Question

Assume the CAPM holds. Portfolio A has a beta of 1.2. Portfolio B has a beta of 2.4. Which of the following is true? none of the answers listed here. the return on Portfolio A is twice the return on portfolio B. The return on Portfolio B is twice the return on Portfolio A. the return on Portfolio A is half the return on portfolio B. 10 points

Answer 1

Correct answer is -

None of the answers listed here.

CAPM equation is widely used to calculate expected return on the security. As per CAPM there is positive and linear relationship between expected return and systematic risk as measured by beta.

According to capital asset pricing model -

Expected Return = RFR + (ER(market) ​− RFR) * beta of stock

Where,

RFR=Risk-free rate of return

ER(market) ​= Expected Return from the market​.

Note : ( E(Rm) - Rf ) is nothing but market risk premium and ( E(Rm) - Rf ) * beta of the security is risk premium on the security i.e return undertaken for taking extra risk.

As the beta of portfolio B is twice the beta of portfolio A, portfolio B's the risk premium (( E(Rm) - Rf ) * beta) will be twice that of portfolio A, not the expected return.

This can be proved with the below example-

Suppose,

Risk free return = 1 %

Market return = 2 %

As given,

Portfolio A beta = 1.2

Portfolio B beta = 2.4

Expected return on portfolio A -

Expected Return = RFR + (ER(market) ​− RFR) * beta of stock

= 1 + (2 -1 ) * 1.2

= 1 + 1 * 1.2

= 1 + 1.2

= 2.2 %

Expected return on portfolio B-

Expedted Return = RFR + (ER(market) ​− RFR) * beta of stock

= 1 + (2 -1 ) * 2.4

= 1 + 1 * 2.4

= 1 + 2.4

=3.4 %

Return on Portfolio B is not twice of that of portfolio A.

Hope it helps!