Question

An investor holds two well-diversified portfolios on US securities. The expected return on portfolio A is 13% and the expected return on portfolio B is 8%, and βA = 1 and βB = 0.7.

What should be the risk-free rate according to the CAPM?

Answer 1

as per CAPM,

expected return = risk free return + (Beta * market risk premium)

for portfolio A,

13% = risk free return + (1 * market risk premium)

market risk premium = (13% - risk free return) / 1

for portfolio B,

8% = risk free return + (0.7 * market risk premium)

market risk premium = (8% - risk free return) / 0.7

(13% - risk free return) / 1 = (8% - risk free return) / 0.7

(8% - risk free return) = (13% - risk free return) * 0.7

(8% - risk free return) = 9.1% - ( 0.7 * risk free return)

0.3 * risk free return = 8% - 9.1%

0.3 * risk free return = -1.1%

risk free return = -1.1% / 0.3

risk free return = -3.67%

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