A stock has a beta of 1.05 and an expected return of 19 percent. A risk-free asset currently earns 5.7 percent.
a. The expected return on a portfolio that is equally invested in the two assets is _______%. (Input answer as a percent rounded to 2 decimal places, without the percent sign.)
b. If a portfolio of the two assets has a beta of 0.75, the weight of the stock is _________% and the weight of the risk-free is _________% (Input answers as a percent rounded to 4 decimal places, without the percent sign).
c. If a portfolio of the two assets has an expected return of 7 percent, its beta is _________. (Round answer to 6 decimal places.)
d. If a portfolio of the two assets has a beta of 2.35, the weight of the stock is _________% and the weight of the risk-free is ________% (Input answers as a percent rounded to 2 decimal places, without the percent sign).
How do you interpret the weights for the two assets in this case? Explain
Before answering these questions, we need to know how to find the beta and the returns of a portfolio given the weights, betas and returns of its components. These are the formulas for the case of a two-security portfolio (in your case, there are two securities: the stock and the risk-free asset)
Beta of a portfolio = w1*B1 + w2*B2
where w1 and w2 are the weights in the portfolio of securities 1 and 2 respectively; and B1 and B2 are the betas of securities 1 and 2. Furthermore, since the sum of the weights of the securities must be equal to 1 (w1+w2=1), we can rewrite the above equation as:
Beta of a portfolio = w1*B1 + (1-w1)*B2
The expected return of a portfolio as a function of the weights and returns of tis components has a very similar formula:
Exp. return of portfolio = w1*R1 + (1-w1)*R2
where R1 and R2 are the expected returns ...
The solution calculates expected return on a portfolio, weight of stock and beta.