average estimated value of β for industrialized countries in equation (4)4 to be -0.88 for
data of maturity more than one day and less than one year. Surveys by Macdonald and
Taylor (1992) and Isard (1996) came to similar conclusions. Tests of the alternative
specification in (5) yield similar results. Backus, Gregory and Telman (1993) estimated
equation (5) and find estimated b1 close to 2, consistent with an estimated β close to -1 in
(4). A b1 different from zero implies excess returns that are predictable, and therefore
exploitable. Similar results can be found in Fama (1984) and Bilson (1981). Chinn and
Meredith (2004) use data from 1980-2000 at 3, 6 and 12 month horizons for 6 major
currencies and find an average coefficient also of -0.8, with four of the estimated
coefficients having the wrong sign and being significantly different from unity. Another
important finding is that estimates from the arbitrage equations tend to be highly
imprecise, so even where one cannot reject the null of unity coefficient one can often also
not reject the null of zero coefficient.
Several explanations have been forwarded for this failure of unbiasedness to hold
at horizons less than a year and more than a few hours. These basically fall into three
categories: Risk Premium, Forecast Errors, and Non-Linearities.
Risk Premium models include static Capital Asset Pricing Models (and the
portfolio balance models) [Branson and Henderson, 1985; Frankel 1983, 1984] and
dynamic general equilibrium models [Lewis, 1995; Lucas, 1982]. Fama (1984) showed
that any explanation relying on risk-premium to explain the negative estimated betas (or
any beta less than half) must satisfy two criteria: One, there must be a negative
correlation between the risk premium and expected depreciation. Two, risk premium
4 No distinction is made here between estimates of (3) and (4). For industrialized countries, the series for
interest differentials and forward premia are so highly correlated that estimates from the two specifications
are similar.