### Putting volatility to work

BY RAVI KANT JAIN
April, 2001 Volatility_to_work.pdf
(size=789K) Volatility is both the boon and bane of all traders  you can't live with it and you can't really trade without it.

Most of us have an idea of what volatility is. We usually think of "choppy" markets and wide price swings when the topic of volatility arises. These basic concepts are accurate, but they also lack nuance.

Volatility is simply a measure of the degree of price movement in a stock, futures contract or any other market. What's necessary for traders is to be able to bridge the gap between the simple concepts mentioned above and the sometimes confusing mathematics often used to define and describe volatility.

But by understanding certain volatility measures, any trader  options or otherwise  can learn to make practical use of volatility analysis and volatility-based strategies. We'll explore these volatility calculations and discuss how to use them.

Volatility defined
There are two main measures of volatility: historical volatility and implied volatility.

Historical volatility is the measure of a stock's price movement based on historical prices. It measures how active a stock price typically is over a certain period of time. Usually, historical volatility is measured by taking the daily (close-to-close) percentage price changes in a stock and calculating the average over a given time period. This average is then expressed as an annualized percentage. Historical volatility is often referred to as actual volatility or realized volatility.

Short-term or more active traders tend to use shorter time periods for measuring historical volatility, the most common being five-day, 10-day, 20-day and 30-day. Intermediate-term and long-term investors tend to use longer time periods, most commonly 60-day, 180-day and 360-day.

Historical volatility
There's some unavoidable math involved here, but understanding the concepts is the important thing, since you'll never have to calculate historical volatility by hand  any piece of analytical software will do it for you.

To calculate historical volatility:
1 . M e a s u re the day-to-day price changes in a market. Calculate the natural log of the ratio (Rt) of a stock's price (S) from the current day (t) to the previous day (t-1): there is a strong trend in the stock in question. The result corresponds closely to the percentage price change of the stock.

2. Calculate the average day-to-day changes over a certain period. Add together all the changes for a given period (n) and calculate an average for them (Rm): 3. Find out how far prices vary from the average calculated in Step 2. The historical volatility (HV) is the "average variance" from the mean (the "standard deviation"), and is estimated as: 4. Express volatility as an annual percentage. To annualize the historical volatility, the above result is multiplied by the square root of 252 (the average number of trading days in a year). For example, if you calculated the 10-day historical volatility using Steps 1-4 and the result was 20 percent, this would mean that if the volatility present in the market over that 10-day period holds constant for the next year, the market could be expected to vary 20 percent from it current price.

Sometimes historical volatility is estimated by "ditching the mean" and using the following formula: The latter formula for historical volatility is statistically called a n o n - c e n t e re d a p p roach. Traders commonly use it because it is closer to what would actually affect their profits and losses. It also performs better when n is small or when there is a strong trend in the stock in question.Calculate the natural log of the ratio (Rt) of a stock's price (S) from the current day (t) to the previous day (t-1): In other words, historical volatility measures how far price swings over a given period tend to stray from a mean or average value.