Question

Problem 19 Intro Assume that the CAPM holds. One stock has an expected return of 10% and a beta of 0.3. Another stock has an expected return of 14% and a beta of 1.5. IB Attempt 4/10 for 5 pts. Part 1 What is the expected return on the market? 3+ decimals Submit

Answer 1

Risk-free Rate = R_F

Expected Return on the Market = R_M

Market-risk Premium = MRP = (R_M-R_F)

According to CAPM, Expected Return on a stock (R_i) with a beta of β_i is given by the equation:

R_i = R_F + β_i*MRP

Return on 1st Stock = R₁ = 10%, Beta of the 1st stock = β₁ = 0.3

CAPM Equation for 1st Stock

R₁ = R_F + β₁*MRP

R₁ = 10%, β₁ = 0.3

10% = R_F + 0.3*MRP

R_F = 10% - (0.3*MRP)

Return on 2nd Stock = R₂ = 14%, Beta of the 2nd stock = β₂ = 1.5

CAPM Equation for 2nd stock

R₂ = R_F + β₂*MRP

14% = R_F + 1.5*MRP

Now, putting the value of R_F = 10% - (0.3*MRP) from the first CAPM quation

14% = 10% -(0.3*MRP) + (1.5*MRP)

14% - 10% = 1.2*MRP

4% = 1.2*MRP

MRP = 4%/1.2 = 3.33333%

Calculating the value of R_F

R_F = 10% - (0.3*MRP) = 10% - (0.3*3.3333%) = 10% - 1% = 9%

Calcuating R_M

MRP = R_M - R_F

MRP = 3.3333%, R_F = 9%

3.3333% = R_M - 9%

R_M = 3.3333% + 9% = 12.3333%

Expected Return on Market = R_M = 12.3333% or 0.123333

Answer -> 0.123333