Chapter 9 - The Capital Asset Pricing Model 9-1 Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. CHAPTER 9: THE CAPITAL ASSET PRICING MODEL PROBLEM SETS 1. 2. If the securitys 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 security would 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 rate 50 = D/0.14 D = 50 0.14 = $7.00 At 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%. 3. a. False. = 0 implies E(r) = rf , not zero. b.False. Investors require a risk premium only for bearing systematic (undiversifiable or market) risk. Total volatility, as measured by the standard deviation, includes diversifiable risk. c. False. Your portfolio should be invested 75% in the market portfolio and 25% in T-bills. Then:(0.751)(0.250)0.75 P 4. The expected return is the return predicted by the CAPM for a given level of systematic risk. $1 $5 ( ) () ().041.5(.10.04).13,or 13% ().041.0(.10.04).10,or 10% ifiMf Discount Everything E rrE rr E r E r ()() .12 .18.06.14.061.5 .08 PfPMf PP E rrE rr Chapter 9 - The Capital Asset Pricing Model 9-2 Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5. According to the CAPM, $1 Discount Stores requires a return of 13% based on its systematic risk level of = 1.5 . However, the forecasted return is only 12%. Therefore, the security is currently overvalued. Everything $5 requires a return of 10% based on its systematic risk level of = 1.0. However, the forecasted return is 11%. Therefore, the security is currently undervalued. 6. Correct answer is choice a. The expected return of a stock with a = 1.0 must, on average, be the same as the expected return of the market which also has a = 1.0. 7. Correct answer is choice a. Beta is a measure of systematic risk. Since only systematic risk is rewarded, it is safe to conclude that the expected return will be higher for Kaskins stock than for Quinns stock. 8. The appropriate discount rate for the project is: rf + E(rM) rf = .08 + 1.8 (.16 .08) = .224, or 22.4% Using this discount rate: 10 1 $15 NPV$40$40$15 1.224 t t Annuity factor (22.4%, 10 years) = $18.09 The internal rate of return (IRR) for the project is 35.73%. Recall from your introductory finance class that NPV is positive if IRR discount rate (or, equivalently, hurdle rate). The highest value that beta can take before the hurdle rate exceeds the IRR is determined by: .3573 = .08 + (.16 .08) = .2773/.08 = 3.47 9. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the stocks return to the market return, i.e., the change in the stock return per unit change in the market return. Therefore, we compute each stocks beta by calculating the difference in its return across the two scenarios divided by the difference in the market return: .02.38.06.12 2.000.30 .05.25.05.25 AD Chapter 9 - The Capital Asset Pricing Model 9-3 Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. b.With the two scenarios equally likely, the expected return is an average of the two possible outcomes: E(rA) = 0.5 ( .02 + .38) = .18 = 18% E(rD) = 0.5 (.06 + .12) = .09 = 9% c.The SML is determined by the market expected return of 0.5 (.25 + .05) = 15%, with M= 1, and rf = 6% (which has f=0). See the following graph: Expected Return - Beta Relationship 0 5 10 15 20 25 30 35 40 00.511.522.53 Beta E x p e c t e d R e t u r n SML DM A A The equation for the security market line is: E(r) = .06 + (.15 .06) d. Based on its risk, the aggressive stock has a required expected return of: E(rA ) = .06 + 2.0 (.15 .06) = .24 = 24% The analysts forecast of expected return is only 18%. Thus the stocks alpha is: A = actually expected return required return (given risk) = 18% 24% = 6% Similarly, the required return for the defensive stock is: E(rD) = .06 + 0.3 (.15 .06) = 8.7% The analysts forecast of expected return for D is 9%, and hence, the stock has a positive alpha: Chapter 9 - The Capital Asset Pricing Model 9-4 Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D = Actually expected return Required return (given risk) = .09 .087 = +0.003 = +0.3% The