Question

Suppose rRF = 5%, rM = 10%, and rA = 8%.

a.)Calculate Stock A's beta. Round your answer to one decimal place.

b.)If Stock A's beta were 1.3, then what would be A's new required rate of return? Round your answer to one decimal place.

Answer 1

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 -

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

Where,

RFR=Risk-free rate of return

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

Here,

RFR = 5%, Return on market portfolio = 10%, and Return on security A = 8%.

a) We need to find Beta.

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

8 = 5 + ( 10 - 5 ) * beta

8 = 5 + 5 *beta

8 - 5 = 5 * beta

3 = 5 * beta

beta = 3 / 5

= 0.6

a) Beta of stock A = 0.6

b) If Stock A's beta were 1.3, new required rate of return can be calculated as -

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

Required return = 5 + ( 10 - 5 ) * 1.3

= 5 + 5 * 1.3

= 5 + 6.5

= 11.5 %

A's new required rate of return = 11.5 %

Hope it helps!