Question

A.) Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%. A stock has an expected rate of return of 4%. What is its beta?

B.) Assume that both portfolios A and B are well diversified, that ?(?a ) = 12%, and ?(?b ) = 9%. If the

economy has only one factor, and ? a = 1.2, whereas ? b = 0.8, what must be the risk-free rate?

Answer 1

A. The beta is computed as shown below:

Expected return on stock = Risk free rate + Beta x ( return on market - risk free rate)

0.04 = 0.06 + Beta x ( 0.16 - 0.06)

0.04 = 0.06 + Beta x 0.10

Beta = - 0.20

B. The risk free rate is computed as shown below:

( Expected return on A - risk free rate ) / beta of A = ( Expected return on B - risk free rate ) / beta of B

( 0.12 - risk free rate) / 1.2 = ( 0.09 - risk free rate) / 0.8

0.8 ( 0.12 - risk free rate ) = 1.2 (0.09 - risk free rate)

0.096 - 0.8 risk free rate = 0.108 - 1.2 risk free rate

3% = risk free rate

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