Mr. X owns a portfolio with the following characteristics: Security A Security B Risk Free security Factor 1 sensitivity 0.80 1.50 0 Factor 2…

(i) Mr. X's position in the two securities are +1.50 in security A and -0.5 in security B. Hence the portfolio sensitivities to the two factors: b prop. 1 =1.50 x 0.80 + (-0.50 x 1.50) = 0.45 b prop. 2 = 1.50 x 0.60 + (-0.50 x 1.20) = 0.30 (ii) Mr. X's revised position: Security A: 3,00,000 /1,00,000 = 3 Security B: - 1,00,000 /1,00,000 = -1 Risk free asset: -100000/100000 = -1 b prop. 1 = 3.0 x 0.80 + (-1 x 1.50) + (- 1 x 0) = 0.90 b prop. 2 = 3.0 x 0.60 + (-1 x 1.20) + (-1 x 0) = 0.60 (iii) Expected Return = Risk Free Rate of Return + Risk Premium Let λ 1 and λ 2 are the Value Factor 1 and Factor 2 respectively. Accordingly 15 = 10 + 0.80 λ 1 + 0.60 λ 2 20 = 10 + 1.50 λ 1 + 1.20 λ 2 On solving equation, the value of λ 1 = 0, and risk premium of factor 2 for Securities A & B shall be as follows: Using Security A's Return Total Return = 15% = 10% + 0.60 λ 2 Risk Premium (λ 2 ) = 5%/ 0.60 = 8.33% Alternatively using Security B's Return Total Return = 20% = 10 + 1.20 λ 2 Risk Premium = 10%/ 1.20 = 8.33%