Dispersion Trading in Finance: All You Need to Know

What is Dispersion Trading?

Dispersion trading involves selling options on an index and buying options on individual stocks. This technique exploits correlations during both routine and major market swings. If individual asset returns are widely scattered, the index may not move much, but individual assets may see significant volatility. This would result in a significant reward for individual asset options but little return on the short index option.

A Short Example

You purchased straddles on SP500 constituents and sold one on the index itself.
On most days, there is little profit or loss on this position, as well as gains or losses on the equities balance and the index. Equities can fluctuate drastically, with one half rising and the other falling, with no impact on the overall index. On this day, you can profit from stock options based on gammas and short index options due to time decay. On that day, individual equities were well distributed.

A Deep Dive into Dispersion Trading

The volatility on an index, , can be approximated by,

There are N constituent stocks with volatilities , weighted by value , and correlations . (I say ‘approximate’ since we are dealing with a sum of lognormals, which are not lognormal, but this approximation is adequate.)

Using the implied volatilities of individual stocks and the index option, you may calculate a ‘average’ across all stocks.

Dispersion trading involves comparing an indicated correlation to one’s own forecast, based on previous study.

The competing effects in a dispersion trade are

• Gamma profits vs time decay for each long equity option.
• Gamma losses against time decay (a source of profit) for short index options.
• The correlation between individual equities.

In the scenario above, half of the stocks increased in value while the other half decreased. If they went beyond their suggested volatilities, they would profit. Profit for each stock is determined by the option’s gamma and implied volatility, with a parabolic relationship with the stock move. The index option’s gamma determines the profit potential, as it is unlikely to change much.
In this situation, the average correlation would be zero, resulting in low index volatility.

If all stocks move in the same direction, individual stock options would generate the same profit, but this would be offset by the gamma loss on index options. This refers to a one-to-one correlation among all stocks and high index volatility.

Why might dispersion trading be successful?

• Market dynamics are complicated and cannot be fully understood through correlation.
• Index options may be pricey due to high demand, making them ideal for selling.
• You can buy options on equities with large dispersion. Consider stocks that exhibit significant volatility during stressful periods. This could be due to industry differences, competition, or potential mergers.
• It is not necessary to buy all of the index constituents. Consider investing in equity options with lower volatility.

Why might dispersion trading be unsuccessful?

• The technique is too detailed to handle a large number of contracts with bid-offer spreads.
• Consider using delta hedging for potentially pricey positions.
• During market crashes, it’s important to consider the potential downside.

Related Readings

• Put-Call Parity: All You Need To Know
• Modelling Approaches in Quantitative Finance: All You Need To Know
• Central Limit Theorem In Finance: Power Your Portfolio Now