Solution to Homework #5 FIN 3710 “Investment Analysis”
Professor Bin Wei
Problem 1 (BKM, Q3 of Chapter 7) (10 points1) What must be the beta of a portfolio with E( rP ) = 20.0%, if the risk free rate is 5.0% and the expected return of the market is E( rM ) = 15.0%? Answer: We use E( rP ) = β P *(E( rM ) – r f ) + r f . We then have: 0.20 = β P *(0.15-0.05) + 0.05. Solving for the beta we get: β P =1.5.
Problem 2 (BKM, Q4 of Chapter 7) (20 points) The market price of a security is $40. Its expected rate of return is 13%. The risk-free rate is 7%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. Hint: Use zero-growth Dividend Discount Model to calculate the intrinsic value, which is the market price. Answer: First, we need to calculate the original beta before it doubles from the CAPM. Note that: β = (the security’s risk premium)/(the market’s risk premium) = 6/8 = 0.75. Second, when its beta doubles to 2*0.75 = 1.5, then its expected return becomes: 7% + 1.5*8% = 19%. (Alternatively, we can find the expected return after the beta doubles in the following way. If the beta of the security doubles, then so will its risk premium. The current risk premium for the stock is: (13% - 7%) = 6%, so the new risk premium would be 12%, and the new discount rate for the security would be: 12% + 7% = 19%.) Third, we find out the implied constant dividend payment from its current market price of $40. If the stock pays a constant dividend in perpetuity, then we know from the original data that the dividend (D) must satisfy the equation for a perpetuity: Price = Dividend/Discount rate 40 = D/0.13 ⇒ D = 40 * 0.13 = $5.20 Last, at the new discount rate of 19%, the stock would be worth: $5.20/0.19 = $27.37. The increase in stock risk has lowered the value of the stock by 31.58%. Problem 3 (BKM, Q16 of Chapter 7)...
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