Optimal Hedge Fund Allocations: Do Higher Moments Matter?

Revere Street Working Paper No. 272-13

23 Pages Posted: 10 Sep 2004

See all articles by Jan-Hein Cremers

Jan-Hein Cremers

State Street Associates

Mark Kritzman

Windham Capital Management

Sebastien Page

State Street Associates

Date Written: September 3, 2004

Abstract

Hedge funds have return peculiarities not commonly associated with traditional investment vehicles. Specifically, hedge funds seem more inclined to produce return distributions with significantly non-normal skewness and kurtosis. There is also growing acceptance of the notion that investor preferences are better represented by bilinear utility functions or S-shaped value functions than by neo-classical utility functions such as power utility. Many investors have therefore concluded that mean-variance optimization is not appropriate for forming portfolios that include hedge funds.

We apply both mean-variance optimization and full-scale optimization to form portfolios of hedge funds, given a wide range of assumptions about investor preferences. We find that higher moments of hedge funds do not meaningfully compromise the efficacy of mean-variance optimization if investors have power utility. We also find, however, that mean-variance optimization is not particularly effective for identifying optimal hedge fund allocations if preferences are bilinear or S-shaped. Finally, we show that investors with bilinear utility dislike kurtosis and that, contrary to conventional wisdom, investors with S-shaped preferences are attracted to kurtosis as well as negative skewness. Mean-variance optimization is insensitive to these preferences.

Keywords: Hedge fund, hedge funds, optimization, portfolio, optimisation, skewness, kurtosis, higher moments, mean-variance, Markowitz, utility, behavioral finance, prospect theory, s-shaped, bilinear utility, convertible arbitrage, event driven, merger arbitrage, equity hedge, full-scale optimization, risk

Suggested Citation

Cremers, Jan-Hein and Kritzman, Mark and Page, Sebastien, Optimal Hedge Fund Allocations: Do Higher Moments Matter? (September 3, 2004). Revere Street Working Paper No. 272-13, Available at SSRN: https://ssrn.com/abstract=587384 or http://dx.doi.org/10.2139/ssrn.587384

Jan-Hein Cremers

State Street Associates ( email )

138 Mount Auburn Street
Cambridge, MA 02138
United States

Mark Kritzman

Windham Capital Management ( email )

5 Revere Street
Cambridge, MA 02138
United States
617-576-7360 (Phone)
617-576-7359 (Fax)

Sebastien Page (Contact Author)

State Street Associates ( email )

138 Mount Auburn Street
Cambridge, MA 02138
United States
617-234-9462 (Phone)
617-234-9478 (Fax)

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