Question

Problem 11-16 Using CAPM

A stock has a beta of 1.05 and an expected return of 11 percent. A risk-free asset currently earns 2.4 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.)

Expected return

%

b.	If a portfolio of the two assets has a beta of .63, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

.

Weight of stock
Risk-free weight

c.	If a portfolio of the two assets has an expected return of 7 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

Beta

  

d.	If a portfolio of the two assets has a beta of 2.10, what are the portfolio weights? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations.)

  

Weight of stock
Risk-free weight

Answer 1

1. E(R) = w₁R₁ + w₂R_q

W₁/W₂ = Weights of securities

R₁/R₂ = Return on securities

E Return = 0.5 *0.11 + 0.5*0.024 = 0.055 + 0.012 = 6.7%

2. Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of risk free asset*Beta of risk free asset

0.63 = W_s *1.05 + W_rf * 0

As beta (Systematic risk) of a risk free asset is zero, the risk free part of the equation becomes zero.

W_{s =} 0.63/1.05 = 60%

If the weight of stock is 60% and the weight of risk free asset is simply (1- W_s) which is 40%.

3. Using the expected return formula.

7% = W_{s *} R_S + W_rf *R_RF

    0.07      = W_s * 0.11+ (1- W_s )* 0.024

             = W_s * 0.11 + 0.024 – 0.024W_s

0.046 = 0.085W_s

W_{s =} 0.5411 or 54.11%

Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of risk free asset*Beta of risk free asset

BETA = 0.5411 *1.05 + 0 = 0.57

4. Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of risk free asset*Beta of risk free asset

2.10 = W_s *1.05 + W_rf * 0

W_{s =} 200%

W_rf = -100%

This means, the extra 100% invested in the stock, was borrowed at a risk free rate and then invested, which also increased the beta of the portfolio.