# A Post on Measuring Historical Volatility

I’ve reblogged a concise yet thorough explanation of the calculation of market volatility. The post makes very clear how input parameters (weighting, time frame, etc.) affect its validity as an estimate of future market movements (link).  The phrase “Fat Tails” is often thrown around like a meaningless buzzword in financial media (Squawk Box, for example), but the concept is explained intuitively here. In a separate post, market data from the S&P500 is used to demonstrate the decay factor’s effect on log returns (link).

Say we are trying to estimate risk on a stock or a portfolio of stocks. For the purpose of this discussion, let’s say we’d like to know how far up or down we might expect to see a price move in one day.

First we need to decide how to measure the upness or downness of the prices as they vary from day to day. In other words we need to define a return. For most people this would naturally be defined as a percentage return, which is given by the formula:

\$latex (p_t – p_{t-1})/p_{t-1},\$

where \$latex p_t\$ refers to the price on day \$latex t\$. However, there are good reasons to define a return slightly differently, namely as a log return:

\$latex mbox{log}(p_t/p_{t-1})\$

If you know your power series expansions, you will quickly realize there is not much difference between these two definitions for small returns- it’s only…

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