Fat Tails and Options Selling, Part II

Previously, we discussed how market returns are distributed by focusing on a single stock. This time, we are going to look at a focused but sector diversified ETF – the Financial SPDR (ticker: XLF). Remember, the tentative conclusions drawn before implied that historical volatility measures lose their value beyond a short time frame, and that returns display leptokurtosis – a fancy statistical term meaning that, unlike a classic Gaussian bell curve, more observations are clustered around the average, as well as more observations being very far from the average.

The first chart displays “leptokurtosis” visually, and shows how using a large amount of historical volatility data leaves one vulnerable to large moves.

As was demonstrated last time, modeling the distribution of returns is better done when used with only a small amount of very recent data about volatility. The chart below uses rolling 30-day volatility paired with randomly generated Gaussian variables to model expected daily fluctuations, and does a better job responding to increased volatility.

Zooming in to focus on the larger sigma events shows the value of the model using shorter, rolling volatility (graph 1) over a longer cumulative estimate (graph 2).

But, there is still the problem that returns cannot be modeled by a bell curve – we need much more advanced math than can be covered here. Hopefully for now, it will suffice to say that properly assessing volatility is a key determinant of risk management for selling options. Next time, we will apply the quantitative framework used above to discuss writing naked options – one of the most advanced, high risk/high reward strategies.

For now, consider the final chart below, which shows the two volatility measures used to generate the models above.

What is the best way to determine the fair value of volatility? As a major component of pricing options, volatility (and its effects) is something options traders need to be familiar with. Because volatility can vary wildly over short amounts of time, relative pricing of volatility on similar securities or across an options chain is generally the easiest method.

In an earlier example, we identified a covered call set-up to create cash flow from commodities based in part on month-to-month implied volatility. When that trade closes at this month’s options expiration, we will have a full re-cap – hopefully one that bears out the thesis that selling relatively cheap volatility is a good strategy. An options calculator makes calculations like implied volatility a breeze to find and analyze.