What is 'Index Arbitrage'

The index arbitrage strategy attempts to profit from the differences between actual and theoretical prices of a stock market index. This is done by simultaneously buying, or selling, a stock index futures contract while selling, or buying, the stocks in that index.

The actual component of this trading strategy is most often a futures contract with the Standard & Poor's 500 being the most popular underlying index. The S&P 500 index arbitrage is often called basis trading. The basis is the spread between the cash and futures market prices.

The theoretical price represents the prices of all the stocks in the index inputted into the specific index calculation, such as capitalization-weighted.

BREAKING DOWN 'Index Arbitrage'

Index arbitrage is at the heart of program trading, where computers monitor both actual and theoretical prices and automatically enter buy or sell orders to exploit the differences. It is a high-speed, electronic trading process. Since major financial institutions actively pursue this strategy, the opportunities are often fleeting and razor-thin. 

Big institutions can execute large trades and still make money on such small differences. The more components of the index, the greater the chances of some of them being mis-priced, and the greater the opportunities for arbitrage. Therefore, arbitrage on an index of just a few stocks is less likely to provide significant opportunities.

Traders can also use arbitrage strategies on exchange-traded funds (ETFs) in the same way. Because most ETFs do not trade as actively as major stock index futures, chances for arbitrage are plentiful. ETFs are sometimes subject to major market dislocations, even though the prices of the underlying component stocks remain stable. 

Trading activity on August, 24, 2015 offered an extreme case where a large drop in the stock market caused erratic bid and ask prices for many stocks, including ETF components. The lack of liquidity and delays to the start of trading for these stocks was problematic for the exact calculation of ETF prices. This delay created extreme gyrations and arbitrage opportunities.

The Role of Arbitrage

All markets function to bring buyers and sellers together in order to set prices. This action is known as price discovery. Arbitrage might connote unsavory dealings used to exploit the market but it actually serves to keep the market in line. For example, some bit of news creates demand for a futures contract but short-term traders overplay it. The basket of underlying stocks, the index, does not move, therefore the futures contract becomes overvalued. Arbitrageurs quickly sell the futures and buy the cash to bring their relationship back in line.

Arbitrage is not an exclusive activity of the financial markets. Retailers can also find lots of goods offered at low prices by a supplier and turn around to sell them to customers. Here, the supplier may have an overstock or loss of storage space requiring the discounted sale. However, the term arbitrage is indeed mostly associated with trading of securities and relates assets.

Fair Value

In the futures market, fair value is the equilibrium price for a futures contract. This is equal to the cash, or spot price, after taking into account compounded interest and dividends lost because the investor owns the futures contract, rather than the physical stock itself, over a specific period. So, a future contract's fair value is the amount at which the security should trade. The spread between this value, also called the basis or basis spread, is where index arbitrage comes into play.

Fair value can show the difference between the futures price and what it would cost to own all stocks in a specific index. For example, the formula for the fair value on the S&P futures contract is (Fair value = cash * {1+r(x/360)} – dividends).

  • Cash is the current S&P cash value
  • r is the current interest rate that would be paid to a broker to buy all the stocks in the S&P 500 index
  • dividends are the total dividends paid until futures contract expiration expressed in terms of points on the S&P contract
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