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The Breakout Bulletin

The following article was originally published in the December 2011 issue of The Breakout Bulletin.

What's Wrong with ATR Stops?

Most traders probably consider protective stops an essential element of their trading strategies. Deciding where to place the stops is another matter. One of the most recommended methods for placing stops uses the average true range (ATR). The ATR is often used as a proxy for market volatility, and ATR stops are intended to adapt the size of the stop to market volatility.

The calculation for an ATR stop is as follows:

LStop = EntryPrice - MMFrL * AvgTrueRange(NATRMML);

This provides the stop price for a long trade given the trade entry price (EntryPrice), a multiplying factor (MMFrL), and the averaging length (NATRMML) for the average true range function (AvgTrueRange). The equation subtracts a multiple of the ATR from the entry price to obtain the protective stop price. For a short trade, you would want the stop price to be above the entry, so you would add a multiple of the ATR to the entry price.

The logic behind the ATR stop seems sound enough. As shown below in Fig. 1, the trend on a price chart can be represented by a line that fits approximately through the center of the price bars. The height of the price bars -- their low-to-high range -- represents fluctuations in price relative to the trend line. These fluctuations appear to be random "noise" relative to the trend line. The bar's range (or true range*) would therefore appear to be a good proxy for the noise in the market.

* true range is essentially the range adjusted for gaps.

Figure 1. Typical price chart illustrating average true range as a proxy for random market fluctuations.

The argument for the ATR stop is that you want to place your protective stop so that you avoid being stopped out on the random fluctuations but you get out on larger moves. Some multiple of the ATR relative to the entry would presumably accomplish that goal assuming the ATR is a good representation of the noise in the market.

A Comparison with Other Stops

Despite the logic behind the ATR stop, a number of traders I've spoken to avoid the ATR stop in favor of simpler stops. They cite either no benefit or, worse yet, find that it doesn't hold up well in out-of-sample testing or real time trading. My own experience is similar. If the ATR stop makes so much sense, the performance advantage should be apparent in back-testing compared to other types of protective stops. Secondly, the parameters of the stop (multiplying factor and look-back length) should hold up in out-of-sample testing and real-time tracking and trading. This rarely seems to be the case, however.

To see why the ATR stop often fails to live up to its promise, it's helpful to compare it to other, common stop types. In particular, consider the fixed dollar stop and the percentage stop. The fixed dollar stop places the protective stop so that if it's hit, the loss will be a specified dollar amount, such as \$500. For example, a \$500 dollar stop for the E-mini S&P futures corresponds to 10 points (10 points x \$50 per point for the E-mini = \$500), so the stop would be placed 10 points below the entry for a long trade.

The percentage stop is commonly used for stock trading. It allows you to specify the maximum percentage loss you want in the trade. With a 2% stop, for example, if the stop is hit, the loss will be 2% of the trade value. To calculate the stop price for a percentage stop, multiply the percentage by the entry price and subtract (for a long trade) the result from the entry price. For example, for a 5% stop, if the entry price is 30, the stop price for a long trade would be 30 - (0.05 x 30) or 28.50. If the stop is hit, the loss would be 30 - 28.5 or 1.5 points per share, which is 5% of the trade.

To compare the three types of stops, I calculated the parameter values for each stop type over the range of stop values from \$100 to \$1000. These are the stop sizes in dollars; that is, the amount lost if the stop is hit. To find the ATR and percentage stop parameter values over this range, it's necessary to know how the ATR and prices, respectively, vary over the price history of interest.

As an example, I took the last six months of 15 minute bars of the E-mini S&P 500 day session futures. The table below shows the min and max values of the E-mini futures price and the 100-bar ATR over the time period.

 Min Max ATR 2.195 11.685 Price 1062.25 1341.25

Based on these values, it's easy enough to calculate the range of multiplying factors required to obtain stop values from \$100 to \$1000. Likewise, for the percentage stop, the range of percentage values required to obtain stop values in the \$100 to \$1000 range can be calculated. The ATR multipliers and stop percentages are shown in the table below.

 Min Max ATR Multiplier 0.911 1.716 Stop Percentage 0.188 1.49

This means that if the ATR multiplier is between 0.911 and 1.716, the ATR stop will be between \$100 and \$1000 for any bar on the chart. Likewise, a stop percentage between 0.188% and 1.49% will give a stop between \$100 and \$1000 for any bar on the chart.

