Pricing of Index Futures

The index futures are the most popular futures contracts as they can be used in a variety of ways by various participants in the market.
How many times have you felt of making risk-less profits by arbitraging between the underlying and futures markets. If so, you need to know the cost-of-carry model to understand the dynamics of pricing that constitute the estimation of fair value of futures.
The cost of carry model
The cost-of-carry model where the price of the contract is defined as:
F=S+C
where:
F Futures price
S Spot price
C Holding costs or carry costs
If F < S+C or F > S+C, arbitrage opportunities would exist i.e. whenever the futures price moves away from the fair value, there would be chances for arbitrage.
If Wipro is quoted at Rs 1000 per share and the 3 months futures of Wipro is Rs 1070 then one can purchase Wipro at Rs 1000 in spot by borrowing @ 12% annum for 3 months and sell Wipro futures for 3 months at Rs 1070.
Here F=1000+30=1030 and is less than prevailing futures price and hence there are chances of arbitrage.
Sale                 = 1070
Cost= 1000+30 = 1030
Arbitrage profit         40
However, one has to remember that the components of holding cost vary with contracts on different assets.

Futures pricing in case of dividend yield

We have seen how we have to consider the cost of finance to arrive at the futures index value. However, the cost of finance has to be adjusted for benefits of dividends and interest income. In the case of equity futures, the holding cost is the cost of financing minus the dividend returns.
Example:
Suppose a stock portfolio has a value of Rs 100 and has an annual dividend yield of 3% which is earned throughout the year and finance rate=10% the fair value of the stock index portfolio after one year will be F= Rs 100 + Rs 100 * (0.10 – 0.03)
Futures price = Rs 107
If the actual futures price of one-year contract is Rs 109. An arbitrageur can buy the stock at Rs 100, borrowing the fund at the rate of 10% and simultaneously sell futures at Rs 109. At the end of the year, the arbitrageur would collect Rs 3 for dividends, deliver the stock portfolio at Rs 109 and repay the loan of Rs 100 and interest of Rs 10.
The net profit would be Rs 109 + Rs 3 - Rs 100 - Rs 10 = Rs 2.
Thus, we can arrive at the fair value in the case of dividend yield.