P Problem 2 (10 pts) Suppose that an asset X is purchased at price P at time t = 0 and later sold at price Q at t=1. Then the rate of return is Q-P (1) Notice that since Q is random and unknown at present, we can take expectation on both sides of (1) and have Q-P Q-P Hz = Er:] = E1% ? where Q = E[Q]. (a) Using the security market line of CAPM, show that - 0p, 2) P (3) 1+rf + Bum -rf) where um denotes the mean return rate of the market, ry denotes the risk-free rate, and denotes the the beta of the underlying asset used in CAPM. (Hints: Use SML: H+ = rf + B(m -rf) combine with (2) then solve for P.) (b) Instead of knowing Orm = Cov(r?, M), suppose only oom = Cov(Q, rm) is known, where rm is the return rate of the market portfolio in CAPM. Show that (3) can be written as O - QM (4) 1+1 where MM". (Hints: Recall 8 = Orm/ and try prove Orm=0QM/P using (1).) P= (c) Suppose there is a stock in the market whose price has the following structure after 1 year: $108, with probability 0.7 S(1) = Q = $50, with probability 0.3. Assume further that Cov(Q,"M) = 7, where I'm is the return rate of the market portfolio in CAPM. Assume ry = 0.1, M = 0.2, o=0.09. Using (3) determine the price of this stock at time t = 0. :{ P Problem 2 (10 pts) Suppose that an asset X is purchased at price P at time t = 0 and later sold at price Q at t=1. Then the rate of return is Q-P (1) Notice that since Q is random and unknown at present, we can take expectation on both sides of (1) and have Q-P Q-P Hz = Er:] = E1% ? where Q = E[Q]. (a) Using the security market line of CAPM, show that - 0p, 2) P (3) 1+rf + Bum -rf) where um denotes the mean return rate of the market, ry denotes the risk-free rate, and denotes the the beta of the underlying asset used in CAPM. (Hints: Use SML: H+ = rf + B(m -rf) combine with (2) then solve for P.) (b) Instead of knowing Orm = Cov(r?, M), suppose only oom = Cov(Q, rm) is known, where rm is the return rate of the market portfolio in CAPM. Show that (3) can be written as O - QM (4) 1+1 where MM". (Hints: Recall 8 = Orm/ and try prove Orm=0QM/P using (1).) P= (c) Suppose there is a stock in the market whose price has the following structure after 1 year: $108, with probability 0.7 S(1) = Q = $50, with probability 0.3. Assume further that Cov(Q,"M) = 7, where I'm is the return rate of the market portfolio in CAPM. Assume ry = 0.1, M = 0.2, o=0.09. Using (3) determine the price of this stock at time t = 0. :{