Index Arbitrage

Index arbitrage is a trading strategy that seeks to profit from differences between the price of a stock market index product, most often an index futures contract, and the combined price of the shares that make up the index. When the two drift apart by more than the cost of trading, an arbitrageur buys the cheaper side and sells the dearer one, expecting them to converge by the time the future expires.

The strategy is one of the oldest forms of program trading and is now carried out almost entirely by computers at banks, proprietary trading firms and market makers. It links the cash market for shares with the markets for index futures, index options and exchange traded funds, and it is the mechanism that keeps their prices consistent with one another.

The benchmark for the trade is the theoretical, or fair, price of the future. Holding the shares costs interest on the money tied up but earns dividends, so the future should trade at the index level adjusted for this net cost of carry:

• $F$ is the fair value of the futures contract.
• $S$ is the current level of the index.
• $r$ is the annual financing rate and $q$ is the annual dividend yield of the index, both as decimals.
• $T$ is the time to expiry in years.

Suppose an index stands at 5,000, the financing rate is 5 percent, the dividend yield is 1.5 percent and the future expires in three months. Fair value is $5{,}000 \times e^{0.035 \times 0.25} = 5{,}043.9$. The gap between the futures price and the index is called the basis, and here its fair level is about 43.9 points.

If the future trades at 5,052 against a fair value of 5,043.9, it is about 8 points rich. The arbitrageur sells the future and at the same moment buys every share in the index in its index weight, a position known as cash and carry. At expiry the future settles at the index level, so the 8 points are locked in, less costs. If the future trades below fair value, the trade is reversed: buy the future and sell the shares, which requires holding them already or short selling them.

The trade is worth doing only when the mispricing exceeds the total transaction cost: commissions and exchange fees, the bid-ask spread on several hundred shares and on the future, transaction taxes where they apply, and stock borrowing fees on the short side. These costs define a band around fair value inside which no arbitrage is possible. For the most liquid indices the band is a small fraction of one percent.

• Futures against a basket. This is the classic form described above. Some traders use a smaller basket that follows the index closely instead of every constituent, which cuts costs but leaves tracking error.
• ETF arbitrage. An ETF's market price is compared with its net asset value. Authorised participants create or redeem ETF shares in exchange for the underlying basket when the two diverge.
• Futures against ETFs or options. The future is traded against an ETF on the same index, or against a synthetic future built from index options.
• Index rebalancing. Trading around announced additions to and deletions from an index is related, but it is not pure arbitrage because it carries price risk.

Index arbitrage is described as riskless in textbooks, but several things can go wrong in practice. Execution risk is the largest: the trader must complete hundreds of share orders and a futures order before prices move, and a partly filled basket is an unhedged position. Dividends may turn out different from the forecast used in the fair value calculation. Financing rates can change, stock on loan can be recalled, and short-selling restrictions can block one direction of the trade. Because the profit on each trade is small, positions are large and are usually financed with borrowed money.

Speed matters because the opportunity is visible to everyone. Firms place servers in exchange data centres through colocation and invest in low latency links between futures and equity markets, such as the route between Chicago and the New York area. Here the strategy overlaps with high-frequency trading.

Index arbitrage became widespread after stock index futures were introduced in the United States in 1982. It drew public attention after the crash of October 1987, when official inquiries examined the part played by program trading and portfolio insurance, and for some years afterwards the New York Stock Exchange restricted index arbitrage orders on days of large market moves. Most economists regard the activity as useful: it carries information between markets, supports price discovery and allows investors to treat futures, ETFs and shares as close substitutes. It differs from statistical arbitrage, which relies on historical relationships that may not hold, whereas index arbitrage relies on a contractual link at expiry.