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Using Four-Moment Tail Risk to Examine Financial and Commodity Instrument Diversification


  • The authors would like to thank Robert Webb and participants of the 2007 China International Conference in Finance in Chengdu, China; Jukka Sihvonen and participants of the 2007 Midwest Finance Association meetings in Minneapolis; participants of the 2007 Financial Management Meetings in Orlando; and a referee of this journal, for their comments and suggestions. We would especially like to thank Lou Ederington, who made a number of important suggestions that significantly improved the focus of this paper.

Corresponding author: Chapman Graduate School of Business, Department of Finance RB206, Florida International University, Miami, FL 33199; Phone: (305) 348-3325; Fax: (305) 348-4245; E-mail:

Mailing Address: Department of Finance and Economics, 601 University Dr., San Marcos, TX, 78666. Phone: 512-245-3215;


We consider the effect of higher moments on diversification, since most assets possess a potential for tail losses. In particular, we examine higher-moment Value-at-Risk measures for individual instruments and diversified portfolios. We find that a naïve futures portfolio is consistently superior to common stock indexes. As few as ten randomly chosen instruments diversify away 85% of the unsystematic four-moment tail risk. We also compare the two- and four-moment tail risks for different size portfolios. Finally, the tail risk for naïve portfolios varies much less over time than other portfolios.