Question

Suppose stock returns can be explained by a two-factor model. The firm-specific risks for all stocks are independent. The following table shows the information for two diversified portfolios:

  

	β1	β2	E(R)
Portfolio A	.81	1.11	15%
Portfolio B	1.41	−.21	13

  

If the risk-free rate is 6 percent, what are the risk premiums for each factor in this model? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Risk premiums
Factor F1	%
Factor F2	%

Answer 1

Expected Return = Risk free rate + Beta*Risk Premium

Let the risk premium of factor A be x and factor B be y

Portfolio A, 15% = 6% + 0.81x + 1.11y

9% = 0.81x + 1.11y............(1)

Portfolio B, 13% = 6% + 1.41x – 0.21y

7% = 1.41x – 0.21y............(2)

Multiplying equation (1) by 1.41 and equation (2) by 0.81

12.69 = 1.1421x + 1.5651y

5.67 = 1.1421x – 0.1701y

Subtracting, we get

7.02% = 1.7352y

Y = 4.05%

Putting in equation (1), x = 5.56%

Hence, factor 1 = 5.56%

factor 2 = 4.05%