Understanding Variance Time

About The concept of variance time acknowledges that the volatility of a stock is not evenly distributed across the year. Business days are more volatile than weekend days. Yet, standard option models assume a year is 365 days and each of those days contributes the same amount of variance time. The “t” term in Black-Scholes is the fraction of a 365-day year remaining until expiration. The 365-day standard year is called the tenor of the option. Implied volatility is just a number that matches a model to what we actually care about — the real-world traded price of options. If you compare models with different tenors, you will observe different implied volatilities for a given straddle price. If I buy a $10 straddle from you and we each use models with different tenors, we think we are trading different levels of implied volatilities even though we are trading at the same price! Who’s right? You’re going to hate my answer — it depends. You may have heard me say that none of the implied vols you’re consuming from off-the-shelf models are correct. This is true but it’s also a bit of shitpost because really, no implied vol is “correct”. The merit of the measure you choose isn’t Truth with a capital T— it’s usefulness. And that depends on what your strategy is primarily focused on. If you are warehousing options because they seem mispriced relative to how you think the underlying moves then your choice of tenor will depend on how you choose to annualize the realized volatility. If you trade cross-asset with some underlyings opening and closing at different times from one another (crypto vs gold futures vs equities) and have short holding periods you are primarily concerned with having a standard ruler so the implied volatilities are self-consistent. This post will expand your understanding, vocabulary, and intuition. Although the math is simple arithmetic, my experience is this topic gives even professional traders headaches. I will do my best to apply anesthetic but whether you walk away understanding it or not — it will profoundly mess with your mind. You will either re-think a lot of your intuition about what implied vol is OR you will walk away with a much healthier understanding of the extent of your ignorance. Both outcomes are seeds of personal growth. Oh yea, if you are a newbie who thinks “theta” is an edge because you took a course with “passive” or “income” in the title, you’re about to find out why Seinfeld described pain as the feeling of “knowledge rushing in to fill a void.”


Let’s establish the basics
Let’s lay out some intuition

Variance Time

The most important observation thus far
Why use variance time

A Custom Calendar

A Variance Schedule

From Dirty Vols To Clean Vols

Cleaning Implied Vols
Demonstrating The Intuition Behind Clean Vols

Closing Remarks

The purpose of clean vols is to represent reality more clearly. You cannot trade relative value if you cannot measure any more than you can’t trade stocks on fundamentals if you can’t normalize accounting for one-off charges or windfalls, cap ex vs op ex, and intangibles.
Once you normalize properly, some “opportunities” turn into yawns and some vols that looked like they make sense might suddenly look dislocated.
Assorted Closing Bits