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A fund manager tries to create a hypothetical index future contract based on the following information pertaining to the index. The current level of the

A fund manager tries to create a hypothetical index future contract based on the following information pertaining to the index. The current level of the index is 3375. A six-month futures contract on the index can be purchased for 3525. The government's T-bill yield is 8%. Further it is also assumed that 60% of the stocks in the index which paid dividends last year will pay for this year too and that the dividend yield of 3.5% on the index will not change in future. The index has a multiple of 100 and the tenure of the futures contract is 6 months.

Required (15 MARKS)

a. Calculate the fair value of the index contract?

b. Verify whether there exists the scope for riskless arbitrage using stock index futures. (You can assume the absence of taxes, transaction costs).

c. Assume that the stock portfolio of an aggressive manager has a beta of 1.25. If markets are likely to go through a bearish phase in the next two years and the manager would like to reduce the beta of his portfolio to 0.75, how can he use index futures to manage his portfolio beta? How is it superior to stock trading?

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