Most investors believe that a long position implies a positive expected excess return and that the larger the position, the larger is the implied view. As we shall see here, that is not necessarily the case; the implied view may not even have the same sign as the position. With the commodity position at 5 percent and the domestic equity position unchanged, the portfolio volatility drops to 9.76 percent. The marginal contributions to portfolio risk, A^ and Ae, become .149 and -.032, respectively. The marginal contribution of domestic equity has declined while the marginal contribution for commodities remains negative, but has increased closer to zero. Consider the new implied view for commodities, the value of e such that: ( 149^ -------- er - .055 = 0 to 26) v-.032j c [ ' -4.65 ec-.055 =0 (2.27) ec = -1.18% (2.28) Here we see a truly counterintuitive result. Despite our positive holding of a significant 5 percent of the portfolio weight in the volatile commodities asset class, the implied view for commodities is a negative expected excess return. Perhaps one might at this point jump to the conclusion that this counterintuitive sign reversal will always be the case when the correlations between two assets are negative. However, that is not so. Let us see what happens when we further increase the size of the commodity position from 5 percent to 15 percent of the portfolio. The volatility of the portfolio remains unchanged at 9.76 percent. The portfolio volatility is minimized at 9.68 when there is a 10 percent weight in commodities. At 15 percent commodities the volatility is increasing as more commodities are added. The marginal contributions to portfolio risk, Ad and Ac, are now .139 and .032, respectively. The contribution of domestic equity continues to decline while the marginal contribution for commodities has increased from a negative value to a positive value. The new hurdle rate for commodities is given by the expected excess return, ec, such that: '.139^ .032 e -.055 = 0 (2.29) 4.35 -ec-.055 =0 (2.30) ec = 1.26% (2.31) Clearly at 15 perceent of portfolio weight, the hurdle rate on commodities has become positive. As the weight on commodities increased from 5 percent to 15 percent the impact on the portfolio changed from being a diversifier to being a source of risk. In fact, there is a weight in commodities for which the portfolio volatility is minimized. This risk-minimizing value for commodities, holding all other assets