Mr. RJ own two securities X and Y are priced according to a two-factor Arbitrage Pricing Model. The factor sensitivities and expected returns are as…

(i) λ₁ = 4% and λ2 = 5% APT required return (X) = Rf + λ₁β1 + λ2β2 + λ3β3 ... + λnβn = 6% + (1.2 x 4%) + (0.5 x 5%) = 13.3% Expected (actual) return 14% > required return 13.3%, Security X is underpriced (offer higher return than required) or Not correctly priced APT required return (Y) = Rf + λ₁β₁ + λ2β2 + λ3β3 ... + λnβn = 6% + (0.8 x 4%) + (1.4 x 5%) = 16.2% Expected (actual) return 16% < required return 16.2%, Security Y is overpriced (offer lesser return than required) or Not correctly priced or approximately correctly priced (ii) Targeted sensitivities F1 = 1.40 and F2 = 0.05, calculation of amount to be invested in Long position indicated as L and Short position as S Security X (F1) = β1 = 1.20; Security Y = β1 = 0.80 Security X (F2) = β2 = 0.5; Security Y = β2 = 1.4 Equation 1.20L – 0.8S = 1,40,000 (i) (sensitivity 1.40 x 100000) Equation 0.50L – 1.4S = 5,000 (ii) (sensitivity 0.05 x 100000) Multiply equation first by 1.4 and second by 0.8 and subtracted (ii) from (i) 1.68L – 1.12S = 1,96,000 0.40L – 1.12S = 4,000 1.28L = 192000 so long position L = 1,50,000 Now put value of L in equation (i) 1,80,000 -0.8S = 1,40,000 So, amount of short position = 40,000/0.8 = 50,000 Analysis Mr. RJ is using - 1,00,000 of his own capital and creating: A larger long exposure - 1,50,000 and financed partly through short selling - 50,000. OR This means the portfolio is leveraged, because total exposure (₹ 2,00,000 is greater than own funds) and the portfolio is highly sensitive to Factor 1.