Suppose that Karen, a risk-averse investor, has $1,500 to invest and is considering investing in the shares of firm XYZ, currently trading for $12. Assume that Karen assesses a 0.78 probability that the shares will increase in market value to $15 over the coming period and a 0.22 probability that they will decrease to $11. Assume also that XYZ will pay a dividend of $2 per share at the end of the period. Karens utility function is given by: (a) 2 - Where: is the expected rate of return on the investment and its variance. a) Compute Karens expected utility if she decides to invest $1,500 in XYZ. Show your computations (Keep 5 decimal points in your computations). Assume that Karen wants to diversify her portfolio and is considering investing in a Dow Jones Industrial Average Index. She assesses a 0.70 probability that the index will increase by 8% for the coming period and a 0.3 probability that it will increase by 2% b) Compute Karens expected utility if she decides to invest $1,500 in the Dow Jones Industrial Average Index. Show your computations (Keep 5 decimal points in your computations). Before making the final decision, Karen wants to assess the riskiness of XYZ by computing its eta coefficient. For that purpose, she uses the return of the Dow Jones Industrial Average Index as a proxy for the market portfolio. Karen assumes the following conditional payoff probabilities of security XYZ and the Dow Jones Index: When the return on the Dow Jones Index (market portfolio - M) is high: Probability that the return on XYZ is high = 0.75 Probability that the return on XYZ is low = 0.25 When return on the Dow Jones Index (market portfolio - M) is low: Probability that the return on XYZ is high = 0.25 Probability that the return on XYZ is low = 0.75 c) Compute the eta coefficients for XYZ and briefly comment on the result. Show your computations (Keep 5 decimal points in your computations).