QUESTION 3 a. Show that if the CAPM holds, then a randomly chosen portfolio will have a negative Fama measure. [5 marks] b. A manager buys four shares of stock today and then sells one of those shares each year for the next four years. His actions and price history are summarized below. The stock pays no dividends. Time Price Action Buy 4 Shares 0 100 1 110 Sell 1 Share 2 112 Sell 1 Share 3 100 Sell 1 Share 4 100 Sell 1 Share Required: i. Calculate the time-weighted geometric average return for the manager. [4 marks] ii. Calculate the time-weighted arithmetic average return for the manager. [4 marks] iii. Explain if you would expect the dollar-weighted (geometric) average would be higher or lower than the time-weighted geometric average? (Do not have to calculate the dollar-weighted average.) [3 marks] c. A portfolio P is invested in two assets A and B and the market portfolio M. The diversifiable components of A and B are uncorrelated with each other. Over the last year, you have the following statistics, where T denotes T-bills in which the portfolio was not invested: A B M T Return 10.0% 8.0% 9.0% 3.0% Beta 0.80 1.20 1.00 Standard Deviation 12.0% 15.0% 10.0% Portfolio weight 20.0% 10.0% 70.0% Required: i. Compute the Jensen measure for each asset and for the portfolio as a whole. [3 marks] ii. Calculate the idiosyncratic standard deviation for both A and B. [4 marks] iii. Calculate the portfolio's beta, total standard deviation and idiosyncratic standard deviation. [6 marks]