Question

Assume that both portfolios A and B are well diversified, that E(r_A) = 7%, and E(r_B) = 5%. If the economy has only one factor, and β_A = 1.2, whereas β_B = 0.8, what must be the risk-free rate? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

This can be calculated using Capital Asset pricing model.

Expected rate of return of portfolio A= Risk Free Rate+(Beta*market risk premium)

Expected rate of return of portfolio B= Risk Free Rate+(Beta*market risk premium)

Let the risk-free rate be X

Let the market risk premium be Y.

7= X+(1.2*Y) for portfolio A.

5= X+(.8*Y) for portfolio B

After calculation of ward equations for both the portfolios using the linear equations.

X= 7-1.2 Y---------------(1)

X= 5-.8Y--------------------(2)

Equating equation 1 and equation 2 --

7-1.2Y=5-.8Y

7-5= -.8Y+1.2Y

Y=( 2/.4)= 5

Risk premium= 5%

Formulating the the amount of risk premium into equation (1) to find the value of X.

Risk free rate=( 7-1.2*5)= (7-6)= 1%

So, Risk Free Rate of Return would be 1%.