Question

Suppose Bank of America Stock has a beta of 1.32, whereas Boeing Stock has a beta of 1.23. If the risk-free interest rate is 1.78% and the expected return of the market portfolio is 10%, according to the CAPM?

A.   What is the expected return of Bank of America Stock? (Please Show Calculations - No excel please)

B.    What is the expected return of Boeing Stock? (Please Show Calculations - No excel please)

C.    What is the beta of a portfolio that consists of 45% Bank of America stock and 55% Boeing stock? (Please Show Calculations - No excel please)

D.   What is the expected return of a portfolio that consists of 45% Bank of America stock and 55% Boeing stock? (Please solve it using two ways) - (Please Show Calculations)

Answer 1

Before getting to the solution we should know the CAPM equation.

E(R_i) = R_f + Beta_stock[ E(R_m) - R_f ]

where, E(R_i) = Expected Return of the Stock

R_f = Risk-free Rate

Beta_stock = Beta of the Stock

E(R_m) = Expected return of the market portfolio

A.) Using the above equation and the information provided in the question,

E(R₁) = 1.78% + 1.32 (10% - 1.78%) = 12.6304%

B.) Using the above equation and the information provided in the question,

E(R₂) = 1.78% + 1.23 (10% - 1.78%) = 11.8906%

C.) Beta of Portfolio = w₁Beta₁ + w₂Beta₂

where, w₁ = weight of Bank of America Stock

Beta₁ = Beta of Bank of America Stock

w₂ = weight of Boeing Stock

Beta₂ = Beta of Boeing Stock

Beta of Porfolio = .45 X 1.32 + .55 X 1.23 = 1.2705

D.) E(R_p) = w₁E(R₁) + w₂E(R₂)

where, E(R_p) = Expected return of the portfolio

w₁ = weight of Bank of America Stock

E(R₁) = Expected Return of Bank of America Stock [From Part A]

w₂ = weight of Boeing Stock

E(R₂) = Expected Return of Boeing Stock [From Part B]

E(R_p) = .45 X 12.6304% + .55 X 11.8906 = 12.2235%

Another way of Calculating Portfolio Expected Return,

As we already know Portfolio Beta, Risk-free Rate and Expected Return on market Portfolio, we can apply CAPM equation.

E(R_p) = 1.78% + 1.2705(10% - 1.78%) = 12.2235%.