Arbitrage is the action of profiting from price anomalies across various markets. In the stock index futures market, such opportunities become available when the futures and the underlying shares move significantly out of line from the theoretical value (fair value) of the futures contract. When such a situation arises, there may be an opportunity to profit from this temporary mispricing in the knowledge that the two markets will return to parity (equality) at the time of futures expiry.
Calculating Fair Value
Theoretically, the price of stock index futures over a given period should approximate the opportunity cost of holding shares (the risk free interest rate) less the amount of dividends (expressed as a percentage) over the period to contract expiry.
The cost of carry can be determined by looking at whether to buy futures or the underlying shares:
- An investor in the share market would have to pay for the shares now but in return would be entitled to receive dividends.
- The futures investor would not need to pay for the shares now. Therefore he can invest the funds and receive interest. However, he foregoes any dividends.
The futures price needs to reflect the interest that can be earned and the dividends that are foregone. In a nutshell, the fair value formula is something like this:
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