Measuring Historical Volatility and the Rule of 16

Level 1 - Zero to Options Hero - How pro traders determine whether an option is cheap or expensive, and a simple rule all options traders have memorized

As we described in the last post, the main driver for the price of an option (otherwise known as option premium) is the market’s expected future volatility of the asset during the time period up to the maturity date.

So how do traders figure out what the expected future volatility of the underlying asset will be? In the case of the 1-month TSLA $300 call mentioned in the last post, how do traders decide what the expected future volatility of TSLA will be over the next month? And how precisely is this volatility number calculated anyway? These will be the main topics of this post.

We can think of the market’s expected volatility (or implied volatility) of an option to be roughly the average daily percentage move of the asset. This is analogous to the idea of historical volatility, which is the average daily percentage move of the asset over a period of time in the past (otherwise known as standard deviation). For example, we can calculate the 1-month historical volatility of TSLA by:

1. taking the closing prices of TSLA over the last month (P_1 to P_n)

2. compute the daily price returns (i.e., (P_2 - P_1)/P_1, (P_i+1 - P_i)/P_i)

3. compute the standard deviation of the daily price returns (STDEV function in Microsoft Excel or Google Sheets, for example)

4. annualize the standard deviation by multiplying the result by the square root of the number of trading days in a year (typically 252 in the case of US equities, although this can be 365 in the case of cryptocurrencies!)

I often get asked why part 4 (annualization) is necessary. The way to think about this is that in order to compare historical volatilities over different periods of time, we need to have some gold standard of measurement (like a yardstick).  The options markets have gone with an annualized volatility measure as the gold standard.

This brings me to the next topic of this post, which is the Rule of 16. This is a simplified rule of thumb that professional options traders use to estimate the future expected standard deviation of an asset over a specific time period. According to the Rule of 16, this future expected standard deviation can be approximated by dividing the implied volatility from the options market by 16, or:

Estimated Standard Deviation = Implied Volatility / 16

In the case of TSLA stock, the current 1-month Implied Volatility at the time of publishing is about 60%, so the Rule of 16 states that the average daily move the options market is telling us to expect in the stock is 60/16 = about 3.75%

For the mathematically curious in the audience, the reason why the Rule of 16 exists is because annualization of the implied volatility involves dividing the daily volatility by the square root of the number of trading days in a year. For US equity markets this is roughly 252 trading days, and the square root of 252 is 15.87 (roughly 16!)

Hope this was useful, happy to answer any questions in the comments and below, and until next time!

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