A stock has a beta of 1.0 and an expected return of 14 percent. A risk-free asse

Question

A stock has a beta of 1.0 and an expected return of 14 percent. A risk-free asset currently earns 4.5 percent a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected return 14.001% b. If a portfolio of the two assets has a beta of 0.85, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Portfolio Weight Stock Risk-free asset c. If a portfolio of the two assets has an expected return of 9.25 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Beta

Explanation / Answer

a. return = 0.5*return on stock +0.5*return on risk free asset = 0.5*14+0.5*4.5 = 7+2.25 = 9.25%

b. portfolio beta = weight of stock*beta of stock + weight of risk free*beta of risk free

=> 0.85 = weight of stock * 1 + weight of risk free * 0

=> weight of stock = 0.85

weight of risk free asset = 1-0.85 = 0.15

c. from answer of par (a) we know portfolio is equally invested in both assests

so beta = 0.5*beta of stock + 0.5*beta of risk free = 0.5*1+0.5*0 = 0.5

d. here beta is more than 1. so portfolio is more than 100% invested in stock. to do so portfolio has to borrow or go short in risk free asset

when portfolio borrows 36% of portfolio weight in risk free and invest it in stock, beta = 1.36*beta of stock +(-0.36)*beta of risk free = 1.36*1 -0.36*0 = 1.36

stock weight = 136%

risk free weight = -36%

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