Question

Stock X has a beta of 0.5 and Stock Y has a beta of 1.5. Which of the following statements is most correct?

Select one:

a. If expected inflation increases (but the market risk premium is unchanged), the required returns on the two stocks will decrease by the same amount.

b. If investors' aversion to risk decreases (assume the risk-free rate unchanged), Stock X will have a larger decline in its required return than will stock Y.

c. If you invest $50,000 in Stock X and $50,000 in Stock Y, your portfolio will have a beta equal to 1.0.

d. If the beta of a company doubles, then the required rate of return will also double.

e. Stock Y's return has a higher standard deviation than Stock X.

Answer 1

The correct option is C

If we invest 50,000 in Stock X and 50,000 in Stock Y with beta of 0.5 and 1.5. then, portfolio beta will be

= W1B1 + W2B2

W1 Is the weightage of stock X

B1 is beta of stock X

W2 is weightage of stock Y

B2 is beta of stock Y

= (50,000 /100000) × 0.5 + (50,000 / 1,00,000) × 1.5

= 0.5 × 0.5 + 0.5 × 1.5

= 0.25 + 0.75

= 1

So, the beta of the portfolio is 1

If the beta of the company doubles then the required return will depends on the return of the risl free return and market return and weightage of it.

The beta and the standard deviation are not related and if the aversion to risk decreases then the return of stock Y has bigger decline as it has higher beta.