Factor Model for Delta-Hedged Options Returns

Options are contracts that allow traders to buy or sell a security at a predetermined price. Options give the holder the right, but not the obligation, to buy (call option) or sell (put option). They are traded on exchanges like stocks and have their own ticker symbols. Options can be used to hedge against risks and/or speculate on price movements. They offer traders the ability to leverage their capital in order to increase potential returns.

Options are versatile instruments that allow traders to express different views on the market. They can be used to speculate not only on the direction of an asset but also on the degree of movement. Options traders can position themselves to benefit from a volatile or range-bound market, as well as capitalize on news events and corporate announcements. Furthermore, options can be used to create synthetic positions that mimic the effects of owning a security, but without actually having to own it.

Reference [1] examined the returns of delta-hedge options positions by applying a factor model. Traditionally, factor models have been used mainly in the equity market. The article pointed out

Motivated by the theory, we construct new empirical factors based on the following five option characteristics: option illiquidity, option price, the difference between option-implied volatility and realized volatility, the difference between option-implied skewness and realized skewness, and the difference between option-implied kurtosis and realized kurtosis. After constructing the factors, we test if they are explained by existing models and find that established factor models for stock, bond, and option markets can hardly explain our new factors for option returns. Then, we conduct a number of asset pricing tests to evaluate the relative performance of our factor model. The tests demonstrate its superior performance; the average absolute alpha on the test portfolios (constructed with 35 option characteristics and 93 stock characteristics) is significantly reduced by the newly proposed factor model, whereas the existing factor models cannot explain a substantial portion of the realized returns on the long-short portfolios of equity options.

This article highlighted some important points that are not discussed often in the trading community, notably,

• Seemingly large options returns are in fact compensation for volatility risk, tail/jump risk, and liquidity risk in the options market.
• Delta-hedged options returns are functions of the differences between the physical and risk-neutral moments (volatility, skewness, and kurtosis) as well as option price and option illiquidity.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Bali, Turan G. and Cao, Jie and Chabi-Yo, Fousseni and Song, Linjia and Zhan, Xintong, A Factor Model for Stock Options (2022) https://ssrn.com/abstract=4308916

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