*.)*

*The Uses And Limits Of Volatility***Tutorial:**Option Volatility

Volatility is easily the most common risk measure, despite its imperfections, which include the fact that upside price movements are considered just as "risky" as downside movements. We often estimate future volatility by looking at historical volatility. To calculate historical volatility, we need to take two steps:

1. Compute a series of periodic returns (e.g. daily returns)

2. Choose a weighting scheme (e.g. unweighted scheme)

A daily periodic stock return (denoted below as u

_{i}) is the return from yesterday to today. Note that if there was a dividend, we would add it to today's stock price. The following formula is used to calculate this percentage:

In our example, we will choose an unweighted 30-day average. In other words, we are estimating average daily volatility over the last 30 days. This is calculated with the help of the formula for sample variance:

Our sample is a 30-day snapshot drawn from a larger unknown (and perhaps unknowable) population. If we open MS Excel, select the thirty day range of periodic returns (i.e., the series: -0.126%, 0.080%, -1.293% and so on for thirty days), and apply the function =VARA(), we are executing the formula above. In Google's case, we get about 0.0198%. This number represents the

*sample daily variance*over a 30-day period. We take the square root of the variance to get the standard deviation. In Google's case, the square root of 0.0198% is about 1.4068% - Google's historical

*daily*volatility.

This simplifies the above to the following equation:

The reason this is an unweighted scheme is that we averaged each daily return in the 30-day series: each day contributes an equal weight toward the average. This is common but not particularly accurate. In practice, we often want to give more weight to more recent variances and/or returns. More advanced schemes, therefore, include weighting schemes (e.g., the GARCH model, exponentially weighted moving average) that assign greater weights to more recent data

**Conclusion**

Because finding the future risk of an instrument or portfolio can be difficult, we often measure historical volatility and assume that "past is prologue". Historical volatility is standard deviation, as in "the stock's annualized standard deviation was 12%". We compute this by taking a sample of returns, such as 30 days, 252 trading days (in a year), three years or even 10 years. In selecting a sample size we face a classic trade-off between the recent and the robust: we want more data but to get it, we need to go back farther in time, which may lead to the collection of data that may be irrelevant to the future. In other words, historical volatility does not provide a perfect measure, but it can help you get a better sense of the risk profile of your investments.

Check out David Harper's movie tutorial,

*Historical Volatility - Simple, Unweighted Average*, to learn more on this topic.