This paper examines the impact of co-kurtosis on asset pricing using a four-moment capital asset pricing model. It is shown that, in the presence of skewness and kurtosis in asset return distribution, the expected excess rate of return is related not only to the systematic variance but also to the systematic skewness and systematic kurtosis. Investors are compensated in higher expected return for bearing the systematic variance and the systematic kurtosis risks. Investors also forego the expected excess return for taking the benefit of increasing the systematic skewness. IntroductionEmpirical and theoretical attacks on the meanvariance capital market theory have given impetus to the investigation of moments of higher order than the variance of returns. The third moment (skewness) and its effect on asset pricing have been explored by numerous studies. Ingersoll [19], Kraus and Litzenberger 1211, Rubinstein [26], and Sears and Wei [29] extend the Capital Asset Pricing Model (CAPM) to incorporate the effect of skewness on the asset valuation. Empirical studies by Barone-Adesi [6], Friend and Westerfield [ E l , Lim [23], Sears and Wei [30], and Singleton and Wingender [31] provide a mixed result of the effect of skewness on the equilibrium asset pricing. In contrast,

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Hsing Fangedging effectiveness is measured to determine the effectiveness of adding a given H futures contract to a hedger's cash portfolio. It is determined by comparing the combined futures-cash position with the cash position alone according to certain criteria. The traditional measure developed by Johnson (1960) and Ederington (1979) has the single objective of minimizing a hedger's risk, which is proper when risk-reduction is his only concern. A second measure pioneered by Howard and D'Antonio (HD) (1984, 1987), and Chang and Shanker (CS) (1987) has the objective of maximizing a hedger's risk-return tradeoff, which is proper when both risk and return are important.' These two measures have been tested empirically by Shanker (1986), Chen, Sears, andTzang (1987), D'Antonio (1986), and Overdahl and Starleaf (1986).These hedging effectiveness measures suffer from a major deficiency: they are derived in a one-period setting. This setting imposes rather restrictive conditions on a hedger's behavior. For example, a hedger is assumed to ignore any new information and, therefore, adjusts neither consumption behavior nor hedging positions to his changing consumptiodinvestment opportunity set during the hedge period. This is inconsistent with evidence in the literature which suggests that an optimum hedge ratio should be time-varying, and tends to be unstable when the market is volatile.' These hedging effectiveness measures are accurate only when the market is stable and tend to be noticeably biased when applied to recent market data. This bias problem, however, can be corrected using an intertemporal measure of hedging effectiveness.The authors would like to thank two anonymous reviewers of the journal and the editor, Mark J. Powers, for very constructive comments.'Strictly speaking, the HDICS measures assume a given long-spot position. In contrast, Levy (1987) derives an alternative measure with a variable spot position. However, as shown in Chang and Shanker (1986). the HDlCS measures can be easily modified to a variable spot position with short-sale constraints, margin requirements, and other transaction costs. Gjerde (1987) also has derived alternative risk-return hedging effectiveness measures that assume a hedger's loss function is based upon dollar-return but not percentage returns. For a discussion of alternative performance models, see Yau, Savanayana, and Schneeweis (1988).'For empirical investigations of the properties of the time-varying hedge ratio, see Lee, Bubnys, andLin (1986), andGrammatikos andSaunders (1983). For the derivation of a stochastic hedge ratio, see Geske and Pieptea (1987). Evidence of this is also seen in the daily movements of trading volume. Initial low volume of a futures contract tends to rise over time, reaches a peak near the contract's termination, and drops off as its maturity nears. 'Fortin and Khoury (1988) derived an intertemporal measure of hedging effectiveness based upon a constant consumptionlinvestment opportunity set. Thus, their measure suffers from the bias prob...

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