Rahul Trivedi, usually invests in stock market for a long run but becomes active whenever he finds that market is going to be volatile. Recently after a long interaction with a stock market expert...

Rahul Trivedi, usually invests in stock market for a long run but becomes active whenever he finds that market is going to be volatile. Recently after a long interaction with a stock market expert during seminar he is thinking of arbitrage opportunities. He tries to create arbitrage opportunity using index future contract based on the following information pertaining to the index. The current level of the index is 4375. A six-month futures contract on the index can be purchased for 4550. Risk free rate (continuous compounding) is 6% per annum. Further it is also assumed that 50% of the stocks in the index which paid dividends last year will pay for this year too and that the dividend yield of 3% 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:
(a) Calculate the fair value of the index futures contract.

 (b) Verify whether there exists the scope for riskless arbitrage using index futures.

 (c) Calculate the investor’s gains/losses if the index stands at 4000, 5000 at the end of six months.

(You can assume the absence of taxes, transaction costs).