Chapter 10: Return and Risk: The Capital-Asset-Pricing Model (CAPM)
Answers to suggested problems
10.1a.= 0.1 (– 4.5%) + 0.2 (4.4%) + 0.5 (12.0%) + 0.2 (20.7%)
= 10.57%
b.2= 0.1 (–0.045 – 0.1057)2 + 0.2 (0.044 – 0.1057)2 + 0.5 (0.12 – 0.1057)2
+ 0.2 (0.207 – 0.1057)2
= 0.0052
= (0.0052)1/2 = 0.072 = 7.20%
10.3a.= 0.25 (–2.0) + 0.60 (9.2) + 0.15 (15.4)
= 7.33%
= 0.25 (5.0) + 0.60 (6.2) + 0.15 (7.4)
= 6.08%
b.HB2= 0.25 (– 0.02 – 0.0733)2 + 0.60 (0.092 – 0.0733)2
+ 0.15 (0.154 – 0.0733)2
= 0.003363
HB= (0.003363)1/2 = 0.05799 = 5.80%
SB2= 0.25 (0.05 – 0.0608)2 + 0.60 (0.062 – 0.0608)2
+ 0.15 (0.074 – 0.0608)2
= 0.000056
SB= (0.000056)1/2 = 0.00749 = 0.75%
c.Cov (RHB, RSB)
= 0.25 (– 0.02 – 0.0733) (0.05 – 0.0608)
+ 0.60 (0.092 – 0.0733) (0.062 – 0.0608)
+ 0.15 (0.154 – 0.0733) (0.074 – 0.0608)
= 0.000425286
Corr (RHB, RSB)
= 0.000425286 / (0.058 0.0075)
= 0.977
10.9a.= 0.3 (0.10) + 0.7 (0.20) = 0.17 = 17.0%
P 2= 0.32 (0.05)2 + 0.72 (0.15)2 = 0.01125
P= (0.01125)1/2 = 0.10607 = 10.61%
b.= 0.9 (0.10) + 0.1 (0.20) = 0.11 = 11.0%
P 2= 0.92 (0.05)2 + 0.12 (0.15)2 = 0.00225
P= (0.00225)1/2 = 0.04743 = 4.74%
c.No, I would not hold 100% of stock A because the portfolio in b has higher expected return but less standard deviation than stock A.
I may or may not hold 100% of stock B, depending on my preference for risk.
10.10If all the weights in the weighted average are positive, the expected return on any portfolio must be less than or equal to the return on the stockwith the highest return. It cannot be greater than this stock’s return because all stocks with lower returns will pull down the value of the weighted average expected return.
Similarly, the expected return on any portfolio must be greater than or equal to the return of the asset with the lowest return. The portfolio return cannot be less than the lowest return in the portfolio because all higher earning stocks will pull up the value of the weighted average.
10.12The wide fluctuations in the price of oil stocks do not indicate that oil is a poor investment. If oil is purchased as part of a portfolio, what matters is only its beta. Since price volatility captures beta plus idiosyncratic risks, observing price volatility is not an adequate measure of the appropriateness of adding oil to a portfolio. Remember that total variability should not be used when deciding whether or not to put an asset into a large portfolio.
10.16The statement is false. Once the stock is part of a well-diversified portfolio, the important factor is the contribution of the stock to the variance of the return of the portfolio. In a well-diversified portfolio, this contribution is the covariance of the return on the stockwith the returns generated by the rest of the portfolio.
10.19The slope of the capital market line is
( - Rf) / M = (12 - 5) / 10 = 0.7
a. = 5 + 0.7 (7) = 9.9%
b.rearrange the equation in part a: P = ( - Rf) / 0.7 = (20% - 5%) / 0.7 = 21.4%
10.21Polonius’ portfolio will be the market portfolio. He will have no borrowing or lending in his portfolio, only stocks.
10.29
a.
- According to the security market line drawn in part a, a security with a beta of 0.80 should have an expected return of:
E(r)= rf + (EMRP)
= 0.07 + 0.8(0.05)
= 0.11
= 11%
Since this asset has an expected return of only 9%, it lies belowthe security market line. Because the asset lies below the security market line, it is overpriced. Investors will sell the overpriced security until its price falls sufficiently so that its expected return rises to 11%.
- According to the security market line drawn in part a, a security with a beta of 3 should have an expected return of:
E(r)= rf + (EMRP)
= 0.07 + 3(0.05)
= 0.22
= 22%
Since this asset has an expected return of 25%, it lies abovethe security market line. Because the asset lies above the security market line, it is underpriced. Investors will buy the underpriced security until its price rises sufficiently so that its expected return falls to 22%.