The Welles Wilder ATR Stop Loss System

NOTE: Our ATR stop loss calculator is not available at this time.  It is being upgraded and expanded.  When it is ready, it wil be possible to order it on our "Products & Prices" page.

The following has more information about the ATR stop loss.  It continues the discussion introduced here: Stop Losses

The Average True Range (ATR) is the average of the True Range over a given period. It is a measure of volatility first introduced by J. Welles Wilder in his book, New Concepts in Technical Trading Systems. Wilder recommended a 14-day average of the True Range.  (Periods ranging from 5 to 21 days have been recommended, depending on the nature of the security traded and the anticipated holding period.)  According to Wilder, large ATR values tend to occur at market bottoms after a panic sell-off (volatility is high).  Small Average True Range values tend to occur when volatility is low. An example would be during times of prolonged sideways movement (as when a market is topping out or undergoing consolidation).

Stocks will sometimes gap up or down.  A volatility formula based only on the high-low range would not accurately capture volatility when gaps occur. Wilder's Average True Range can capture this “missing” volatility.  The Average True Range measures how much fluctuation or "noise" there is in a trending stock's behavior.  If a person wants to place his stop loss outside this envelope of noise, then he will multiply the ATR by a factor greater than 1.  For example, he may multiply the ATR by 1.5 and use the result to calculate his stop. This would help prevent getting stopped out prematurely and will also limit his risk in the trade.  Some will prefer a stop that is a greater distance outside the noise envelope and multiply the ATR by a number greater than 1.5.  However, there is another consideration.  Expert traders prefer to limit risk to 1/3 their potential profit on a position.  They will, therefore, use a multiplier that limits the risk accordingly.  If doing so means they must use a multiple less than 1, then they might conclude that the risk of being stopped out  by mere noise is too great and "walk away" from the trade. [Note: some trading strategies do allow ATR multiples of less than 1]

The ATR is a great tool for determining where to place a stop loss because it increases when volatility increases.  Therefore, as the core of the stop loss calculation, it results in wider stops when market volatility increases and closer stops when volatility is less.  As suggested above, most will multiply the ATR by a number from 1 to 5, but some will use a number less than 1 (day-traders might) or more than 5.

For example, a stop loss that is twice the ATR below the close might be used by some for a short-term stop placement, three times the ATR below the close might be used for a medium-term stop placement, and four times the ATR below the close might be used for a  longer term stop placement.  As of this writing, Yahoo had a closing price of 44.34 and an ATR of .8473.  The above calculations would be as follows.

44.34 - (2 x .8473) = 44.34 - 1.6946 = 42.645
44.34 - (3 x .8473) = 44.34 - 2.5419 = 41.798
44.34 - (4 x .8473) = 44.34 - 3.3892 = 40.951

The most common multiplier is 3 (a recommendation of Wilder), but you might not anticipate the same holding period as most people.  Therefore you must decide for yourself what multiplier to use.

To give you some idea about what the use of different multipliers can mean for stop loss placement, we have found a stock with numerous reversals to illustrate the point.  Below are five charts showing a stop loss relative to the closing price each day (red line).  They show stop losses calculated by multiplying the ATR by 1, 2, 3, 4, and 5, respectively.  Imagine you have bought at any place on one of the charts.  The red line directly below the price bar on the day of purchase represents your stop loss on the purchase date.  As the stock rises, you adjust your stop loss accordingly, using your chosen multiplier and the ATR for the current day.  Eventually, the stock will decline.  When it drops enough that it reaches the level of the highest point reached by the red line since your purchase, the stop loss is triggered and the stock is sold.  Most people place the stop order to sell with their broker so that they do not have to monitor the stock during the day.  Then, in the evening, they adjust the stop loss for the next day.

In the following illustrations, the red line rises and falls with the stock.  In actual practice, stop losses should only be raised as the stock rises.  They should never be lowered.  It is always at the highest level reached since purchase.  When the stock declines, the stop loss does not.  However, if we did that with the illustrations, the red line would go flat or disappear the first time the stop is triggered.  This way, you can imagine buying at any point on the charts.

1 x ATR

2 x ATR

3 x ATR

4 x ATR

5 x ATR

The True Range is the largest of the four following calculations:

Most recent day's high minus the most recent day's low
Absolute value of the most recent day's high minus the previous close (see "A" below)
Absolute value of the most recent day's low minus the previous close (see "B" below)
Absolute value of the most recent day's high minus the previous close (see "C" below)

Absolute values are used because direction (+ or -) is not important. Wilder wanted only to calculate the distance between two points.

From the above, you can see that the ATR is a very conservative measure of the average change in price from one day to the next. What we mean is that the ATR does not take the actual change in closing price each day and average those changes. Instead, the ATR is determined by computing the maximum of several ranges from one day to the next. This range is generally greater than the actual change in closing price and it factors in any price gaps from one day to the next.

To calculate a 14-day Average True Range (ATR), for example, a person would make the above calculation for each of the most recent 14 days of price action and then average those computations. The "normal" ATR calculator would require that you enter the date, open, high, low, and close for each day of the last 14 days for each stock.  Our calculator does not, because the required data is already "built-in" when the calculator is downloaded each day.

Our ATR Stops calculator uses the same approach to data "smoothing" as that specified by Wilder's formula. Many if not most ATR calculators use a smoothing approach that was not recommended by Wilder. They may be quick and simple ways to average, but those procedures were not recommended by Wilder.

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