Question

A stock has a beta of 1.90 and an expected return of 15 percent. A risk-free asset currently earns 3.6 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If a portfolio of the two assets has a beta of .95, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.) c. If a portfolio of the two assets has an expected return of 7 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) d. If a portfolio of the two assets has a beta of 3.80, what are the portfolio weights?

Answer 1

a. E(Rp) = W1 * E(R1) + W2 * E(R2) : W = Weight of risk free asset in portfolio , E(R) = Return of risk free asset

Expected Return of Portfolio = 0.5*3.6 + 0.5*15

Expected Return of Portfolio = 1.8 + 7.5

Expected Return of Portfolio = 9.3%

b. When a portfolio is composed of one risk free asset and one another risky stock

бp = W1 * б1

The S.D. of a stock or portfolio in this case as given by Beta

0.95 = W1 * 1.9

W1 = 0.95/1.9

W1 = 50%

Weight of risk free asset = 1 - 0.5

Weight of risk free asset = 50%

c. E(Rp) = W1 * E(R1) + W2 * E(R2)

7 = W1 * 3.6 + W2 * 15

With Trial and error method: W1 = 0.7, W2 = 0.3

Beta of Portfolio = 0.3 * 1.9

Beta of Portfolio = 0.57

d. Beta of Portfolio = Weight of risky asset * Beta of risky stock

3.8 = W * 1.9

W = 3.8/1.9

W = 2

Weight of risk free asset = 1 - 2

Weight of risk free asset = -1.