms of standard deviation of forecast errors, the current spot rate is a better predictor of the
future spot rate than the current forward rate. However, variation in the premium component of the
forward rate can obscure the power of the prediction of the future spot rate in the forward rate. This
is the problem that the complementary regressions (3) and (4) are meant to alleviate.
Consistent with the previous literature, the autocorrelations of changes in spot rates, S + t1 − S , are
t
ES
+
close to zero. Thus, if the expected component of the changes, ( t1 − S ) t , varies in an autocorrelated
F – S
way, this is not evident in the behavior of the observed changes. The t + t 1 for different countries
ES
also show little autocorrelation. F – S + t 1 is the premium, P , plus the forecast error, ( t1 ) − S + t1 ,
t
+
t
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