8. Mr. A, a HNI invested on 1.4.2014 in certain equity shares as below: Name of Co. No. of shares Cost (₹) X Ltd. 1,00,000 (100 each) 2,00,00,000 Y…

8. (i) Average return from the portfolio for the year ended 31.3.2015 Calculation of return on portfolio for 2014-15 (Calculation in ₹ / share) X Ltd. Y Ltd. Dividend received during the year 10 3 Capital gain/loss by 31.03.15 Market value by 31.03.15 220 290 Cost of investment 200 300 Gain/loss 20 (-)10 Yield 30 (-)7 Cost 200 300 % return 15% (-)2.33% Weight in the portfolio 57.14 42.86 Weighted average return 7.56% (ii) Average return from the portfolio for the year ended 2015-16 shall be calculated using the concept of joint probability as follows: X Ltd. Path Income from Dividend Gain from Market Price (₹) Total Yield (₹) Joint Prob. Exp. Yield (₹) 1 10 220 – 220 = 0 10 0.20 x 0.20 = 0.04 0.40 2 10 250 – 220 = 30 40 0.20 x 0.50 = 0.10 4.00 3 10 280 – 220 = 60 70 0.20 x 0.30 = 0.06 4.20 4 15 220 – 220 = 0 15 0.30 x 0.20 = 0.06 0.90 5 15 250 – 220 = 30 45 0.30 x 0.50 = 0.15 6.75 6 15 280 – 220 = 60 75 0.30 x 0.30 = 0.09 6.75 7 20 220 – 220 = 0 20 0.50 x 0.20 = 0.10 2.00 8 20 250 – 220 = 30 50 0.50 x 0.50 = 0.25 12.50 9 20 280 – 220 = 60 80 0.50 x 0.30 = 0.15 12.00 Expected Yield (₹) = 49.50 Market Value on 01.04.2015 (₹) = 220 % Return = 22.50 Y Ltd. Path Income from Dividend (₹) Gain from Market Price (₹) Total Yield (₹) Joint Prob. Exp. Yield (₹) 1 1.50 290 – 290 = 0 1.50 0.20 x 0.20 = 0.04 0.06 2 1.50 310 – 290 = 20 21.50 0.20 x 0.50 = 0.10 2.15 3 1.50 330 – 290 = 40 41.50 0.20 x 0.30 = 0.06 2.49 4 2.00 290 – 290 = 0 2.00 0.30 x 0.20 = 0.06 0.12 5 2.00 310 – 290 = 20 22.00 0.30 x 0.50 = 0.15 3.30 6 2.00 330 – 290 = 40 42.00 0.30 x 0.30 = 0.09 3.78 7 3.50 290 – 290 = 0 3.50 0.50 x 0.20 = 0.10 0.35 8 3.50 310 – 290 = 20 23.50 0.50 x 0.50 = 0.25 5.88 9 3.50 330 – 290 = 40 43.50 0.50 x 0.30 = 0.15 6.52 Expected Yield (₹) = 24.65 Market Value on 01.04.2015 (₹) = 290 % Return = 8.50 Weight in portfolio (1,00,000 x 220): (50,000 x 290) = 60.27:39.73 Weighted average (Expected) return (0.6027 x 22.50 + 0.3973 x 8.50) = 16.94% (iii) To analyze the risk of each investment we need to calculate the Standard Deviation of each investment as follows: X Ltd. Path Prob. (1) Yield (₹) Dev. (P X -P̄ X ) Square of dev. (2) (1) X (2) 1 0.04 10 -39.50 1560.25 62.41 2 0.10 40 -9.50 90.25 9.03 3 0.06 70 20.50 420.25 25.22 4 0.06 15 -34.50 1190.25 71.42 5 0.15 45 -4.50 20.25 3.04 6 0.09 75 25.50 650.25 58.52 7 0.10 20 -29.50 870.25 87.03 8 0.25 50 0.50 0.25 0.06 9 0.15 80 30.50 930.25 139.54 σ² X = 456.27 Standard Deviation (σ X ) = 21.36 Y Ltd. Path Prob. (1) Yield (₹) Dev. (P Y -P̄ Y ) Square of dev. (2) (1) X (2) 1 0.04 1.50 -23.15 535.92 21.44 2 0.10 21.50 -3.15 9.92 0.99 3 0.06 41.50 16.85 283.92 17.04 4 0.06 2.00 -22.65 513.02 30.78 5 0.15 22.00 -2.65 7.02 1.05 6 0.09 42.00 17.35 301.02 27.09 7 0.10 3.50 -21.15 447.32 44.73 8 0.25 23.50 -1.15 1.32 0.33 9 0.15 43.50 18.85 355.32 53.30 σ² Y = 196.75 Standard Deviation (σ Y ) = 14.03 Although Expected Return is higher in case of X Ltd. but it also has higher risk due to High S.D.