Question

3. Assume that the CAPM holds, and the following is known about the market: a. The market portfolio has an expected return of 15% and standard deviation of 20%, b. The risk-free rate is 3%. c. Stock A has an expected return of 25% d. Stock B has standard deviation of 15% and correlation of 0.6 with the market portfolio What is the beta of a portfolio with 30% in stock A and 70% in stock B?

Answer 1

The concept tested in the question is CAPM along with the other concepts of portfolio theory.

Solution :

> Given Facts

RM = 15%

SDM = 20% , Variance of Market = 400

Rf = 3%

RA = 25%

SDB = 15%

rA,M = 0.6

> Formula

Beta = Covariance ( Stock, Market) / Variance (market)

Covariance ( Stock, Market) = rA,M * SDStock * SDMarket

> Calculation

- Stock A

CAPM Equation

ERi​ = Rf ​+ βA​ (ERm ​− Rf​)

Thus, puttin values'

=> 25 = 3 + βA(15-3)

=> βA = 1.8333

- Stock B

Covariance ( Stock B, Market) = rB,M * SDStock * SDMarket

                                                         = 0.6 * 15 *20

                                                = 180

Beta Stock B = Covariance ( Stock, Market) / Variance (market)

                       = 180 / 400

                       = 0.45

> Answer

Beta of porfolio = Weighted average of stock betas

                        = 30% * 1.8333 + 70% * 0.45

                        = 0.865 Answer

Hope you understand the solution.