# Volatility

**Volatility**can refer to any basic process that complements a trigger mechanism.

In financial economics, volatility is a quantification of risk based on the standard deviation of an asset's historical return.

To fix ideas, imagine that over the relevant period, a given asset has never returned more than 20% in a financial quarter on any dollar invested. Over the same period, the worst performance is a loss of 5% of the dollar.

In such a situation, a full plot of the returns by quarter would generally take the shape of the famous *bell curve*, or normal distribution. The 20% gain would be one "tail" of that curve. The 5% loss would be the other tail. Given an unskewed curve, 7.5% gain would be the mean asset return.

The "standard deviation" measures the width of the central hump of such a bell curve. One arrives at this number by taking every quarterly return, subtracting the average return, and squaring the result, then averaging the new numbers, and taking the square root of that average. That is also called the "volatility" of that asset because by definition the higher the standard deviation number, the more wildly results may vary from quarter to quarter.

The volatility of an asset is directly related to the statistical concept of "Value at Risk" or VaR. When an investor or institution wants to answer the question, "what is the most money I could lose on this investment 19 times out of 20" it multiplies the vol by 1.65.