Question

Using CAPM

A stock has a beta of 1.15 and an expected return of 11.4

percent. A risk-free asset currently earns 3.5 percent.

a. What is the expected return on a portfolio that is equally invested in the

two assets?

b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights?

c. If a portfolio of the two assets has an expected return of 9 percent, what

is its beta?

d. If a portfolio of the two assets has a beta of 2.30, what are the portfolio

weights? How do you interpret the weights for the two assets in this

case? Explain.

Answer 1

Given:

Beta of stock = 1.15

Expected return of stock= 11.4% or 0.114

Risk free assets = 3.5% or 0.035

a. Expected return = (50% * Return of stock) + (50% * Risk free assets)

= (0.50 * 0.114) + (0.50 * 0.035)

= 0.057 + 0.0175

= 0.0745 or 7.45%

b. Assume weight of stock = X

Portfolio Beta = Weight of stock * Beta of stock + Weight of risk free asset + Beta of risk free assets

0.7 = X * 1.15 + 0

X= 0.7 / 1.15

X = 0.6086 or 60.86%

Weight of stock = 60.86%

Weight of Risk free assets = 1 - Weight of stock

= 1 - 0.6086

= 0.3914 or 39.14%

c. Expected Return = Weight of stock * Return of stock + (1 - weight of stock) * Risk free assets

0.09= Weight of stock * 0.114 + (1 - Weight of stock) * 0.035

0.09 - 0.035 = Weight of stock * (0.114 - 0.035)

Weight of stock = (0.09 - 0.035) / (0.114 - 0.035)

Weight of stock = 0.055 / 0.079

Weight of stock = 0.6962 or 69.62%

Weight of Risk Free Assets = 1 - Weight of stock

= 1 - 0.6962

= 0.3038 or 30.38%

Beta = Weight of stock * Beta of stock

= 0.6962 * 1.15

= 0.80

d. Weight of stock = Beta of Assets / Beta of Equity

= 2.30 / 1.15

= 2

Weight of Risk Free Assets = 1 - Weight of stock

= 1 - 2

= -1

The portfolio is represent that the amount is being borrowed at risk free rate and invested in stock. A negative percentage means that you are borrowing using risk free rate.