Question

1) A stock has a beta of 1.08 and has expected rate of return of 11.6 percent. A risk-free asset currently earns 3.6 percent. What is the expected rate of return on a portfolio that is equally invested in the two assets?

A) 12.12%

B) 11.15%

C) 12.24%

D) 11.24%

2) A stock has a beta of 1.08 and has expected rate of return of 11.6 percent. A risk-free asset currently earns 3.6 percent. If a portfolio of the two assets has a beta of 0.50, what are the portfolio weights?

A) 0.46; 0.54

B) 0.63; 0.37

C) 0.57; 0.43

D) None of these

3) A stock has a beta of 1.08 and has expected rate of return of 11.6 percent. A risk-free asset currently earns 3.6 percent. If a portfolio of the two assets has an expected return of 10.5 percent, what is the beta?
A) 0.90

B) 0.93

C) 0.98

D) 0.89

4) A stock has a beta of 1.08 and has expected rate of return of 11.6 percent. A risk-free asset currently earns 3.6 percent. If a portfolio of the two assets has a beta of 2.16, what are the portfolio weights? How do you interpret the weights of the two assets in this case? Explain.

A) 1.50; -0.50

B) 0.82; 0.18

C) 0.65; 0.35

D) 2.00; -1.00

Answer 1

• Portfolio return can be calculated as the weighted average return on all the stocks held in the portfolio.
• Beta of the portfolio is the weighted sum of the individual asset betas

1)

Return	%	Weight	Multiple
Stock	11.6	0.5	5.8
Risk Free Asset	3.6	0.5	1.8
Total Return			7.6

2) We know, beta of risk free asset is zero (As value of risk free asset will not change for any change in market value)

Portfolio Beta is weighted average of individual asset beta

i.e 0.5 = 1.08 * Stock Weight + 0* Risk free asset weight

0.5 = 1.08 * X

i.e x = 46.30%

Weight of Stock = 46.30% And Risk free Asset weight = 53.70%

3) Inorder to find the beta of the portfolio, we need to find the weight of the portfolio.

Portfolio Return = Stock Return * Stock Weight + RF Return * RF Weight

10.50 = 11.6 * X + 3.6 (1-X)

i.e X = 0.86

Weight of Stock 86% Weight of RF Asset = 14%

Portfolio Beta is weighted average of individual asset beta

= 1.08* 86% + 0*14%

= 0.93

4) We know, beta of risk free asset is zero (As value of risk free asset will not change for any change in market value)

Portfolio Beta is weighted average of individual asset beta

i.e 2.16 = 1.08 * Stock Weight + 0* RF Asset Weight

Stock Weight = 2

i.e RF Asset Weight = -1

We observe that RF Asset weight is negative. i.e instead of investing, we are borrowing. We are borrowing money and investing the same in the stocks. So asset weights is as below:

Return	Weight
Stock	2
Risk Free Asset	-1
Total Weight	1