Question

A stock has a beta of 0.9 and an expected return of 8 percent. A risk-free asset currently earns 3 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Expected return b. If a portfollo of the two assets has a beta of O.8, what are the portfolio welghts? (Round your answers to 2 declmal places. Omit the "%" sign In your response.) Weight % Xrf c. If a portfolio of the two assets has an expected return of 6 percent, what is its beta? (Round your answer to 2 decimal places.) Beta d. If a portfolio of the two assets has a beta of 3.60, what are the portfolio weights? (Negatlve amounts should be indicated by a minus sign. Omlt the "%" sign In your response.) Weight % Xrf

Answer 1

a. The expected return on the portfolio, that is equally invested in the two assets are :

Rp = 0.5* return on stock + 0.5* return on risk free rate

= 0.5* 8 + 0.5* 3

= 5.5%

So, the return on the portfolio, that is equally invested in the stock and the risk free rate is 5.5%.

b. As the risk free rate is free of risk, the beta is zero,

So, the portfolio beta is 0.8,

Weight on stock * beta of stock = 0.8

weight * 0.9 = 0.8

weight of stock is : 88.88%

The weight on the risk free asset = 100 - 88.88 = 11.11%

c. Let the weight on the risk free asset be w, so the weight on the risky assets is (1 - w),

The expected return on the portfolio is 6%,

So,

W * 3 + (1 - W) * 8 = 6

3W + 8 - 8w = 6

5w = 2

Weight of risk free rate is 40% and the weight of risky asset is 60%.

d. Let the weight of risky asset be W,

W* 0.9 = 3.6

So, weight of risky asset is 400%.

So, the weight of risk free asset is -300%.

Negative weight indicates borrowing at the risk free rate,