Volatility Revisited
I have gotten a number of questions about volatility and I’d like to offer a little more insight about this important subject.
Volatility is usually quoted as a percentage and as an annualized figure, as it is in the tables on this site. However, if you are looking at an option with three months to expiration, you are really interested in the volatility of the underlying over the next three months.
I explained in an earlier commentary that the three-month volatility is not one fourth of the annual volatility, as you might naively expect, but rather one half of the annual volatility. So if the annualized volatility is 40%, the three-month volatility is 20%. This is the so-called “square root law.” The three-month volatility that is pertinent to this option today is the volatility over the next three months. There are several relevant questions: what does a three-month volatility of, say, 20% mean; how would you calculate it; and how reliable is your calculation as an estimate of the future volatility?
If you have ever seen the formula, the calculation of volatility may look fairly complicated to you, but volatility’s intuitive meaning is easy to grasp. The three-month volatility tells you how large a percentage change the underlying can be expected to experience over a three month period. How would you compute that? The naive way would be to look at all three-month periods in the past, compute the percentage change that occurred in each period, and average them all, ignoring the sign. This would not be terribly wrong, and you can use that intuition to understand volatility. Let’s assume you do this.
Of course you want to use, as much as possible, the most recent prices because they most closely represent the underlying’s status today. Unfortunately there are not that many non-overlapping three-month periods that are recent — if you go back a year you will find only four, and your estimate may be quite skewed by one abnormal three-month period. If you drop the requirement that the three-month periods be non-overlapping and go back one year, you will find about 180 three-month (some overlapping, of course) periods and thus 180 percentage changes, and it would not be wrong to use this collection of 180 percentage changes for your calculation.
The computer routines that use volatility usually use an annualized figure, corresponding to the customary way of quoting volatility, so you would have to use the square root law to convert your base three-month volatility to an annualized figure. You would multiply it by two, as discussed earlier.
What we do on this site is a little different computationally, but in the end not much different intuitively. We compute the daily volatility by looking at the past 100 days, and use this as our base volatility. To get the annualized figure, we multiply it by the square root of 252, the number of trading days in the typical year.
Enough for today. I will be follow up on this topic in future commentaries. The notion of volatility is crucial for an understanding of options, and I recommend that you digest these comments thoroughly. You will find that a good intuitive understanding of volatility will pave the way to an easier understanding of many other options topics.