投资学夏普第二章答案Word文件下载.docx

1、 as a violation of the first assumption, consider a one-factor model where the factor is growth in gdp. if it were the case that a security had a positive random error term value every time gdp was higher than expected, then the factor model has been misspecified and should be adjusted to take into

2、account this unexplained sensitivity. as a violation of the second assumption, suppose that whenever security a had a positive random error term value, security b also had a positive random error term value, then thefactor model has been misspecified. in this case there must be some source of common

3、 responsiveness between the two securities that has not been captured by the factor model. 5. by the term similar stocks cupid presumably means that they display similar sensitivities to various economic and financial factors. if a factor model is correctly specified, then two stocks with similar se

4、nsitivities to the models factors should generate returns that are roughly the same over time. in the short run their returns may differ by the differences in the values of their respective random error terms. given that the expected value of the random error term is zero, over the long-run one woul

5、d expect the random error term to equal zero and thus the average return on the two securities to be the same. 7. a. in a one-factor model, a portfolios factor risk is expressed as bpf22 ?. since the sensitivity of the portfolio to the factor is the weighted average of the component securities sensi

6、tivities （with their proportions serving as weights）, then: factor risk = （.40 ? .20 + .60 ? 3.50）2 ? 225 = 1,069.3 b. non-factor risk （expressed as ?ep2 is the weighted average of the component securities random error term variances （with the square of the securities proportions serving as weights）

7、, then: non-factor risk = .402 ? 49 + .602 ? 100 = 43.8 c. the standard deviation of the portfolio is given by:?ppfepb?（）/22212 = （1,069.3 + 43.8）?= 33.4% 9. the covariance between two securities in a one-factor world is given by:ijijf bb?2 in this case, the equation should be solved for f. that is:

8、 f = ij/bibj? = （-312.50）/（-0.50 ? 1.25）? = 22.4% 10. in a one-factor model world, the standard deviation of a security is given by:iifeib? for security a: a = （.8）2 ? （18）2 + （25）2?= 28.9% for security b: b = （1.2）2 （18）2 + （15）2?= 26.3% 11. the nonfactor risk of a portfolio is given by:epiei in x?

9、221 assuming that the securities in the portfolio are equal-weighted, the portfolios nonfactor risk is the average nonfactor risk of the securities divided by the number of portfolio securities. thus the nonfactor risks of the various portfolios are: 10-security portfolio: 225/10 = 22.5 100-security

10、 portfolio: 225/100 = 2.25 1,000-security portfolio: 225/1,000 = 0.225 13. in order to calculate the expected return and standard deviation of a thirty-stock portfolio based on a five-factor model （with uncorrelated factors）, the following parameters must be estimated:zero-factor for each security 3

11、0sensitivity of each security to each factor （5 ? 30） 150variance of the random error term for each security 30variance of each factor 5expected value of each factor5total 220 if the factors are correlated, then there will be （n2 - n） factor covariances to estimate in addition to the parameters list

12、ed above. in this case, the number of additional parameters would be （52 - 5） = 20. 14. factors thought to pervasively affect security returns are usually viewed as macroeconomic or microeconomic in nature. the text discussed several possible macroeconomic factors. other such factors might include m

13、oney supply growth, the size of the budget deficit （or surplus）, the size of the trade deficit （or surplus）, or the level of consumer confidence. microeconomic factors （or at least proxies for those factors） that might pervasively influence security returns include dividend yield, earnings growth ra

14、te, earnings growth momentum （that is, the rate of change in earnings growth）, book value -to-price ratio, market capitalization, and financial leverage. 15. a portfolios sensitivity to a factor is the weighted average of the componentsecurities factor sensitivities. therefore in this case: bp1 = （.

15、60 ? -.20） + （.20 ? .50） + （.20 ? 1. 50）= 0.28 bp2 = （.60 ? 3.60） + （.20 ? 10.00） + （.20 ? 2.20）= 4.60 bp3 = （.60 ? 0.05） + （.20 ? .75） + （.20 ? 0.30）= 0.24 16. in the context of a factor model, the expected return on securities is a function of the values expected to be attained by the factor （or f

16、actors）. surprises in the actual outcomes for the factor values will determine the actual returns earned on the securities, with the exact nature of those actual returns depending on the structure of the factor model. mathematically, the expected return on security based on a single-factor model can

17、 be expressed as: ri = ai + bif where ri and f are the expected return for security i and the expected value of the factor, respectively. further, realized returns on a security can be expressed as: ri = ai + bif + ei substituting （ri - bif） for a in the preceding equation gives: ri = ri + bi（f - f）

18、 + ei that is, the actual return on the security is a function of its expected return and the surprise （or unexpected change） in the value of the factor. the underlying correlations among securities is represented by the sensitivities of the securities to surprises in the factor value, combined with

19、 the volatility of the factor value. 18. the time-series approach to factor model estimation begins with the assumption that the factors are known in advance. typically, the identification of the factors proceeds from an analysis of the economics of the firms involved. with the factors specified, hi

20、storical information concerning the values of the factors and security returns are collected from period to period. these data are used to estimate securities sensitivities to the factors, the securities zero factors and unique returns, and the standard deviations of factors and their correlations.t

21、he cross-sectional approach to factor model estimation begins with estimates of the securities sensitivities to certain factors. then, in a particular time period, the values of the factors are estimated based on the securities returns and their sensitivities to the factors. by repeating the process

22、 over multiple time periods, statistically significant estimates of the factors standard deviations and correlations can be computed. the factor analysis approach to factor model estimation begins simply with a set of securities and their corresponding returns. a statistical procedure known as facto

23、r analysis is used to identify the number of significant factors and the securities sensitivities to those factors as well as the standard deviations of the factors and the correlations among the factors. 19. security prices represent investors consensus expectations about the future prospects for t

24、he firms that issue the securities. past factor values will already be incorporated into security prices. thus past factor values will have no effect on security price changes and, therefore, security returns. instead it is what investors expect will be the value of factors in the future that should

25、 be related to security price changes and, therefore, security returns. 22. based on a two-factor model, the variance of a security is:iififiiei bbbbcovff212222212122 1 2 2?（,） therefore for the two securities in this problem:a = （1.5）2 ? （20）2 + （2.6）2 ? （15）2 + （2 ? 1.5 ? 2.6 ? 225） + 25= 4,201 a = （4,201）? = 64.8%b = （0.7）2 ? （20）2 + （1.2）2 ? 0.7 ? 1.2 ? 225） + 16= 914 b