A portfolio manager has the following five stocks in his portfolio: Security No. of Shares Price/Share (₹) Beta A 10,000 50 1.2 B 5,000 20 2.0 C 8,000 25 0.7 D 1,000 100 1.0 E 500 200 1.3 Required: (a) Calculate Portfoli

(a) Computation of Portfolio Beta Security No. of Shares Market Price of Share Market Value (in ₹) W₁ Beta (β) Portfolio Beta W₁ × β A 10,000 50 5,00,000 0.5 1.2 0.60 B 5,000 20 1,00,000 0.1 2.0 0.20 C 8,000 25 2,00,000 0.2 0.7 0.14 D 1,000 100 1,00,000 0.1 1.0 0.10 E 500 200 1,00,000 0.1 1.3 0.13 10,00,000 1.17 Portfolio Beta = 1.17 Alternatively, Security No. of Shares Market Price of Share Market Value (a) (in ₹) Beta (β) (b) Product (a) x (b) A 10,000 50 5,00,000 1.2 6,00,000 B 5,000 20 1,00,000 2.0 2,00,000 C 8,000 25 2,00,000 0.7 1,40,000 D 1,000 100 1,00,000 1.0 1,00,000 E 500 200 1,00,000 1.3 1,30,000 10,00,000 11,70,000 Therefore, portfolio beta = Product / Market Value = 11,70,000 / 10,00,000 = 1.17 (b) Reduce beta to 0.8 Value of the Portfolio To reduce the beta from 1.17 to 0.8, the portfolio manager may sell off a portion of the portfolio and use the proceeds to buy the risk free securities. Let the percentage investment in existing Portfolio is W₁ and percentage investment in risk free securities is 1-W₁ Beta of the Portfolio = (W₁ x Existing Portfolio β) + [(1-W₁) x β of R f ] 0.8 = 1.17 W₁ + (1-W₁) 0 W₁ = 0.8 / 1.17 = 0.6838 Conclusion: This implies that a portfolio consisting of ₹6,83,800 (0.6838 x 10,00,000) invested in the 5 securities above and ₹3,16,200 in R f investment will have a beta of 0.8. Alternate Solution Beta can be reduced replacing High Beta stocks in the portfolio with Risk Free investments, which carry a Beta of Zero Security Beta Proportion (Amt. Invested) Product Risk Free Investments 0 X 0 Risky Securities 1.17 1-x 1.17-1.17x 1 1.17-1.17x Therefore, portfolio Beta = Product ÷ Amount Invested = (1.17 - 1.17x) / 1 = 0.8 1.17 - 1.17x = 0.8 1.17x = 1.17 - 0.8 = 0.37 x = 0.37 / 1.17 = 0.3162 or 31.62% for Risk Free Investments and 68.38 for risky investments. Therefore, amount to be invested in Risk Free Investments is as follows - (a) Alternative One - Overall Portfolio value is retained at ₹10,00,000 Amount to be invested in Risk free Investments = 31.62% × ₹10,00,000 = ₹3,16,200 Therefore, Risky Investments will constitute = 68.38% × ₹10,00,000 = ₹6,83,800