offers an expected rate of return of 20%, with a standard deviation of 15%. Gold has an expected rate of return of 6%, with a standard deviation of 17%. In view of the markets higher expected return and lower uncertainty, will anyone choose to hold gold in a portfolio?   To quantify the hedging or diversification potential of an asset, we use the concepts of covariance and correlation. The covariance measures how much the returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means that they vary inversely, as in the case of Best and SugarKane. To measure covariance, we look at return "surprises," or deviations from expected value, in each scenario. Consider the product of each stocks deviation from expected re- turn in a particular scenario:   [rBest E(rBest)][rKane E(rKane)]   This product will be positive if the returns of the two stocks move together, that is, if both returns exceed their expectations or both fall short of those expectations in the sce- nario in question. On the other hand, if one stocks return exceeds its expected value when the others falls short, the product will be negative. Thus a good measure of the degree to which the returns move together is the expected value of this product across all scenarios, which is defined as the covariance:   Cov(rBest, rKane) Pr(s)[rBest(s) E(rBest)][rKane(s) E(rKane)] (6.4) s In this example, with E(rBest) 10.5% and E(rKane) 6%, and with returns in each scenario summarized in the next table, we compute the covariance by applying equation 6.4. The co- variance between the two stocks is   Cov(rBest, rKane) .5(25 10.5)(1 6) .3(10 10.5)( 5 6) .2( 25 10.5)(35 6) 240.5   The negative covariance confirms the hedging quality of SugarKane stock relative to Best Candy. SugarKanes returns move inversely with Bests. II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           166 PART II Portfolio Theory       Normal Year for Sugar Abnormal Year