Now that the three types of stops are normalized to the same range of values, consider how the stop sizes vary over the bars in the chart for a given stop parameter value. Using the midpoint values for the ATR and percentage stops from the table above gives, respectively, an ATR multiple of 1.31 and a percentage stop value of 0.84%. To see how the respective stop sizes vary, these values can be applied to the min and max ATR and price values from the first table. The result is shown below in Fig. 2.

Figure 2. Range of stop sizes for different types of protective stops over six months of E-mini S&P prices.

The midpoint of the fixed dollar stop is shown as the thin horizontal line on the left ("Fixed"). This is simply the fixed dollar stop of \$550 (half-way between \$100 and \$1000). The percentage stop calculated using the midpoint percentage value is shown as the "%" bar. Because the percentage stop is calculated from price, it varies over the six-month price history of the E-mini as the price itself varies. This gives a range of stops from about \$450 to \$560.

Now consider the ATR stop. The long vertical bar ("ATR") in the chart represents the range of stop sizes calculated using the midpoint ATR multiplier. Because the ATR varies from roughly 2 to 12 over the price history, the size of the ATR stop varies from about \$150 to \$770. In terms of E-mini points, this means that the size of the protective stop could be anywhere from 3 points to 15 points, depending on when the stop is placed.

Keep in mind that this range of stop values for the ATR stop is for a given parameter value calculated over only six months of history. If the same parameter value were used over a longer history, the range of stop values would be even greater. In my opinion, it's this wide range of stop sizes that's the Achilles heel of the ATR stop. Only if you believe that the market volatility changes so much over six months that you would want a stop size of 3 points one day and 15 points a few days later does the ATR stop make sense.

Why Does the ATR Vary so Much?

Although the ATR appears to be a reasonable way to quantify volatility, it varies much more than one would expect. The reason for this may have to do with how the ATR is plotted. The calculations above were performed on a chart of 15 min bars. Anyone who follows the markets on an intraday basis knows that during certain periods, the markets can be very quiet, with relatively little volume. These periods are often followed by periods of intense action, with high volume and volatility.

During periods of low volume, it's likely that the bars on a time-based price chart will have a low range. Bars that overlap periods of high volume will likely have a higher range. Roughly speaking, the price change per unit of trading volume may be approximately constant, whereas the price change per unit of time is likely to vary quite a bit. This may account for the high variation in the ATR on time-based price charts.

To confirm this hypothesis, the same analysis performed above was repeated for a 20,000 tick chart of the same six months of E-mini price history. Tick bars were chosen because each tick bar represents the same number of transactions and therefore approximately the same volume (volume bars could also be plotted in TradeStation with similar results). The tick size was set to 20,000 because that value gave nearly the same number of bars as on the 15 min bar chart.

The results are shown above in Fig. 2. The bar on the right-hand side ("Tick ATR") shows the range of stop sizes for an ATR stop calculated from the 100-bar ATR obtained from the tick chart using the midpoint fraction for stop sizes between \$100 and \$1000. As can be seen, the range is much lower when tick bars are used, with stops ranging from \$240 to \$630. This supports the idea that the variation in ATR on price bars is related to the variation in volume from bar to bar on those charts.

Conclusions

If you've found that ATR stops don't work as well as you expected, it may be because the ATR calculated on time-based bars, such as 15 min bars, varies more than you realize, resulting in stops that vary in size too much to be practical for your strategy. One way to address this may be to use tick bars that are roughly equivalent in number to the time-based bars you were using. As shown above, this can reduce the range of the ATR over the price history. Other alternatives include using a fixed dollar stop or a percentage stop. However, neither of these may vary enough with the market's volatility to avoid stopping you out on the market's random fluctuations.

Another option is illustrated above in Fig. 2 above the label "Sqrt ATR". This bar shows the range of stop values for a protective stop calculated the same way as the ATR stop on 15 min bars but using the square root of ATR, rather than the ATR itself. The square root function tends to attenuate the high and low values, compressing the range. This can compensate to some extent for the wide variation in ATR values on time-based bars, leading to a stop that still varies with market noise but not as widely as the basic ATR stop. The range compression will be greater for larger ranges of ATR.

I'm not suggesting that ATR stops should be avoided on time-based bars. Rather, the goal of this study was to understand why they often seem to perform worse than expected given their apparent attributes. If you conclude the ATR stop in your strategy is not performing as you think it should, perhaps this analysis can help explain the problem. And hopefully one of the suggestions offered above can help as well.

Mike Bryant

Breakout Futures

HYPOTHETICAL OR SIMULATED PERFORMANCE RESULTS HAVE CERTAIN INHERENT LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT ACTUALLY BEEN EXECUTED, THE RESULTS MAY HAVE UNDER- OR OVER-COMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PROGRAMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN.