CHAPTER 9: THE CAPITAL ASSET PRICING MODEL1. c.2. d.From CAPM, the fair expected return = 8 + 1.25158 = 16.75% Actually expected return = 17%= 1716.75 = 0.25%3. Since the stock s beta is equal to 1.2, its expected rate of return is: 6 + 1.216 6 = 18%9-10E rD 1P1P0P06P1500.1850P1$534. The series of $1,000 payments is a perpetuity. If beta is 0.5, the cash flow should be discounted at the rate:6 + 0.516 6 = 11%PV = $1,000/0.11 = $9,090.91If, however, beta is equal to 1, then the investment should yield 16%, and the price paid for the firm should be:PV = $1,000/0.16 = $6,250The difference, $2,840.91, is the amount you will overpay if you erroneously assume that beta is 0.5 rather than 1.5.Using the SML: 4 = 6 +16 6= 2/10 = 0.26. a.7. ErP = rf +P Er M rf 18 = 6 +P14 6P = 12/8 = 1.58. a.False.= 0 implies Er = rf , not zero.b. False. Investors require a risk premium only for bearing systematic undiversifiable or market risk. Total volatility includes diversifiable risk.c. False. Your portfolio should be invested 75% in the market portfolio and 25% in T-bills. Then:P = 0.751 + 0.250 = 0.759. Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower than the expected return for Portfolio B. Thus, these two portfolios cannot exist in equilibrium.10. Possible. If the CAPM is valid, the expected rate of return compensates only for systematic market risk, represented by beta, rather than for the standard deviation,which includes nonsystematic risk. Thus, Portfolio A s lower rate of return can be paired with a higher standard deviation, as long as A s beta is less than B s.11. Not possible. The reward-to-variability ratio for Portfolio A is better than that ofthe market. This scenario is impossible according to the CAPM because the CAPM predicts that the market is the most efficient portfolio. Using the numbers supplied:S1610121810ASM240.50.33Portfolio A provides a better risk-reward tradeoff than the market portfolio.12. Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A has both a lower standard deviation and a higher expected return.13. Not possible. The SML for this scenario is: Er = 10 + 18 10 Portfolios with beta equal to 1.5 have an expected return equal to:Er = 10 + 1.518 10 = 22%The expected return for Portfolio A is 16%; that is, Portfolio A plots below the SML A = 6%, and hence, is an overpriced portfolio. This is inconsistent with the CAPM.14. Not possible. The SML is the same as in Problem 1.3 Here, Portfolio A s required return is: 10 + 0.98 = 17.2%This is greater than 16%. Portfolio A is overpriced with a negative alpha:A = 1.2%15. Possible. The CML is the same as in Problem 11. Portfolio A plots below the CML, as any asset is expected to. This scenario is not inconsistent with the CAPM.16. If the security s correlation coefficient with the market portfolio doubles with all other variables such as variances unchanged, then beta, and therefore the risk premium, will also double. The current risk premium is: 14 6 = 8%The new risk premium would be 16%, and the new discount rate for the securitywould be: 16 + 6 = 22%If the stock pays a constant perpetual dividend, then we know from the original data that the dividend D must satisfy the equation for the present value of a perpetuity:Price = Dividend/Discount rate50 = D/0.14D = 500.14 = $7.00At the new discount rate of 22%, the stock would be worth: $7/0.22 = $31.82 The increase in stock risk has lowered its value by 36.36%.17. d.18. a.Since the market portfolio, by definition, has a beta of 1, its expected rate of return is 12%.b.= 0 means no systematic risk. Hence, the stock s expected rate of return in market equilibrium is the risk-free rate, 5%.c.Using the SML, the fair expected rate of return for a stock with= 0.5 is: Er = 5 + 0.512 5 = 1.5%The actually expected rate of return, using the expected price and dividend for next year is:Er = $41 + $1/40 1 = 0.10 = 10%Because the actually expected return exceeds the fair return, the stock is underpriced.19.a.ErP = rf +P Er M rf = 5% + 0.8 15% - 5% = 13%= 14%13% = 1%You should invest in this fund because alpha is positive.b. The passive portfolio with the same beta as the fund should be invested 80% in the market-index portfolio and 20% in the money market account. For this portfolio:ErP = 0.815% + 0.25% = 13%14% - 13% = 1% =20. d.You need to know the risk-free rate21. d.You need to know the risk-free rate22. a.Expected ReturnAlphaStock X5% + 0.814%5% = 12.2%14.0%12.2% = 1.8%Stock Y5% + 1.