Question

A fund manager has a portfolio worth $50 million with a beta of 0.87. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on a well-diversified index to hedge its risk. The current level of the index is 1250, one contract is on 250 times the index, the risk-free rate is 6% per annum, and the dividend yield on the index is 3.15% per annum. The current 3-month futures price is 1260. a. What position should the fund manager take to eliminate all exposure to the market over the next two months? b. Calculate the effect of your strategy on the fund manager's returns if the level of the market in two months is 1,000,1,100,1,200, 1,300, and 1,400. Assume that the one-month futures price is 0.3% higher than the index level at this time.

Answer 1

Solution :- a portfolio worth $50 milion with a bela 0.87 rent lever of the index is 1250, one Contract is an 950 times. a) position should the fund manager take to hedge all exposure to the market over the next & months the fund managed is wooried about the performance - market over the next a months he expects that the Market would do down. In order to hedge the to man in order to hedge the risk of any fall in the index, the manager should take a short position in the futures. Next, we need to decide how many contracts need to be short. Here, the given beta of 0.87 is the optimal hedge ratio & the number of Contracts to be shorted is given as M B X amount of fonds available amount of futur escontracts 0.87 X 50,000,000 - (1259 Xa50) = 138.20 .: 138 futures Contracts need to be short

The effect of your strategy on the fond managers, futures price spot price x (1+0.025) Strike price : 1280 in from futures = (strike- spot) x 138 x 250 divident yield = 0.0382 - 12. index Return (spot price/1250)-1 total market Return = dividend yield & index Reforn CAPM Return = Rp + B x (Rm - Rf) profit portfolio Loss login - CAPM Retorn x 50,000,000 Total Loss Chain - port folio Loss laain + Cain from futur index Future price strike-spot gain from futures dividend freed index Return Total Market Return 1000 10025 256.5. 8849250 0.50% -20%. -19.50%. 1100 1102.75 15625 S390625 0-507. -28. -4.507. -3.504. 56 1932000 0.50% -4% 1303.25 -4.25 -1526625 0.50%. A 4.50% 12.50% 1400 1403.5 -104.5 0.50%. 12 x -CA85250 Portfolio Loss Total gain/Loss CAPMI Return - 16.83 . -8417500 431750 -9.87% -4937500 u53125 471500 -2.91% -1457500 4.ouz 11.07. 2023500 5502500 495875 517250

the index has fallen down from 1250 in an five cases, there is loss in the portfolio but garn from the futures ! Contrack