Historical Volatility Historically Low

By Lawrence G. McMillan

Recently the historical (also called actual or statistical) volatility of many of the major indices and their derivatives reached extremely low levels. For example, the 10-day historical volatility of $SPX dropped to 3.7%! In this article, we’ll examine how often this has occurred in the past and what it has meant for the broad stock market going forward from that low volatility reading.

Historical Volatility

Just to be sure everyone is on the same page, let’s review how historical volatility is calculated. Mathematicians most frequently define historical volatility as the standard deviation of daily percent price changes. Note that this is different than merely computing the standard deviation of the last n closing prices.

So, for example, if one is computing a 10-day standard deviation, he would use the percentage price changes for the last 10 days. Then the standard deviation of that set of numbers would be computed. That gives one a daily volatility, based on the last 10 trading days. Finally, that resulting daily volatility is annualized – typically by multiplying by the square root of 255 (if one assumes there are 255 trading days is a year)...

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