Cost of Carry Model
The theoretical framework for pricing futures contracts, which derives the fair futures price as the spot price compounded at the risk-free interest rate over the holding period, adjusted for dividends and other carrying costs, forming the foundation of cash-futures arbitrage in Indian markets.
The cost of carry model was the bedrock of futures pricing theory. It answered the question: given a spot price today, what should the futures price be for delivery at some future date? The answer rested on the principle of no-arbitrage — that two instruments with identical cash flows should sell at the same price, or else risk-free profit opportunities would arise.
In the simplest continuous compounding formulation, the fair futures price F equalled the spot price S multiplied by e raised to the power of (r minus q) multiplied by T, where r was the continuously compounded risk-free interest rate, q was the continuous dividend yield on the underlying, and T was time to expiry in years. For an index like Nifty, dividends were relevant because the futures contract tracked the price index (not the total return index), so futures sellers did not receive dividends. This made Nifty futures trade at a slight discount to what a pure interest-rate formula would suggest.
For individual stocks, the dividend adjustment was critical. If a company was expected to pay a large dividend before the futures expiry date, the ex-dividend drop in the stock price would reduce the futures price by an amount roughly equal to the present value of the expected dividend. Traders who tracked upcoming dividend dates for F&O stocks incorporated expected dividends into their fair value calculations.
In India, arbitrage funds — a category of mutual funds — systematically exploited deviations from cost-of-carry fair value. These funds bought the spot portfolio and shorted the corresponding futures to lock in the futures premium as a return, which was treated as capital gains (and later as equity fund returns for tax purposes). Their collective activity kept the basis — the difference between futures price and spot price — close to the theoretical cost-of-carry band during normal market conditions.
Deviations from the cost-of-carry model were informative. When futures traded at a steep premium beyond theoretical carry costs (positive basis significantly exceeding interest-adjusted fair value), it signalled strong demand for leveraged long positions. When futures traded at a discount to spot, it indicated bearish sentiment or forced selling pressure in the derivatives market.