Question

An investor currently holds the following portfolio of 4 stocks, each having equal weight:

Stock Expected Return (rs) Beta

A 13.2% 1.70

B 12.00% 1.5

C 6.0% 0.5

D 7.8% 0.8

a. What is the portfolio’s expected return?

b. What is the portfolio’s beta risk? Is it more or less risky than the market?

c. Is the portfolio more or less risky than the market? How do you know?

The investor is not comfortable with holding a portfolio that has a risk not equal to that of the market. She is thinking about purchasing a fifth stock, stock E, in order to change the risk of the portfolio.

d. What should the beta of Stock E be in order to make the portfolio have market risk? Assume all stocks have the same weight in the new portfolio.

e. According to the CAPM, what is E’s expected return if the risk-free rate is 3% and the market risk premium (RP_M) is 6%?

f. What will be the expected return of the portfolio with E included?

Answer 1

Expected return on portfolio is equal to weighted average return

= 13.2%*1/4 + 12%*1/4 + 6%*1/4 + 7.8%*1/4

= 9.75%

b.Portfolio bets is equal to weighted average beta

= (1.70+1.5+0.5+0.8)/4

= 1.125

More risky, as market beta is equal to 1

c.More risky, since higher beta

d.Let beta of E be x

(1.70+1.5+0.5+0.8)/5 + x/5 = 1

0.9 + x/5 = 1

X = 0.5

Hence, beta of E = 0.5

e.Expected return as per CAPM = risk free rate + beta*market risk premium

= 3% + 0.5*6%

= 6%

f.Expected return of portfolio = (13.2%+ 12% + 6%+ 7.8%+6%)/5

= 9%