risk return and the three-moment capital asset pricing model - another look

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Journal of Banking and Finance I5 (1991) 449-460. North-Holland Risk return and the three-moment capital asset pricing model: Another loo k Kai-Jiaw Tan* Unicersir , of Alabama in Huntscille Huntsville .4 L 35899. USA Received March 1990, linal version received September 1990 Most studies on three-moment capital asset pricing models have found a strong and consistent relationship between an asset’s returns and its higher statistical moments. Other studies report results which are opposite to what the theory would suggest. This paper re-examines the empirical evidence of the three-moment capital asset pricing model on 43 randomly selected mutual funds from 1970-1986. The results indicate that trade-offs of risks for returns on the selected mutual funds are less than predicted and inconsistent. 1. Introduction One o f the research areas of the multidimensional capital asset pricing model and p ortfolio theory is the relationship between a portfolio’s returns and its higher statistical moments. The importance of higher moments in investor’s utility function is evidenced in papers by Jean (1971, 1973), Ingersoll (19754 S cott and Horvath (1980) and Kane (1982) . Some empirical tests of these hypothesized relationships between a portfolio’s return and its third statis tical moments have been conducted by Arditti (1971), Francis (1975), Le vy and Sarnat (1972), Kraus and Litzenberger (KC % ) (1976) and Friend and Westerfield (F&W) (1980), among others. Most of their findings tend to support the theoretical relationship between the first three statistical moments. That is, in order to maximize the expected utility of portfolio return, risk-averters would prefer higher expected return to smaller, smaller variance to larger, and higher (and p ositive) third statist ical moment about the mean to lower (and negative), other things being constant. Accordingly, they are willing to accept a lower expected rate of return or to take a higher variability risk for a higher positive skewness if the market is also positively skewed. In a recent study, F&W (1980) have p rovided some, but not conclusive, evidence to support the importance of skewness in the pricing of risky assets. *The author wishes to thank an anonymous referee for his helpful comments. 037&i266/91/$03.50 Q 1991-Elsevier Science Publishers B.V. (North-Holland)

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