How to Find Cheap Options to Buy and Expensive Options to Sell

If you want to make money trading, you’re going to need a way to identify when an asset is likely to be cheap and when it is likely to be expensive.

You want to be a net buyer of the cheap stuff and a net seller of the expensive stuff.

Thanks, Capitain Obvious.

You’re welcome.

How does this relate to equity options?

If we take the (liquid) US Equity options market as an example then there are an absolute ton of options contracts you could be trading.

95% of them are sufficiently fairly valued that you won’t make much money trading them once you’ve paid all the costs to buy and sell them and hedge your risk.

The remaining 5% are worth looking for.

Options have a positive dependency on volatility. In looking for “cheap” or “expensive” options, we’re really looking for cheap or expensive “volatility”.

So we ask the following questions:

• When does the forward volatility “implied” by options prices tend to be lower than the volatility that realises in the subsequent stock price process? We would look to buy these options.
• When does the forward volatility “implied” by options prices tends to be higher than the volatility that realises in the subsequent stock price process?  We would look to sell these options.

We want a quantitative way to our very large universe of potential stock options by criteria that have historically been predictive of under/over-pricing of volatility in options prices.

One good starting place is the many academic papers entitled “X and the cross-section of options returns”. 

This family of papers look at the extent to which historic under/over-pricing of volatility in options prices can be explained by causal factors such as size and momentum.

Here’s a summary of the key results:

• Value Factor – Options on value stocks tend to be overpriced relative to growth stocks
• Size Factor – Small-cap options tend to have overpriced volatility
• Idiosyncratic Vol Factor – Options on stocks with high idiosyncratic volatility tend to be overpriced. Options on stocks with low idiosyncratic volatility tend to be underpriced
• Beta Convexity Factor – Options on stocks with convex betas to the index tend to be underpriced (high downside beta / low upside beta)
• IV Term Structure Factor – Options for which shorter-term implied volatility (IV) is greater than longer-term IV tend to be underpriced. Options, where shorter-term IV is lower than longer-term IV, tend to be overpriced
• IV Premium Factor – Options with the lowest difference between historical realised and implied volatility tend to be underpriced. Options with a large difference tend to be overpriced.
• Momentum Volatility Factor – Options on stocks with high absolute momentum tend to be underpriced. Options on stocks with low absolute momentum tend to be overpriced.

Source Papers

• Ammann, Skovmand, Verhofen – Implied and Realized Volatility in the Cross-Section of Equity Options
• Cao, Han – Cross-Section of Option Returns and Idiosyncratic Stock Volatility
• Vasquez – Equity Volatility Term Structures and the Cross-Section of Option Returns
• Goyal, Saretto – Option Returns and Volatility Mispricing
• Sinclair- Volatility Trading
• Wilmott – CrashMetrics

A Word of Caution

Be aware that the “cross-section of options returns” literature tends to make these effects look juicier than they really are because:

• they don’t tend to model the opportunity cost of the margin you’d need to hold on your shorts
• they tend to assume midpoint execution, which is optimistic for less liquid options.