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# What is index arbitrage?

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Index Arbitrage is a trading strategy that profitably exploits price differences between the market value and the theoretical value of a stock index futures. If the index futures is seen trading below its theoretical value, it is anticipated that the futures is underpriced and the strategy will be to place long trades on the index futures and correspondingly short the underlying stocks that make up the index. On the contrary, if the index futures is trading above its theoretical value, it is considered to be overpriced, and the arbitrage strategy will be to short the futures and buy the underlying stocks.

The theoretical or the fair value of a futures/ forward contract is the spot price plus the cost carrying the underlying asset; in this case, equities, until the maturity/expiry of the futures contract. In this particular instance, the fair value of the futures contract will take into account the loss of income arising from the interest on the cost of margins on the index futures, losses arising from non-receipt of dividends and bonus since the investor is holding a futures contract instead of the underlying stocks that are included in the index. So, the fair value of the index futures is the value at which it should trade taking into account the costs involved, as mentioned earlier.

However, if there is a spread between the fair value and the market value of the index futures, and the spread is wide or narrow enough to cover trading costs such as commissions and taxes, it will give rise to Index Arbitrage opportunities.

The formula to calculate the fair value of a Stock Index futures is highlighted below

Fair value   = Cash X (1 + r (x/360) – dividends)

Cash           = Cash price of the stock index

R                  = Risk-free interest rate

X                  = Time to maturity/ expiry

Dividends   = Total dividends paid by the listed companies in the index until the maturity of the futures contract.

#### Limitations of Index Arbitrage-

• The strategy is complex and cannot be implemented manually since it involves placing trades within a small window of opportunity on a large number of stocks that make up the index.
• These strategies are generally automated, and the cost of purchasing and maintaining such systems is astronomical.
• Index Arbitrage comes with huge transaction costs since it involves the simultaneous purchase and sale of a large number of securities along and the Index futures.

To conclude, index arbitrage is a relatively low-risk arbitrage strategy, but the massive costs, manpower and time required to successfully employ the strategy make it a hard bargain for retail investors, which is why it is primarily used by Institutional brokers and money managers.