#### Derivatives

| Updated on October 16, 2021

## Determining whether futures contract is overpriced is key

Derivatives can be used to set up arbitrage strategies aimed at capturing the difference between two traded prices. In this article, we discuss one such trade — spot-futures arbitrage.

## Implied rate

Spot-futures arbitrage involves buying a stock equivalent to the permitted lot size of its derivatives contract and shorting the near-month futures contract on the stock. Suppose you want to set up this position in Reliance Industries. You should buy 250 shares of Reliance Industries (or in multiples) and short one near-month futures contract.

There are two principles relating to the spot-futures arbitrage. First, you should determine if futures contract is overpriced relative to its theoretical price. Shorting the futures contract — because its price is greater than the spot price — will not generate profits; for futures, price must be typically greater than the spot price.

There is a simple way to determine if futures contract is overpriced relative to its theoretical price. You must input the futures price, the stock price, and the time to maturity into a (no-arbitrage) futures valuation model. This way, you can find the implied rate — the rate that market participants are willing to pay to buy the near-month futures contract. If this implied rate is greater than prevailing market interest rate for similar maturity, then the futures contract is overpriced. So, if the implied rate is 8.5 per cent whereas the market rate is 5.5 per cent, you can earn three percentage points on this trade without considering transaction costs.

The second principle is based on price convergence. Based on the no-arbitrage argument, futures price must converge with the spot price at expiry. Therefore, the difference between the futures price and the stock price when you initiate the trade will be your profit (excluding transaction costs) if you hold the position till expiry. Suppose you buy 250 shares of Reliance Industries at 2655 and short one near-month futures contract at 2665. You will lock in to 2500 points (10-point price differential times 250), whether the stock trades below or above 2655 at the expiry of the futures contract. Note that the trade will be profitable only if this differential is greater than the costs associated with the strategy.

Arbitrage opportunities do not exist for extended periods of time because market participants are always trying to set up such trades. There are mutual funds (called arbitrage funds) that specialise in spot-futures arbitrage. You can buy one such fund if you are unable to set up this strategy for lack of time and resource.

You do not have to keep your spot-futures position open till maturity of the contract. This decision assumes relevance because derivatives are now delivery-based unlike the cash-settlement system earlier. You can close your position any time before expiry if unwinding gives you handsome profits. The trade will be profitable if the difference between futures price and spot price at the time of unwinding is lower than the difference when you set up the position.

You can also carry your arbitrage position for a longer time by simply rolling your short futures position to the next month while continuing with your long stock position. Suppose you carry a long stock position in Reliance Industries. You could roll over your October futures short position to the next month during the expiry week. Your objective is to shift to the next month at a price closer to the current month price, if not at a higher price. A higher price is better because you are rolling a short position.

A reverse arbitrage is when the stock trades at a higher price to futures contract. So, you must set up a short stock, long futures position to capture price differential. But setting this up can be difficult and expensive because you must borrow the shares to deliver in spot (cash) market.

The author offers training programmes for individuals to manage personal investments

Published on October 16, 2021