A significant portion of trading in equity index futures actually comes from hedging activities where investors use futures to offset exposure in other equity positions. One common approach is to sell index futures to hedge a long equity portfolio. If the index declines, this short futures position will gain in value helping to offset losses in the investors' long position in their equity portfolio. To determine the number of futures contracts required for an equity hedge, investors calculate the hedge ratio. The hedge ratio ensures that the notional value of the future's position matches the value of the portfolio being hedged and is calculated by dividing the value of the equity portfolio by the futures contract size. Which itself is calculated as the future's price multiplied by the contract multiplier or the value of one index point in the futures contract. Let's dive into an example to see how equity index futures can help hedge an underlying equity portfolio and how the hedge ratio is calculated. Here we have an investor who holds a long position in S&P 500 companies with a portfolio valued at $100 million. This investor expects a short term correction in the stock market and wants to temporarily hedge their exposure.

The relevant E-mini S&P 500 futures contracts is currently trading at 4,565.75. Given a contract multiplier of 50, meaning each index point is worth $50, the contract size is $228,287.50.

To calculate the hedge ratio, we divide the value of the equity portfolio $100 million by the future's contract size, $228,287.50. This gives us approximately 438.04 contracts. Since it's not possible to trade fractional contracts, the investor would likely sell 438 contracts to set up this hedge, let's assume the hedge is put in place by selling 438 contracts at 4,565.75. Now, suppose that over the next few trading sessions, the equity index along with the investor's portfolio declines by 10%. The loss on the cash portfolio is straightforward to calculate, it's 10% of 100 million, which is $10 million. Now let's look at the future's position. The investor sold futures at 4,565.75, and with a 10% market drop, the index falls by approximately 456.6 points to 4,109.15.

Since the investor is short futures, they can now buy back the contracts at this lower price. Realizing a profit on the short position, the total gain per contract is 456.6 points, and with 438 contracts, the overall gain on the future's position, ignoring transaction costs throughout this example, is calculated as the 438 contracts times the 456.6 gain per contract times the $50 multiplier, which equals $9,997,350. This almost completely offsets the cash portfolio loss of $10 million.

The slight difference is due to rounding down to 438 contracts resulting in a minor under hedge. However, compared to the 10 million portfolio loss, a net difference of $2,650 is a minimal cost for a close to perfect hedge.