Question

CAPM Question

Problem 1 (15pts). Given the following data: Security Beta Expected Return 1.3 20% 0.8 14% 18% 1.2 (a) (10pts). Assume Securities 1 and 2 are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk-free rate? (b) (5pts). Would you recommend buying Security 3 according to CAPM? Why or why not?

Answer 1

Ans : As per CAPM

Expected Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)

a) Computation of Expected return on Market and risk free rate

Step 1 : Create Equation for Security 1 and Security 2

Security 1

Expected Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
0.20 = Risk Free Rate + 1.3 (Market Return - Risk Free Rate)
0.20 = Risk Free Rate + 1.3Market Return - 1.3 Risk Free Rate
0.20 = 1.3 Market Return - 0.3 Risk Free Rate ------ Equation (1)

Security 2

Expected Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
0.14 = Risk Free Rate + 0.8 (Market Return - Risk Free Rate)
0.14 = Risk Free Rate + 0.8Market Return - 0.8 Risk Free Rate
0.14 = 0.8Market Return + 0.2 Risk Free Rate --------Equation (2)

Multiply both the equations 1 by 2 and equation 2 by 3 because then Risk Free Rate in both the equations will become equal.

Equation 1 = 2 * (0.20 = 1.3 Market Return - 0.3 Risk Free Rate )
Equation 2 = 3 * (0.14 = 0.8Market Return + 0.2 Risk Free Rate )

Step 2 : Solve the Equation and find the market Return

Solving Equation 1 and Equation 2

0.40 = 2.6 Market Return - 0.6 Risk Free Rate --Eq (1)
0.42 = 2.4 Market Return + 0.6 Risk Free Rate --Eq (2)
+ + +
-------------------------------------------------------------
0.82 = 5 Market Return + 0

Market Return = 0.82/5 = 0.164 = 16.4%

Step 3 : Substitue the Market return in Equation 1 and find risk free rate

0.20 = 1.3 Market Return - 0.3 Risk Free Rate ------ Equation (1)

Subsituting the market return = 16.4% in equation 1 we get,

0.20 = 1.3 (0.164) - 0.3Risk Free Rate
0.3 Risk Free Rate = 0.2132 - 0.20
0.3 Risk Free Rate = 0.0132
Risk free Rate = 0.0132 / 0.3
Risk Free Rate = 0.044 = 4.4%

Ans : Market Return = 16.4%
Risk Free Rate = 4.4%

b) Decision on Security 3 according to CAPM

Lets compute Expected return as per CAPM for Security 3

Expected Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
= 4.4% + 1.2 (16.4% - 4.4%)
= 4.4% + 14.4%
Expected Return = 18.8%

Ans : The Expected Return as per CAPM i.e. 18.8% on security 3 is greater then the expected return estimated i.e.18%. This means that the stock is currently overvalued in the market because it is offering less then the required given its systematic risk. Thus it is not recommended to buy security 3 according to CAPM.