Gavin Jones is good at math, but his friends tell him that he doesn't always see the big picture. Right now, Gavin is thinking about investing in a mutual fund. This fund invests 40% of its funds at the risk-free rate of 6% and the remaining 60% in a widely diversified portfolio that closely approximates the market portfolio, which has an expected rate of return equal to 15% One share of the mutual fund represents $1000 of assets in the fund. Having just studied both CAPM pricing formulas, Gavin wants to apply them to double-check the value of a share. Denote by Q the value of the fund in 1 year. (Keep 2 decimal places to your answers, e.g. xxx.12.) 1. Evaluate E(Q), the expected value of a share after 1 year. 2. Suppose the price of a share is indeed equal to the value of the funds it represents. Calculate the beta of the fund, and by making use of the certainty equivalent form of the pricing equation, calculate cov(Q, nd in terms of M2. Beta ; cov(Q, rM)- OM 3. Prove to Gavin Jones that the results he obtained were not accidents. Specifically, for a fund with return arf+ (1 - a) r, show that both CAPM pricing formulas give the price of $1000 worth of fund assets as $1000. (No need to key in here.)