Suppose that Lore, a risk-averse investor, has $1,500 to invest and is considering investing in the shares of firm Kappa, currently trading for $12. Assume that Lore assesses a 0.78 probability that the shares will increase in market value to $14 over the coming period and a 0.22 probability that they will decrease to $11. Assume also that Kappa will pay a dividend of $2 per share at the end of the period. Lore's utility function is given by: Ui(a)=2xaa2 Where: xa is the expected rate of return on the investment and a2 its variance. a) Compute Lore's utility if she decides to invest $1,500 in Kappa. Show your computations (keep 5 decimal points in your computations). Assume that Lore wants to diversify her portfolio and is considering thvesting in a S\&P Composite Index fund. She assesses a 0.85 probability that the fund will increase by 8% for the coming period and a 0.15 probability that it will increase by 3% b) Compute Lore's utility if she decides to invest $1,500 in the Composite Index fund. 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 S\&P Composite Index fund as a market portfolio. Lore assumes the following conditional payoff probabilities of security Kappa and the S\&P Index: When return on the S\&P Composite Index (market portfolio - M) is high: Probability that the return on Kappa is high =0.75 Probability that the return on Kappa is low =0.25 When return on the S\&P Composite Index (market portfolio - M ) is low: Probability that the retum on Kappa is high =0.25 Probability that the return on Kappa is low =0.75 c) Compute the Beta coefficients for Kappa and briefly comment on the result. Show your computations (keep 5 decimal points in your computations)