Using regression analysis estimate the CAPM equation Rpi = Rf +Bpi (Rm-Rf)+ Ei for each of the 3 portfolios. Interpret the meaning of the Bpi value in each of the 3 portfolios. Are there any surprises?

Question

 

Below is a list of 17 US companies across 8 industries. The data file provided to you contains monthly returns on the 17 company stocks beginning in January 1993. Time series of the risk free rate and returns on the market index are also provided in the data file.

 

Industry                         Company                                   Code

Oil                                Mobil                                        MOBIL

Texaco                                      TEXACO

Computers                    IBM                                          IBM

Digital Equip. Co.                       DEC

Data General                             DATGEN

Electric Utilities              Consolidated Edison                 CONED

Pub Service of New Hamp.          PSNH

Forest Products             Weyerhauser                             WEYER

Boise                                        BOISE

Electronic

Components                  Motorola                                    MOTOR

Tandy                                       TANDY

Airlines                          Pan American Airlines                PANAM

Delta                                         DELTA

Banks                           Continental Illinois                      CONTIL

Citicorp                                      CITCRP

Foods                           Gerber                                      GERBER

General Mills                             GENMIL

 

Choose one industry from the list that you think is relatively risky and another industry that is relatively safe. Choose two companies in the safe industry and two companies in the relatively riskier industry.

 

(a) Calculate the means and standard deviations of the returns of each of the four companies over the period. Do the risk-return patterns for these companies correspond with your prior expectations? Why or why not?

 

(b)   Assume that you have $1m to invest. Construct 3 alternative portfolios as follows:

Portfolio 1: 50% in a company in the safe industry and 50% in a company in the risky industry. Portfolio 2:  50% in each of the 2 companies in the safe industry. Portfolio 3: 50% in each of the 2 companies in the risky industry. Calculate the sample correlation coefficient between the two companies in each of the 3 portfolios, comment on the size and interpretation of these correlations. For each of the 3 portfolios calculate the means and standard deviations of the returns over the period. Are there any surprises?

 

(c)  Distinguish between specific and market risk. Which of the 3 alternative portfolio diversifications would have been most justifiable in terms of reducing the specific risk of investment?

 

(d)  Using regression analysis estimate the CAPM equation Rp_i = Rf +Bp_i (Rm-Rf)+ E_i for each of the 3 portfolios. Interpret the meaning of the Bp_i value in each of the 3 portfolios. Are there any surprises?

 

(e) For portfolio 1, compare the R² from the portfolio regression in part (d) with the R² values from separate CAPM equation estimations for the 2 companies within portfolio Would you expect the R² from the portfolio equations to be higher than that from the two individual equations? Why or why not?

 

(f)  Using any sample of 10 stocks calculate the mean return and estimate the B_i for each stock. With these 10 means and 10 values of B_i, use regression analysis once again to estimate the equation of the Security Market Line (SML). Select any one of the remaining 7 stocks and determine whether it lies on the estimated SML. Assuming that the CAPM is a valid risk/return model, explain how you would exploit a situation where your chosen stock is temporarily lying either above or below the SML.