Question

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

a.  Find the required return for an asset with a beta of 0.54 when the​ risk-free rate and market return are 6 ​% and 8 % ​, respectively.

b.  Find the ​risk-free rate for a firm with a required return of 6.368 ​% and a beta of 0.26 when the market return is 11 % .

c.  Find the market return for an asset with a required return of 16.130 ​% and a beta of 1.18 when the​ risk-free rate is 8 % .

d.  Find the beta for an asset with a required return of 11.945 ​% when the​ risk-free rate and market return are 6 ​% and 10.1 % ​, respectively.

Answer 1

As per Capital Asset Pricing Model,

Re = Rf + ( Rm – Rf ) x Beta

Where,

Re = Required rate of return

Rf = Risk free rate of interest

Rm = Return on market

Beta = Beta of the stock

So, using the above equation

a)

Rf = 6%

Rm = 8%

Beta = 0.54

So, Re = 6 + (8 – 6) x 0.54

= 6 + 2 x 0.54

= 6 + 1.08

= 7.08%

b)

Re = 6.368%

Rm = 11%

Beta = 0.26

So, 6.368 = Rf + (11 – Rf) x 0.26

So, 6.368 = Rf + 2.86 – 0.26 x Rf

So, 6.368 – 2.86 = 0.74 x Rf

So, Rf = 3.508 / 0.74

= 4.74%

c)

Re = 16.130%

Rf = 8%

Beta = 1.18

So, 16.130 = 8 + ( Rm – 8) x 1.18

So, 16.130 – 8 = ( Rm – 8) x 1.18

So, 8.13 / 1.18 = Rm – 8

So, Rm = 6.89 + 8

= 14.89%

d)

Re = 11.945%

Rf = 6%

Rm = 10.1%

So, 11.945 = 6 + (10.1 – 6) x Beta

So, 11.945 – 6 = 4.1 x Beta

So, Beta = 5.945 / 4.1

= 1.45