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.