Suppose that Lore, a risk-averse investor, has $1,100 to invest and is considering investing in the shares of firm Kappa, currently trading for $11. Assume that Lore assesses a 0.75 probability that the shares will increase in market value to $13 over the coming period and a 0.25 probability that they will decrease to $9. Assume also that Kappa will pay a dividend of $1 per share at the end of the period. Lore's utility function is given by: U(a)= Xa- o Where: xa is the expected rate of return on the investment and on its variance. a) Compute Lore's expected utility if she decides to invest $1,100 in Kappa. Show your computations (Keep 5 decimal points in your computations). Assume that Lore wants to diversify her portfolio and is considering investing in a Dow Jones Industrial Average Index. She assesses a 0.80 probability that the index will increase by 7% for the coming period and a 0.2 probability that it will increase by 3% b) Compute Lore's expected utility if she decides to invest $1,100 in the Dow Jones Industrial Average Index. Show your computations (Keep 5 decimal points in your computations). Before making the final investment decision, Lore wants to assess the riskiness of Kappa by computing its Beta coefficient. For that purpose, she uses the return of the Dow Jones Industrial Average Index as a proxy for the market portfolio. Lore assumes the following conditional payoff probabilities of security Kappa and the Dow Jones Index: When return on the Dow Jones Index (market portfolio - M) is high: Probability that the return on Kappa is high = 0.83 Probability that the return on Kappa is low = 0.17 When return on the Dow Jones Index (market portfolio - M) is low: Probability that the return on Kappa is high = 0.17 Probability that the return on Kappa is low = 0.83 c) Compute the Beta coefficients for Kappa and briefly comment on the result. Show your computations (Keep 5 decimal points in your computations). Suppose that Lore, a risk-averse investor, has $1,100 to invest and is considering investing in the shares of firm Kappa, currently trading for $11. Assume that Lore assesses a 0.75 probability that the shares will increase in market value to $13 over the coming period and a 0.25 probability that they will decrease to $9. Assume also that Kappa will pay a dividend of $1 per share at the end of the period. Lore's utility function is given by: U(a)= Xa- o Where: xa is the expected rate of return on the investment and on its variance. a) Compute Lore's expected utility if she decides to invest $1,100 in Kappa. Show your computations (Keep 5 decimal points in your computations). Assume that Lore wants to diversify her portfolio and is considering investing in a Dow Jones Industrial Average Index. She assesses a 0.80 probability that the index will increase by 7% for the coming period and a 0.2 probability that it will increase by 3% b) Compute Lore's expected utility if she decides to invest $1,100 in the Dow Jones Industrial Average Index. Show your computations (Keep 5 decimal points in your computations). Before making the final investment decision, Lore wants to assess the riskiness of Kappa by computing its Beta coefficient. For that purpose, she uses the return of the Dow Jones Industrial Average Index as a proxy for the market portfolio. Lore assumes the following conditional payoff probabilities of security Kappa and the Dow Jones Index: When return on the Dow Jones Index (market portfolio - M) is high: Probability that the return on Kappa is high = 0.83 Probability that the return on Kappa is low = 0.17 When return on the Dow Jones Index (market portfolio - M) is low: Probability that the return on Kappa is high = 0.17 Probability that the return on Kappa is low = 0.83 c) Compute the Beta coefficients for Kappa and briefly comment on the result. Show your computations (Keep 5 decimal points in your computations)
