Answer to Question #272649 in Financial Math for cliffe

Question

Question two (8 marks)

The risk free rate is 10% and the expected return on the market portfolio is 15%. The expected returns for 4 securities are listed below together with their expected betas

SECURITY EXPECTED RETURN EXPECTED BETA

A 17.0% 1.3

B 14.5% 0.8

C 15.5% 1.1

D 18.0% 1.7

REQUIRED:

a. On the basis of these expectations, which securities are overvalued? Which are undervalued?

b. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, which securities would be overvalued? which would be under-valued? (Assume the expected returns and the betas remain the same).

Answer 1

a) ​ERi​=Rf​+βi​(ERm​−Rf​)

​

ERi​=expected return of investment

Rf​=risk-free rate

βi​=beta of the investment

(ERm​−Rf​)=market risk premium

​

17.0%=10%+1.3(17.0%-10%)

17.0/100=10/100-1.3(17.0/100-10/100)

17.0%=0.19

The security was overvalued.

14.5%=10%+0.8(14.5%-10%)

14.5%=0.14

The security was undervalued.

15.5%=10%+1.1(15.5%-10%)

0.16

The security was overvalued.

18.0%=10%+1.7(18.0%-10%)

0.24

The security was overvalued.

b) 16%=12%+1.3(16%-12%)

0.17 ; overvalued.

16%=12%+0.8(16%-12%)

0.15 ; undervalued.

16%=12%+1.1(16%-12%)

0.16 ; fairly valued.

16%=12%+1.7(16%-12%)

0.19 ; overvalued.