Consider the CAPM. The expected return on the market is 18%. The expected return on a stock with a beta of 1.2 is 20%. What is the risk-free rate

Risk-free rate = 8%

Explanation:

The Capital Asset pricing Model (CAPM) can be used to determined the beta.

According to the Capital Asset pricing Model the return on equity is dependent on the level of reaction of the the equity to changes in the return on a market portfolio.

These changes are captured as systematic risk. The magnitude by which a stock is affected by systematic risk is measured by beta.  

Under CAPM, Ke= Rf + β(Rm-Rf)  

Rf-risk-free rate (treasury bill rate), β= Beta, Rm= Return on market.  

Using this model,  we can work out the risk free rate as follows:

DATA

Ke-20%

Rf- ?

β-1.2

Rm- 18%

substituting, we have

0.2= Rf +  1.2× (0.18-Rf )

0.2 = Rf + 0.216 - 1.2Rf

collecting like terms

1.2Rf-Rf= 0.216 - 0.2

0.2Rf = 0.016

Dividing both sides by 0.2

Rf =0.016/0.2=0.08

Rf = 0.08 × 100 = 8%

Risk-free rate = 8%