strategy is a powerful alternative to the simple risk- reduction strategy of including a risk-free asset in the portfolio. In later chapters we will see that, in a rational market, hedge assets will offer relatively low expected rates of return. The perfect hedge, an insurance contract, is by design per- fectly negatively correlated with a specified risk. As one would expect in a "no free lunch" world, the insurance premium reduces the portfolios expected rate of return. II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           CHAPTER 6 Risk and Risk Aversion 167       Suppose that the distribution of SugarKane stock were as follows:         CONCEPT C H E C K ☞ QUESTION 6 Bullish Bearish Stock Market Stock Market Sugar Crisis   7% 5% 20%     a. What would be its correlation with Best? b. Is SugarKane stock a useful hedge asset now? c. Calculate the portfolio rate of return in each scenario and the standard deviation of the portfo- lio from the scenario returns. Then evaluate P using rule 5. d. Are the two methods of computing portfolio standard deviations consistent?       SUMMARY 1. Speculation is the undertaking of a risky investment for its risk premium. The risk pre- mium has to be large enough to compensate a risk-averse investor for the risk of the in- vestment. 2. A fair game is a risky prospect that has a zero-risk premium. It will not be undertaken by a risk-averse investor. 3. Investorspreferences toward the expected return and volatility of a portfolio may be ex- pressed by a utility function that is higher for higher expected returns and lower for higher portfolio variances. More risk-averse investors will apply greater penalties for risk. We can describe these preferences graphically using