Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           CHAPTER 6 Risk and Risk Aversion 169     Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 70 years has averaged about 8.5% more than the Treasury bill return and that the S&P 500 standard deviation has been about 20% per year. Assume these val- ues are representative of investorsexpectations for future performance and that the current T-bill rate is 5%. Use these values to solve problems 10 to 12. 10. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows:   Wbills Windex   0 1.0 0.2 0.8 0.4 0.6 0.6 0.4 0.8 0.2 1.0 0   11. Calculate the utility levels of each portfolio of problem 10 for an investor with A 3. What do you conclude? 12. Repeat problem 11 for an investor with A 5. What do you conclude?   Reconsider the Best and SugarKane stock market hedging example in the text, but as- sume for questions 13 to 15 that the probability distribution of the rate of return on Sug- arKane stock is as follows:     Bullish Stock Market Bearish Stock Market Sugar Crisis   Probability .5 .3 .2 Rate of return 10% 5% 20%   13. If Humanexs portfolio is half Best stock and half SugarKane, what are its expected re- turn and standard deviation? Calculate the standard deviation from the portfolio returns in each scenario.