Question

Suppose that a portfolio is made up of the following three stocks:

Stock

Ace Bees Seas

Investment Beta

$ 3,000 0.75 $ 4,500 1.5 $ 7,500 1.4

The expected rate of return on the market is 13% and the risk-free rate is 7%.

a) Compute the beta of the portfolio.

b) Compute the required rate of return on the portfolio.

c) If the expected return on the portfolio is 18%, would you invest in it? Why or why not?

Answer 1

A) In order to find the beta of portfolio we need to take a weighted average of all three stocks beta.

So, In order to find the weight of a given stock, we will divide stock value by the total value of the portfolio. Eg, 'Ace' weight would be 3,000/15,000 = 0.2

So Beta of portfolio would be (0.2*0.75)+(.03*1.5)+(0.5*1.4) = 1.30

B) In order to find the required rate of return, we will use CAPM.

CAPM = 7% + 1.3(13%-7%) = 14.8%

C) Yes, we would invest as our expected return is more than the required return.

Stock	Price	Beta	Weights
Ace	3,000	0.75	0.20
Bees	4,500	1.50	0.30
Seas	7,500	1.40	0.50
Total Portfolio Amount	15,000
Expected Rate of Return on market	13.0%
Risk-Free Rate	7.0%
A) Portfolio Beta	1.30
B) The required rate of return of the portfolio	14.8%
C) If the expected return on the portfolio is 18%	YES