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University of California, San Diego, and the IMF, respectively. We would like to thank Peter Wickham and Blair Rourke for encouragement and advice. Raja Hettiarachchi and Huyen Le provided excellent research assistance.
The notion of risk premium was apparently first advanced by Keynes even earlier in an article in the Manchester Guardian Commercial in 1923. It gradually developed into a formal theory with contributions from Kaldor (1938) and Hicks (1946).
Although the information set at t+n is different from that at t, if markets are efficient, on average there is no presumption that Ft+n would exceed, or be less than, Ft.
Since here we are only considering contracts of the same maturity date, in order to simplify the notation, we denote (ft, T) by ft, (ft+n, T) by ft+n and so on.
As Dusak (op.cit.) emphasized, in contrast to the portfolio measure of risk, the Keynesian view would regard the risk of a futures market asset solely with respect to its price variability.
As indicated above, there had been a number of statistical tests of risk premia before this study. These studies, however, had relied on some rather stringent assumptions and used ad hoc methodologies. For an interesting discussion of the studies, see, for instance, Peck (1985).
This situation, termed ‘contango’, is the opposite of ‘normal backwardation’ discussed earlier.
In the latter case, one would view participation in futures markets as assumed by Hardy (op. cit.), that is, being more akin to gambling, which could lead to very different welfare implications from those in which these markets are perceived as means of sharing risk.
Hazuka also imposed the condition that the consumption betas were constant over time.
In foreign currency futures markets, although the random walk hypothesis has usually been rejected, most models of time varying risk premia have met with very limited empirical success. See, for instance, the surveys by Boothe and Longworth (1986), Hodrick (1987) and Meese (1989).
This is the Jarque-Bera test for normality.
This applies only to the one month rate of return. It is not the case for the six-month excess returns because the sampling interval (one month) does not equal the forecasting interval (six months). In the latter case, as Hansen and Hodrick (1980) show, excess returns will be moving averages of the order (k-1) where k is the forecast horizon. To eliminate this source of serial correlation, Table 1 presents the summary statistics using non-overlapping observations. In this case, too, under the null hypothesis of market efficiency excess returns should be serially independent.
As noted above, the errors in equation (8) may not be uncorrelated since the sampling interval does not necessarily equal the forecasting interval.
The critical value, with 42 degrees of freedom, at the 5 and 10 percent significance levels, is 58.1 and 52.3 respectively.
In all the estimations we use only the corresponding basis to model the excess expected return on the benchmark portfolio.