Homework 5: CAPM Model
Homework # 5
1. Assume asset j’s βj = 0.75 and that μf = 3% and μM =10%.
1. (a) Assume that the CAPM theory holds, what is μj, the average return of asset j equal to?
2. (b) If actually μj = 9%, is asset j overpriced, underpriced or correctly priced?
2. Do problems 3 and 6 on page 513 (Chapter 17)
3. The Security Market line (SML) of an asset relates the excess return of an asset to the excess return of the market portfolio. It says that the risk premium of a security j is proportional to the risk premium on the market portfolio, that is
μj −μf =βj(μM −μf)
(We will derive this equation next week in class). Here μj and μf are the returns of securty j and risk-free asset, respectively, and μM is the returm on the market portfolio. βj is the jth security’s ”beta” value. Investors usually want an estimate of a stock’s beta before purchasing it. The econometric model is obtained by including an intercept in the model (even though theory says it should be zero) and an error term and is given
Rj,t − Rf,t = α + βj(Rm,t − Rf,t) + εj,t.
The data (CAPM, posted on courseworks under assignments) is the data on the monthly returns of four firms (Microsoft, GE, GM, IBM), the rate of return on the market portfolio (MKT) and the rate of return of risk free asset (RKFREE). The 120 observations cover January 1995 to December 2004. The columns in the data set are given in the follow- ing order Microsoft, GE, GM, IBM, MARKET PORTFOLIO, RISK FREE RATE (30 day T-Bill). Use this data to answer the following questions.
(a) Estimate the CAPM model for each firm and comment on their estimated beta values.
(b) Finance theory says that the intercept parameter α should be zero. Does this seem correct given your estimates (you need to test H0 :α=0againstHa :α̸=0foreachfirmat0.05significance level.
(c) Construct a 95% for each βj using the model and interpret your results
(d) Test at the 5% level of significance the hypothesis that each stock’s β is 1 against the alternative that it is not equal to 1.
(e) Test at the 5% level of significance the hypothesis that the beta of Microsoft is 1 against the alternative that it is greater than 1.
