Question#4 Suppose there are two independent economic factors, F1 and F2. The ri

Question

Question#4 Suppose there are two independent economic factors, F1 and F2. The risk-free rate is 5%. Portfolio A and B are both well diversified and their expected returns are shown in the following table. Portfolio Expected Return 25% 20% Beta on F1 Beta on F2 Portfolio 0 1.2 0.5 1.5 1) What are the expected risk premiums of the two factors? 2) There is another portfolio C. Its beta on F1 is 1.6 and its beta on £2 is 1.2. What is the expected return of portfolio C? [4=x y ~ lo-t lf-@10-4.67-s.33 Cp

Explanation / Answer

Risk free rate = 5%

Expected return of portfolio A = 5% + 1.2F1 + 0.6F2

                                          25% = 5% + 1.2F1 + 0.6F2                                         

                                          20% = 1.2F1 + 0.6F2 ------------------ (1)

Again

Expected return of portfolio B = 5% + 0.5F1 + 1.5F2

20% = 5% + 0.5F1 + 1.5F2

15% = 0.5F1 + 1.5F2------------------- (2)

Now by solving equation 1 and equation 2

Multiply equation 2 by 0.6 and multiply equation 1 by 1.5 and subtract them both equation

30% - 9% = 1.8F1 - 0.3F1 + 0.9F2 – 0.6F2

          21% = 1.5F1

F1 = 14%

Now Value of F2

20% = 1.2 × 14% + 0.6F2

0.6F2 = 3.20%

F2 = 5.33%

So equation for relation between beta of expected return is mention below:

Expected return = 5% + 14% ×1 + 5.33% × 2

b.

Expected return of C = 5% + (14% ×1) + (5.33% × 2)

   = 5% + (14% × 1.6) + (5.33% × 1.2)

   = 5% + 22.40% + 6.40%

   = 33.80%

Expected return of Portfolio C is 33.80%.

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