Question

1. You have a portfolio that is invested 21% in Stock A, 34% in Stock B, and 45% in Stock C. The betas of the stocks are .66, 1.21, and 1.50, respectively. What is the beta of the portfolio? a. 1.17.b. 1.12.c. 1.38.d. 1.00.e. 1.23.2. The risk-free rate is 3.7% and the market expected return is 11.6%. What is the expected return of a stock that has a beta of 1.22?

Answer 1

Answer:

1.

Portfolio Beta = 1.225 rounded off to 1.23

Option e is the correct answer.

2.

r = 0.13338 or 13.338% rounded off to 13.34%

Explanation:

1.

The portfolio beta is a function of the weighted average of the individual stocks' betas that form up the portfolio. To calculate the beta of a portfolio, we use the following formula,

Portfolio Beta = wA * Beta of A  +  wB * Beta of B  + ... + wN * Beta of N

Where,

w is the weight of each stock

Portfolio Beta = 0.21 * 0.66  +  0.34 * 1.21  +  0.45 * 1.5

Portfolio Beta = 1.225 rounded off to 1.23

2.

Using the CAPM, we can calculate the required rate of return on a stock. This is the minimum return required by the investors to invest in a stock based on its systematic risk, the market's risk premium and the risk free rate.

The formula for required rate of return under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

rRF is the risk free rate

rM is the market return

r = 0.037  +  1.22 * (0.116 - 0.037)

r = 0.13338 or 13.338% rounded off to 13.34%