Chapter 9 - The Capital Asset Pricing Model
This is greater than 16%. Portfolio A is overpriced with a negative alpha: ? A = –1.2%
16. Possible. The CML is the same as in Problem 12. Portfolio A plots below the CML,
as any asset is expected to. This scenario is not inconsistent with the CAPM.
17. Since the stock’s beta is equal to 1.2, its expected rate of return is:
.06 + [1.2 ? (.16 – .06)] = 18%
E(r)?D1?PP?$50?$61?P0?0.18?1?P1?$53 P0$50
18. The series of $1,000 payments is a perpetuity. If beta is 0.5, the cash flow should be
discounted at the rate:
.06 + [0.5 × (.16 – .06)] = .11 = 11% PV = $1,000/0.11 = $9,090.91
If, 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 = $6,250
The difference, $2,840.91, is the amount you will overpay if you erroneously assume that beta is 0.5 rather than 1.
19. Using the SML: .04 = .06 + β × (.16 – .06) ? β = –.02/.10 = –0.2
20. r1 = 19%; r2 = 16%; β1 = 1.5; β2 = 1
a.
To determine which investor was a better selector of individual stocks we look at abnormal return, which is the ex-post alpha; that is, the abnormal return is the difference between the actual return and that predicted by the SML.
Without information about the parameters of this equation (risk-free rate and market rate of return) we cannot determine which investor was more accurate. If rf = 6% and rM = 14%, then (using the notation alpha for the abnormal return):
α1 = .19 – [.06 + 1.5 × (.14 – .06)] = .19 – .18 = 1% α 2 = .16 – [.06 + 1 × (.14 – .06)] = .16 – .14 = 2%
Here, the second investor has the larger abnormal return and thus appears to be the superior stock selector. By making better predictions, the second
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b.
Chapter 9 - The Capital Asset Pricing Model
investor appears to have tilted his portfolio toward underpriced stocks.
c.
If rf = 3% and rM = 15%, then:
α1 = .19 – [.03 + 1.5 × (.15 – .03)] = .19 – .21 = –2% α2 = .16 – [.03+ 1 × (.15 – .03)] = .16 – .15 = 1%
Here, not only does the second investor appear to be the superior stock selector, but the first investor’s predictions appear valueless (or worse). Since the market portfolio, by definition, has a beta of 1, its expected rate of return is 12%.
β = 0 means no systematic risk. Hence, the stock’s expected rate of return in market equilibrium is the risk-free rate, 5%.
Using the SML, the fair expected rate of return for a stock with β = –0.5 is:
E(r)?0.05?[(?0.5)?(0.12?0.05)]?1.5%
21. a.
b.
c.
The actually expected rate of return, using the expected price and dividend for next year is:
E(r)?$41?$3?1?0.10?10% $40Because the actually expected return exceeds the fair return, the stock is underpriced.
22. In the zero-beta CAPM the zero-beta portfolio replaces the risk-free rate, and thus:
E(r) = 8 + 0.6(17 – 8) = 13.4%
23. a.
E(rP) = rf + βP × [E(rM ) – 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:
E(rP) = (0.8 × 15%) + (0.2 × 5%) = 13% 14% ? 13% = 1% = ?
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Chapter 9 - The Capital Asset Pricing Model
24. a.
We would incorporate liquidity into the CCAPM in a manner analogous to the way in which liquidity is incorporated into the conventional CAPM. In the latter case, in addition to the market risk premium, expected return is also dependent on the expected cost of illiquidity and three liquidity-related betas which measure the sensitivity of: (1) the security’s illiquidity to market
illiquidity; (2) the security’s return to market illiquidity; and, (3) the security’s illiquidity to the market return. A similar approach can be used for the CCAPM, except that the liquidity betas would be measured relative to consumption growth rather than the usual market index.
b. As in part (a), nontraded assets would be incorporated into the CCAPM in a
fashion similar to part (a). Replace the market portfolio with consumption growth. The issue of liquidity is more acute with nontraded assets such as privately held businesses and labor income.
While ownership of a privately held business is analogous to ownership of an illiquid stock, expect a greater degree of illiquidity for the typical private business. If the owner of a privately held business is satisfied with the
dividends paid out from the business, then the lack of liquidity is not an issue. If the owner seeks to realize income greater than the business can pay out, then selling ownership, in full or part, typically entails a substantial liquidity discount. The illiquidity correction should be treated as suggested in part (a). The same general considerations apply to labor income, although it is probable that the lack of liquidity for labor income has an even greater impact on security market equilibrium values. Labor income has a major impact on portfolio decisions. While it is possible to borrow against labor income to some degree, and some of the risk associated with labor income can be ameliorated with insurance, it is plausible that the liquidity betas of
consumption streams are quite significant, as the need to borrow against labor income is likely cyclical.
CFA PROBLEMS
1. a. Agree; Regan’s conclusion is correct. By definition, the market portfolio lies on
the capital market line (CML). Under the assumptions of capital market theory, all portfolios on the CML dominate, in a risk-return sense, portfolios that lie on the Markowitz efficient frontier because, given that leverage is allowed, the CML creates a portfolio possibility line that is higher than all points on the efficient frontier except for the market portfolio, which is Rainbow’s portfolio. Because Eagle’s portfolio lies on the Markowitz efficient frontier at a point other than the market portfolio, Rainbow’s portfolio dominates Eagle’s portfolio.
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Chapter 9 - The Capital Asset Pricing Model
b.
Nonsystematic risk is the unique risk of individual stocks in a portfolio that is diversified away by holding a well-diversified portfolio. Total risk is composed of systematic (market) risk and nonsystematic (firm-specific) risk.
Disagree; Wilson’s remark is incorrect. Because both portfolios lie on the
Markowitz efficient frontier, neither Eagle nor Rainbow has any nonsystematic risk. Therefore, nonsystematic risk does not explain the different expected returns. The determining factor is that Rainbow lies on the (straight) line (the CML) connecting the risk-free asset and the market portfolio (Rainbow), at the point of tangency to the Markowitz efficient frontier having the highest return per unit of risk. Wilson’s remark is also countered by the fact that, since nonsystematic risk can be eliminated by diversification, the expected return for bearing
nonsystematic risk is zero. This is a result of the fact that well-diversified
investors bid up the price of every asset to the point where only systematic risk earns a positive return (nonsystematic risk earns no return).
2.
E(r) = rf + β × [E(r M ) ? rf ]
Furhman Labs: E(r) = .05 + 1.5 × [.115 ? .05] = 14.75% Garten Testing: E(r) = .05 + 0.8 × [.115 ? .05] = 10.20%
If the forecast rate of return is less than (greater than) the required rate of return, then the security is overvalued (undervalued).
Furhman Labs: Forecast return – Required return = 13.25% ? 14.75% = ?1.50% Garten Testing: Forecast return – Required return = 11.25% ? 10.20% = 1.05% 3. 4.
Therefore, Furhman Labs is overvalued and Garten Testing is undervalued. a. d.
From CAPM, the fair expected return = 8 + 1.25 × (15 ? 8) = 16.75% Actually expected return = 17% ? = 17 ? 16.75 = 0.25%
5. 6. 7. 8.
d. c. d. d.
[You need to know the risk-free rate]
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