Question

Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following situations.

a. Find the required return for an asset with a beta of 2.2 when the risk-free rate and market return are 5% and 32%, respectively.

b. Find the risk-free rate for a firm with a required return of 23.75% and a beta of 1.25 when the market return is 20%.

c. Find the market return for an asset with a required return of 18% and a beta of 1.2 when the risk-free rate is 8%.

d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 3% and 15%, respectively.

Answer 1

Ans : As per CAPM,

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

a) Requried Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
= 0.05 + 2.2 ( 0.32 - 0.05)
= 0.05 + 2.2 (0.27)
= 0.644
Required Return = 64.4%

b) Requried Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
0.2375 = Risk Free Rate + 1.25 * (0.20 - Risk Free Rate)
0.2375 = Risk Free Rate + 0.25 - 1.25 Risk Free Rate
0.2375 - 0.25 = Risk Free Rate - 1.25 Risk Free Rate
- 0.0125 = - 0.25 Risk Free Rate
Risk Free Rate = 0.0125 / 0.25
Risk Free Rate = 0.05 = 5%

c) Requried Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
0.18 = 0.08 + 1.2 (Market Return - 0.08)
0.18 = 0.08 + 1.2 Market Return - 0.08
0.18 = 1.2 Market Return
Market Return = 0.18 / 1.2
Market Return = 0.15 = 15%

d) When the required return is equal to market return the beta is always 1.

Requried Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)
0.15 = 0.03 + Beta * ( 0.15 - 0.03)
0.15 - 0.03 = 0.15 Beta - 0.03 Beta
0.12 = 0.12 Beta
Beta = 1