More About Volatility

In the previous article, I received a question with regards to comparing implied volatility (IV) and historical volatility, so I’ll talk a bit about that.

Firstly I want to concentrate on HV. As I’ve pointed out in previous articles, HV looks backwards. A period of time is selected, that is, the most recent x days of data is used to calculate the historical volatility mathematically as per my previous article on volatility.

This begs the question, how many days should we look back over: 10 days, 20 days, 30, 100, 250? The general rule of thumb is either 20 or 30 days, roughly one month. But depending on the look-back period, we can get vastly differing figures for HV.

Consider the following chart where 10, 20, 30 and 100 day HV is plotted: click to enlarge

This shows the vastly differing values that can be derived, depending on the look-back period.

And below, the IV mean compared against 30 day HV for the same chart:

The thing to remember here is that IV is trying to predict future realized volatility. As this chart is of near expiry IVs, it is trying to predict actual volatility about 20 – 30 days ahead, so to truly make a comparison; IV should be compared with HV about a month into the future.

Three things to note here:

1) The market does a reasonably good job of it at times, but drastically wrong at other times.

2) It is not possible to do in real time as we cannot see into the future.

3) Volatility is mean reverting; it tends to oscillate up and down around the mean.

We can use this information to make a “guess” as to what volatility (not direction) will do next. It is suggested in many texts to buy options when IVs are low and to sell options when IVs are high. It is also suggested that options are overpriced when IV is higher than HV, and under priced when IV is lower than HV.

That may be the case at times, but at other times it is absolutely false. It is then clear that assumptions such as these can get you into trouble if applied indiscriminately. But it is a good starting point; just don’t treat it as gospel.

How can the trader tell when options are overpriced or under priced? You can’t! You can only do it in retrospect.

However as traders, we get paid for taking risk. The options trader must make a volatility bet along with a bet on direction (or no direction). So if IVs are high, the question is whether the underlier is about to get very volatile for some reason, or whether option traders have just got a bit carried away and realized volatility does not increase, or falls; and visa-versa.