On January 1, 2023 an investor has a portfolio of 5 securities as given below: Security Price (Rs.) No. of shares Beta A 612.65 3000 ? B 334.20 5000…

(i) Calculation of beta of Security A Let beta of Security A is β A Security Price of the Stock No. of shares Value Weightage w i Beta B i Weighted Beta A 612.65 3,000 18,37,950 0.113 β A 0.113 β A B 334.20 5,000 16,71,000 0.102 1.15 0.117 C 454.45 6,000 27,26,700 0.167 0.40 0.067 D 775.10 10,000 77,51,000 0.475 0.95 0.451 E 781.05 3,000 23,43,150 0.143 0.85 0.122 1,63,29,800 0.757 + 0.113 β A Since the Portfolio beta is 0.859, the beta of Security A shall be: 0.757 + 0.113 β A = 0.859 β A = 0.903 or 0.90 (ii) Calculation of Theoretical Value of Future Contract Cost of Capital = 10.5% p.a. Accordingly, the Continuously Compounded Rate of Interest In (1.105) = 0.0998 For February 2023 contract, t = 58/365 = 0.1589 Further F= S e rt F= 6,500e (0.0998)(0.1589) F= 6,500e 0.015858 F= 6,500 X 1.01598 = 6,603.87 Alternatively, it can also be taken as follows: = 6500 e 0.105×58/365 = 6500 e 0.01668 = 6500 x 1.01682 = 6,609.33 (iii) When total portfolio is to be hedged: = (Value of Spot Position requiring hedging / Value of Future Contract) × Portfolio Beta = (16329800 / (6603.87 × 200)) × 0.859 = 10.62 contracts say 11 contracts Or = (16329800 / (6609.33 × 200)) × 0.859 = 10.61 contracts say 11 contracts (iv) Revised Portfolio Beta if 4 Future contracts are sold to investor: 4 = (β P - 0.859) × (16329800 / (6603.87×200)) β P = 1.18 Or 4 = (β P - 0.859) × (16329800 / (6609.33×200)) β P = 1.18