发布时间 : 星期日 文章投资学第10版习题答案09更新完毕开始阅读210d7f9f551810a6f524867d
Chapter 9 - The Capital Asset Pricing Model
PROBLEM SETS
1. E(rP)?rf?βP?[E(rM)?rf] .12 .18?.06?βP?[.14?.06]?βP??1.5.08
2. 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 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%. a. b.
False. β = 0 implies E(r) = rf , not zero.
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
3.
4.
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:βP?(0.75?1)?(0.25?0)?0.75
The expected return is the return predicted by the CAPM for a given level of systematic risk.
E(ri)?rf?βi?[E(rM)?rf]
E(r$1Discount)?.04?1.5?(.10?.04)?.13,or 13% E(rEverything$5)?.04?1.0?(.10?.04)?.10,or 10%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
5.
According to the CAPM, $1 Discount Stores requires a return of 13% based on its systematic risk level of β = 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 β = 1.0. However, the forecasted return is 11%. Therefore, the security is currently undervalued.
Correct answer is choice a. The expected return of a stock with a β = 1.0 must, on average, be the same as the expected return of the market which also has a β = 1.0. 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 Kaskin’s stock than for Quinn’s stock. The appropriate discount rate for the project is:
rf + β × [E(rM ) – rf ] = .08 + [1.8 ? (.16 – .08)] = .224, or 22.4% Using this discount rate:
NPV??$40??$15??$40?[$15?Annuity factor (22.4%, 10 years)] = $18.09 t1.224t?110
6. 7.
8.
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 + β × (.16 – .08) ? β = .2773/.08 = 3.47
9.
a.
Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the stock’s return to the market return, i.e., the change in the stock return per unit change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return:
βA??.02?.38?2.00.05?.25βD?.06?.12?0.30
.05?.25
9-2
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
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 βM = 1, and rf = 6% (which has βf = 0). See the following graph:
Expected Return - Beta Relationship 40 35 SML Expected Return 30 25 20 15 10 5 0 0 0.5 1 1.5 Beta 2 2.5 3 ? A D M A The equation for the security market line is:
E(r) = .06 + β × (.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 analyst’s forecast of expected return is only 18%. Thus the stock’s alpha is:
αA = 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 analyst’s forecast of expected return for D is 9%, and hence, the stock has a positive alpha:
9-3
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
αD = Actually expected return – Required return (given risk)
= .09 – .087 = +0.003 = +0.3%
e.
The points for each stock plot on the graph as indicated above.
The hurdle rate is determined by the project beta (0.3), not the firm’s beta. The correct discount rate is 8.7%, the fair rate of return for stock D.
10. 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.
11. 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.
12. Not possible. The reward-to-variability ratio for Portfolio A is better than that of the
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:
SA?.16?.10?0.5.12SM?.18?.10?0.33 .24Portfolio A provides a better risk-reward trade-off than the market portfolio.
13. Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A has
both a lower standard deviation and a higher expected return.
14. Not possible. The SML for this scenario is: E(r) = 10 + β × (18 – 10)
Portfolios with beta equal to 1.5 have an expected return equal to:
E(r) = 10 + [1.5 × (18 – 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.
15. Not possible. The SML is the same as in Problem 14. Here, Portfolio A’s required
return is: .10 + (.9 × .08) = 17.2%
9-4
Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.