The range of market prices gives a non-high-tech measure of historical volatility* throughout a trading interval, usually a day or a week. The range of prices is defined as the difference between the high and the low for that given trading interval. For example, if the current day’s range lies beyond the previous day’s range (Gap- up or down), the current day’s range must include the distance between the current day’s range and yesterday’s close. This is what is referred to as the “True Range.” The difference between yesterday’s settlement price and today’s low is the valid range for a gap-down day. Conversely, the true range for a gap-up day is the difference between today’s high and the previous day’s settlement price.

#### The Significance of Tick Value

To grind this down a bit further, a tick is the smallest increment by which prices can move in a given futures or commodity market. The next step would be to translate the dollar value for one tick in the given market being traded (Ex: The minimum tick value in corn futures is \$12.50 or ¼ cent). To use corn data as an example, data shows that 90 percent of all observations between 2004- 2014 had a true daily range equal to or less than 26 ¼ cents. Therefore a CTA who was long corn futures may want to set a protective sell stop 26 ¼ cents below the previous day’s close, as the probability of being whip-sawed out of the market is 1 in 10. Similarly, a CTA with short-sold corn would want to stop at least 26 ¼ cents above the previous day’s closing price. The dollar value for this stop would be \$1,312.50 per contract in corn.

#### Average True Range as a Volatility Indicator

Now, instead of concentrating on the true range for a day or a week, it may be more suitable and efficient for a CTA to work with the average true range over the past “N” trading sessions, wherein “N” is any number found to be most effective through backtesting their trading methodology (Ex: 9 days, 20 days, four weeks, etc.). The theory is that the range for the past “N” periods is a more reliable and consistent volatility indicator than the true range from the immediately preceding trading session. An example would be calculating the average true range over the past 20 trading sessions in corn futures and using this number to place protective stops. Of course, this philosophy could be flipped around and used for entry, which I’ll cover in a future article.

#### Modifying Average True Range

As one last example, this average true range methodology could be slightly modified by working with a fraction or multiple of the volatility estimate. Ex: A CTA might want to set their protective stop equal to 150 percent of the average true range for the past “N” trading sessions, (The famous Turtle traders used this methodology by taking the 20-day average true range and then setting their stops equal to 200 percent or 2x this number). The theory is that the fraction or multiple enhances and increases the probability of not being taken out of a valid trade due to market “noise.”

*Historical Volatility – HV’ is a financial instrument’s realized volatility over a period. Generally, this measure is calculated by determining the average deviation from the average price of a financial instrument in a given period.

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