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1、1. The auto industrys earnings are highly cyclical. Therefore auto company stocks possess a high sensitivity (in a positive direction) to the trend in economic activity.Savings and loan companies (whose primary business is home loans) generally have large portfolios of fixed-rate loans. When interes
2、t rates rise (fall), their cost of funds rises (falls), while revenues remain relatively stable. As a result, their earnings fall (rise). Thus the stocks of these companies are often responsive (in a negative direction) to movements in real interest rates. For the real estate and air line, it is a n
3、egative signal.Electric utilities operate in regulatory environments. They may have trouble passing on cost increases to consumers, especially in the short run. Thus their stocks are sensitive (in a negative direction) to unexpected inflation.Crude oil producers and their stocks are sensitive (in a
4、positive direction) to the level of oil prices.2. In order to derive the curved Markowitz efficient set, the investor needs to estimate the expected returns, variances, and covariances for all assets. One can show that without a factor model, the investor must estimate (N + 3N)/2 parameters to deriv
5、e the efficient set.On the other hand, based on the assumptions underlying a factor model, the common responsiveness of securities to the factor(s) eliminates the need to estimate directly the covariances between securities. These covariances are captured by the securities sensitivities to the facto
6、r(s) and the factor(s) variance(s). As a result the number of parameters that must be estimated to derive the efficient set with a factor model is significantly reduced.4. Factor model relationships are based on two critical assumptions. The first is that the random error term and the factor are unc
7、orrelated, meaning that the outcome of the factor has no bearing on the outcome of the random error term.The second assumption is that the random error terms of any two securities are uncorrelated, meaning that the outcome of the random error term of one security has no bearing on the outcome of the
8、 random error term of any other security.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 misspecif
9、ied and should be adjusted to take into 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 the factor model has been misspecified. In this
10、case there must be some source of common 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 spe
11、cified, then two stocks with similar sensitivities 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 t
12、erm is zero, over the long-run one would 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 . bpF2Since the sensitivity of the portfolio to the factor is the weighted averag
13、e of the component securities sensitivities (with their proportions serving as weights), then:Factor risk = (.40 .20 + .60 3.50)2 225= 1,069.3b. Non-factor risk (expressed as is the weighted average of the ep2component securities random error term variances (with the square of the securities proport
14、ions serving as weights), then:Non-factor risk = .40 49 + .60 100= 43.8c. The standard deviation of the portfolio is given by:pFpb()/212= (1,069.3 + 43.8)= 33.4%9. The covariance between two securities in a one-factor world is given by:ijijF2In this case, the equation should be solved for F. That is
15、: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:iiFib()/212For security A:A= (.8) (18) + (25)= 28.9%For security B:B= (1.2) (18) + (15)= 26.3%11. The nonfactor risk of a portfolio is given by:pieiX21Assuming that the securi
16、ties 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 = 22.5100-security portfolio: 225/100 = 2.251,000-security portfolio: 225/1,000 = 0.22513. In order to calculate the expected return and standard deviation o
