Question

A particular stock has a beta of 1.8 and an expected return of 12%. If the expected return on the market portfolio is 8%. What is the risk-free rate in the market right now?

Answer 1

As per Capital Asset Pricing Model [CAPM], The Expected Rate of Return is computed by using the following equation

Expected Rate of Return = Risk-free Rate + Beta(Market Rate - Risk-free Rate]

Expected Rate of Return = Rf + Beta(Rm – Rf)

Here, we’ve Expected Rate of Return = 12%

Return on the market portfolio (Rm) = 8%

Beta of the stock = 1.8

Risk-free Rate = ?

After substituting the given data into the equation,

Expected Rate of Return = Rf + B[Rm-Rf]

0.12 = Rf + 1.8(0.08 – Rf)

0.12 = Rf + 0.1440 - 1.8Rf

0.1440 – 0.12 = 1.8Rf – Rf

0.0240 = 0.80Rf

Rf = 0.0240 / 0.80

Rf = 0.03 or 3%

“Therefore, The Risk-free rate in the market would be 3%”