Question

2. Bond Yields: Y At the begi $1.000 years Part : Problems - questions (50 pts.) ve THREE of the following FOUR numerical problems. You must show all work for full credit. Partial Credit will be given 1. CAPM / Portfolio Theory An investor currently holds the following portfolio of 4 stocks, each having equal weight. Stock Expected Return ) Beta 11.4% 10.2% 8.4% 72 0.7 1.4 12 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? 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 c. What should the bota of Stock Ebe in order to make the portfolio have market rink? Assume al stocks have equal weight in the new portfolio d. According to the CAPM, what is Es expected return if the risk tree rate is 3% and the market risk premium (RPM) is 6%? e. What will be the expected return of the portfolio with E included?

Answer 1

1]

a]

Expected return of portfolio = sum of weighted expected return of each stock.

There are 4 stocks, and each stock has equal weight in the portfolio. Hence, the weight of each stock is 0.25.

Expected return of portfolio = (0.25 * 11.4%) + (0.25 * 10.2%) + (0.25 * 8.4%) + (0.25 * 7.2%)

Expected return of portfolio = 9.30%.

b]

portfolio beta = weighted beta of each stock in portfolio.

portfolio beta = (0.25 * 1.4) + (0.25 * 1.2) + (0.25 * 0.9) + (0.25 * 0.7)

portfolio beta = 1.05

It is more risky than the market because the market beta is always equal to 1.

c]

If there are 5 stocks with equal weight in the portfolio, each stock will have a weight of 0.2.

For the portfolio to have market risk, the portfolio beta should be 1.

Let us say the beta of Stock E is "B". Then :

1 =  (0.2 * 1.4) + (0.2 * 1.2) + (0.2 * 0.9) + (0.2 * 0.7) + (0.2 * B)

0.2B = 1 - 0.84

B = 0.8

The beta of Stock E should be 0.8

d]

Expected return = risk free rate + (beta * market risk premium)

Expected return = 3% + (0.8 * 6%)

Expected return = 7.8%