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© BrainMass Inc. brainmass.com June 3, 2020, 6:26 pm ad1c9bdddf
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.