Higher order moment risk in efficient futures portfolios

Abstract This study examined whether mean–variance (M–V) framework helps to efficiently diversify away tail risk due to skewness, kurtosis, and other higher moments. We found that M–V efficient portfolios do not have significant higher moment risk, because the risk measured by the two-moment value-at-risk (VaR) was not significantly different from risk measured by the higher moment VaRs. This result was not caused by the large number of assets included in the portfolio. With only nine assets in the M–V portfolio, about 85% of the diversifiable loss measured by higher moment VaR was diversified away. Furthermore, with less than nine assets in M–V efficient portfolios, the M–V technique diversified away the higher moment risk even more efficiently than did volatility.

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