Page 165 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

Unit 14 : Exchange Rate : Meaning and Components

ES
P
In the special case where t and ( t1 − S ) t are uncorrected, the regression coefficients β and β 2 Notes
+
1
split the variance of F – S into two parts : the proportion due to the variance of the premium and
t
t
the proportion due to the variance of the expected change in the spot rate. When the two components
ES
F – S
+
t
t
t
of F – S are correlated, the contribution of covariation between P and ( t1 − S ) t to σ 2 ( t ) t
is divided equally between β , and β . The regression coefficients still include the proportions of
2
1
P and σ
σ 2 ( t ) t due to σ 2 ( ) t 2 ( (ES + t1 − S t )) , but the simple interpretation of β and β 2
F – S
1
ES
P
+
( t
( t
obtained when t and ( t1 − S ) t are uncorrected is lost. The troublesome cov P ,E S +1 − S t )) in
(5) and (6) is a central issue in the empirical tests.
Since F – S + t 1 and S + t1 − S , sum to F – S , the sum of the intercepts in (3) and (4) must be zero, the
t
t
t
t
sum of the slopes must be 1.0, and the disturbances, period-by-period, must sum to 0.0. In other
words, regressions (3) and (4) contain identical information about the variation of the P and
t
ES + − S ) t components of F – S , and in principle there is no need to show both. I contend,
t
t
( t1
however, that joint analysis of the regressions is what makes clear the information that either contains.
Thus, regression (4) of the change in the spot rate, S + t1 − S , on the forward rate minus the current
t
spot rate, F – S , is common in the literature. It is also widely recognized that deviations of β in (4)
t
t
2
from 1.0 can somehow be due to a time varying premium in the forward rate. To my knowledge,
however, the explicit interpretation of the regression coefficients provided by (5) and (6) is not well
known. In particular, it is not widely recognized that, given an efficient or rational exchange market,
the deviation of β from 1.0 is a direct measure of the variation of the premium in the forward rate.
2
The complementarity of the regression coefficients in (3) and (4) which is described in (5) and (6)
helps us to interpret some of the anomalous results observed for estimates of (4).
Economics
Since a major conclusion of the empirical work is that variation in forward rates is mostly variation in
premiums, some discussion of the economics of premiums is warranted. Using more precise notation,
ij
let f ij and s be the forward and spot exchange rates (units of currency i per unit of currency j)
t t
observed at t, and let R and R be the nominal interest rates observed at t on discount bonds
jt
it
denominated in currencies i and j. The bonds have either zero or identical default risks, and they
have the same maturity as f t ij .
With open international bond markets, the no arbitrage condition of interest rate parity (IRP) implies
f t ij /s ij = ( +1R it ) ( +/ 1 R jt ) . ... (7)
t
Thus, the difference between the forward and spot exchange rates observed at t is directly related to
the difference between the interest rates on nominal bonds denominated in the two currencies. Any
premium in the forward rate must be explainable in terms of the interest rate differential.
For example (and keep in mind that it is just an example), suppose (a) that exchanges rates are
characterized by complete purchasing power parity (PPP), and (b) that the Fisher equation holds for
nominal interest rates. Let V and V be the price levels in the two countries, let ∆ i,t +1 =
jt
it
r
r
V
ln ( i,t +1 /V it ) and ∆ j,t +1 = ( Vln j,t +1 /V jt ) be their inflation rates, and let i,t +1 and j,t +1 be the ex
post continuously compounded real returns on their nominal bonds. Taking logs in (7) and applying
the Fisher equation to the resulting continuously compounded nominal interest rates, we have
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