I. INTRODUCTIONTHE COMMENTARY on mutual fund behavior during the last half of the past decade has shown rather consistent concern over a shift toward speculative investment policies. The evidence that such a shift actually took place is normally expressed in at least two rather subjective measures:(1) The dramatic increase in portfolio turnover by mutual funds1 relative to the turnover in the early 1960's as well as relative to the contemporary turnover in the securities market generally, and(2) The rise of mutual fund investment in letter stock and small, less seasoned corporations generally.Concern over this shift in behavior stems from the risk which attended the apparently new disposition of fund managers to strive for quick gains from short-term, extrinsic increases in the price-earnings ratios of securities. The risk derives from the vulnerability of such securities to a severe fall in price which may result from a loss of institutional partisanship or a downturn in market prices generally. The instinctive characterization of an investment policy which favors such securities as speculative seems appropriate. Unfortunately the measures of speculative behavior noted above seem deficient in rigor. This paper will show that an extension of portfolio theory which incorporates the third moment of the distribution of returns from a portfolio is a potentially useful means with which to quantify the speculative risk incurred by managers of mutual funds. The role of the third moment in investors' preferences is discussed in Section II. This role is formalized in a general portfolio analysis framework in Section III and the relevant measure of speculative risk in widely diversified portfolios is developed. It is found that this measure approximates the measure developed by Jean [6] in an equilibrium capital market model. Finally, the investment behavior of 92 mutual funds vis a vis parameters which quantify speculative risk and the more familiar variability risk during 1961-70 is examined in Section IV.
II. THE ROLE OF SPECULATIVERISK Markowitz [9] formally associated the notion of speculative behavior with the third moment or skewness of portfolio returns in his pioneering work on * University of New Mexico School of Business and Administrative Sciences. I owe an intellectual debt to William H. Jean. In addition, I appreciate the interest in this study shown by
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