Mr. A owns a portfolio with the following characteristics: Security X Security Y Risk Free security Factor 1 sensitivity (λ1) 0.80 1.50 0 Factor 2…

CA Final · Advanced Financial Management · MTP · November 2024
Mr. A owns a portfolio with the following characteristics: Security X Security Y Risk Free security Factor 1 sensitivity (λ1) 0.80 1.50 0 Factor 2 sensitivity (λ2) 0.60 1.20 0 Expected Return* 15% 20% 10% * Generated by a two-factor model. Required: (i) Compute the sensitivity of Mr. A's portfolio to the two factors if Mr. A has - 3,00,000 to invest and sells short - 1,50,000 of security Y and purchases - 4,50,000 of security X. (ii) Compute the sensitivity of the portfolio to the two factors if Mr. A borrows - 3,00,000 at the risk free rate and invests the amount he borrows along with the original amount of 3,00,000 in security X and Y in the same proportion as described in part (i). (iii) Suppose Mr. D, one of the friend of Mr. A says the expected return premium of factor 1 is zero. Do you agree with this statement. Substantiate your answer with required calculations.

Suggested Answer and Working Notes:

(i) Mr. A's position in the two securities are +1.50 in security X and -0.5 in security Y. Hence the portfolio sensitivities to the two factors:- λ1 = 1.50 x 0.80 + (-0.50 x 1.50) = 0.45 λ2 = 1.50 x 0.60 + (-0.50 x 1.20) = 0.30 (ii) Mr. A's revised position:- Security X 9,00,000 /3,00,000 = 3 Security Y -3,00,000 /3,00,000 = -1 Risk free asset -300000 /300000 = -1 λ1 = 3.0 x 0.80 + (-1 x 1.50) + (- 1 x 0) = 0.90 λ2 = 3.0 x 0.60 + (-1 x 1.20) + (-1 x 0) = 0.60 (iii) Expected Return = Risk Free Rate of Return + Risk Premium for each sensitivity factor Accordingly 15 = 10 + 0.80 λ1 + 0.60 λ2 20 = 10 + 1.50 λ1 + 1.20 λ2 On solving equation, the value of λ1 = 0 Yes, Mr. D is correct in his observation.

Topics: Portfolio Management

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