威廉夏普 投资学课后习题答案解析第九章

There are ten key assumptions underlying the CAPM:

1. Investors evaluate portfolios by analyzing expected returns and standard

deviations over a one-period time horizon.

2. Everything else equal, investors prefer portfolios with greater expected

returns.

3. Everything else equal, investors prefer portfolios with lower standard

deviations.

4. Assets are infinitely divisible.

5. Investors may borrow or lend at a single riskfree interest rate. 6. Taxes and transaction costs are immaterial.

7. All investors have the same one-period time horizon. 8. All investors borrow and lend at the same riskfree rate.

9. All investors have immediate and costless access to all relevant information. 10. Investors possess homogeneous expectations regarding the expected returns

and risks of securities. The separation theorem states that an investor's optimal risky portfolio can be determined without reference to the investor's risk-return preferences.

Assuming that every investor has the same expectations regarding expected returns and risks for available securities, and assuming that everyone faces the same riskfree rate, then the efficient set must be the same for all investors. This implies that every investor will hold the same risky portfolio. (That risky portfolio is represented by the point of tangency between a ray emanating from the riskfree asset and extending into risk-return space and tangent to the curved Markowitz efficient set.) The only difference in portfolios held by investors will be with respect to the amount of riskfree lending or borrowing undertaken, which will depend on the investors' individual risk-return preferences.

If investors wish to hold more units of a security than are available, then they will bid up the price of the security, thereby reducing its expected return. The lower expected return will cause investors to reduce their desired holdings of the security.

Conversely, if investors wish to hold fewer units of a security than are available, then they will bid down the security's price, thereby increasing its expected return. The higher expected return will cause investors to wish to hold more units of the security.

This process will drive the price of the security toward its equilibrium value at which point the number of units investors wish to hold will equal the number of units outstanding. This equilibrating process will produce market clearing prices for all securities. Further, the riskfree rate will move to a level where the total amount of money borrowed will equal the supply of money available for lending. Investor does not require any adjustments by an investor in the market portfolio. Every security in the market portfolio is represented in proportion to its market

6.

7.

value relative to the market value of all securities. The market value of a security is the units of the security outstanding times the market price of the security. Thus as relative prices of securities change, their relative market values and therefore their proportions of the market portfolio change concomitantly. No adjustment is required on the part of the investor.

10. The equation of the Capital Market Line (CML) is:

rp = rf + [(rM - rf)/

M]*

p

In this case, the market portfolio is composed of two securities, A and B. Thus the expected return of the market portfolio is:

rM = (XA  rA) + (XB  rB)

= (.40  10%) + (.60  15%) = 13.0%

The standard deviation of the market portfolio is:

2222MXAAXBB2XAXBABAB

1/2 = {[(.40)²  (20)²] + [(.60)²  (28)²] + [2  (.40)  (.60)  (.30)  (20)  (28)]}½ = [64 + 282.2 + 80.6]½ = 20.7%

Therefore the equation for the CML is:

rp = 5.0% + [(13.0% - 5.0%)/20.7%] 

p

= 5.0% + .39p

12. The standard deviation of the market portfolio can be shown to equal the square

root of the weighted average of the covariances of all its component securities with it. In the case of the this four security portfolio:

½

M = [.20  242 + .30  360 + .20  155 + .30  210] = (250.4)½ = 15.8%

14. According to the CAPM, all investors will hold the market portfolio combined

with riskfree borrowing or lending. Therefore all investors will be concerned with the risk (or standard deviation) of the market portfolio. The standard deviation of the market portfolio can be shown to be a function of the covariances with it of each of the securities that make up the market portfolio. Therefore the contribution that each security makes to the market portfolio's risk will be directly related to its covariance with the market portfolio. Risk averse investors will demand higher returns from securities exhibiting higher covariances with the market portfolio.

15. With respect to risk, the investor ultimately is concerned with the standard

deviation of his or her portfolio. Therefore, in evaluating a well-diversified portfolio, the relevant measure of risk is standard deviation. However, the contribution of an individual security to a portfolio's standard deviation is not the standard deviation of the security. That is, a portfolio's standard deviation is not simply the weighted average of the standard deviations of the component securities. The appropriate measure of a security's risk is the contribution that it makes to the standard deviation of a well-diversified portfolio. That contribution is reflected in the security's covariance with the portfolio.

18. Oil is incorrect. The CAPM implies that it is possible for a security to have a

positive standard deviation and an expected return less than the riskfree rate. The CAPM relationship specifies that:

rp = rf + (rM - rf)

iM

Thus a security with a negative covariance with the market portfolio would have an expected return less than the riskfree rate. In practice, however, few, if any, securities have a negative covariances with surrogates for the market portfolio.

19. The beta of a security is calculated as:

iiM 2MTherefore:

292130. 152180B20.80

15225C2100.

15A

20. The beta of a portfolio is given by:

pXii

i1nIn Kitty's case: ßp = (.30  .90) + (.10  1.30) + (.60  1.05) = 1.03

22. a.

24Expected Return (%)1812AMBRf =600.000.501.001.502.00Beta

b. c.

ri = rf + (rM - rf)i

= 6% + (10% - 6%)ßi = 6% + (4%)ßi

rA

= 6% + (4%)(.85) = 9.4%

= 6% + (4%)(1.20)

rB

= 10.8%

24. A security that plots above the SML would be considered an attractive investment.

The expected return offered by such a security is greater than that required given its risk. Investors should wish to add such a security to their portfolios.

26. Market (or systematic) risk is the portion of a security's total risk that is related to

movements in the market portfolio and hence to the beta of the security. By definition, because the market portfolio is perfectly diversified, market risk in a portfolio cannot be reduced through diversification. Nonmarket (or unique or unsystematic) risk is the portion of a security's total risk

that is not related to moves in the market portfolio. Rather, it is related to events specific to the security. As a result, unique risk in a portfolio can be reduced through diversification.

28. Two relationships are necessary to identify the missing data in the table:

(1)

ri = rf + (rM - rf)i

22(2) i2pM2i

Using these equations, consider security D first: 7.0 = rf + (rM - rf)  0 rf = 7.0%

Next consider security B: 19.0 = 7.0 + (rM - 7.0)  1.5

rM = 15.0%

Next consider security C: 15.0 = 7.0 + (15.0 - 7.0) ßC ßC = 1.0 Further:

2

(12)² = (1.0)²  M + 0 2 = 12% MNext consider security A:

rA = 7.0 + (15.0 - 7.0)(.8) rA = 13.4%

Further:

 (12)² + 81]½ = 13.2% A = [(.8)²

Returning to security B:

 (12)² + 36]½ B= [(1.5)²

= 19.0%

Finally, consider security E: 16.6 = 7.0 + (15.0 - 7.0) ßE ßE = 1.2 Further:

(15)² = (1.2)²  (12)² + 2i

2i = 17.6