should have a particular purpose for doing so. Although not always possible, if one can trade a bar length that divides the day into even increments, meets risk criteria, and generates a Fibonacci number of bars per day (3, 5, 8 etc. bars per day), this is preferable as the Fibonacci sequence catches natural market rhythms. The first few Fibonacci numbers are 1, 2, 3, 5, 8, 13, 21, 34, 55 ... . Each additional number in the sequence is the sum of the two numbers preceding it.

Bar Length and risk

Many traders are taught to set stops based on what they can afford to risk. For example, if a trader can afford to risk $ 1,000 and wants to trade five wheat contracts, he would set his stops at 4 cents. (One cent in a wheat contract is equivalent to $50, so 4 cents is $200, and five contracts total $ 1,000.) This method, while serving to keep the trader from losing much more than he can afford, is a very ineffectual method for trading profitably. The reason is that market risk is not determined by what a trader can afford to lose, but by market volatility and its variability.

If this trader sets his stops narrower than dictated by volatility, that is, sets his stops within the band of erratic, random noise in the market, he will continually be stopped out by the noise. Consequently, he will not be in the market long enough to either enter or exit a trade properly. Conversely, if the trader sets his stops too wide, simply because he can afford to take a greater loss than the market dictates, he will give back more profit than necessary before exiting his trade.

For readers who may not be familiar with how to set stops based on volatility, two methods are described, both based on price range. Range is directly proportional to volatility. Risk is also directly proportional to volatility. The system I developed- Kase exit system-is based on true range. In this system, we take the average true range and its standard deviation. The true range as the chart shows is the maximum of either of the three following values:

1. The high minus low (see Figure 12.5A).

2. The high minus the previous close (see Figure 12.5B).

3. The previous close minus the low (see Figure 12.5C).

In essence, the true range is very similar to the high/low range but captures any gap between the previous days close and the current days activity. If the market gaps up whereby the low of the following day is above the close of a day on which we were short, we are going to lose money equivalent to that gap plus the high/low range. The same would be true if we are long going into a gap down day as well. Thus, gaps on the chart need to be considered when looking at risk.

The Kase DevStop© system is based on a method that incorporates three stops. To calculate the first stop, take the average (mean) and standard deviation of true range over a set of N bars. Next, add the standard deviation to the mean. Finally, if your position is long, subtract the resultant value from the largest profit point, or if

Figure 12.5 True range. It is calculated from the largest value of either the high minus low (in 5a), the high minus yesterdays close (in 5b), and yesterdays close minus todays low (in 5c).

Figure 12.6 S&p comstock range distribution, showing right hand skew.

s&p 500 True Range Distribution 6/74 to 9/92

50 100 150 200 250 300 350 400 450 500 550 600 650 651

True Range * 100

short, add. The second and third stops are set by adding approximately two and three standard deviations to the mean, respectively, but slightly increased to account for skew in our assumption that price range is log-normally (as opposed to normally) distributed. Figure 12.6 shows the distribution of S&P prices.1

The "Kase Average Risk" or KAR is formulated to show the amounts at risk at DevStops© 1, 2, and 3. Similarly, another method for measuring risk is called "Value at Risk," or VAR. VAR is a standard technique used by risk managers to assess risk over a given time frame. The default risk is a two standard deviation move against the current price, based on volatility. However, unlike KAR, the VAR method uses volatility based on close-to-close price changes and not true range. For traders placing only market-on-close or market-on-open orders (MOC or MOO orders) and unable to execute during the trading day, this approach may be of interest.

The following formula can be used for calculating VAR lines modified for intraday futures. In this formula, "close[BB]" represents the closing price BB bars ago, and N specifies the number of samples needed for the standard deviation and average functions. Scaling variable Z by 1, 2, and 3 produces the three VAR lines.

input: BB { default value = 4 }

input: N {default value = 30 } W=Log (close/close[BBj)

X = stddev (W, N)

Y = X • average (close, N)

Z = average (Y, 30) plotl (Z X 1, "risk at 1 stdev") plot2 (Z x 2, "risk at 2 stdev, VAR line") plot3 (Z X 3, "risk at 3 stdev, max line")

To return to the case of the trader who does not want to lose more than $200 per contract under normal conditions, assume that this trader has been using a 45-minute March 1997 Wheat chart. In Figure 12.7, the middle set of four curves (KAR group) show the average risk as well as the three amounts of risk at DevStops© 1, 2, and 3. The VAR method produced the bottom set of lines. The second line from the bottom in the KAR group is at the 6 cents per bushel level at the most recent bar. This means average risk is at $300 per contract. This is more than the trader wants to risk; however, if use used only a 4 cents stop, he would frequently be stopped out on noise. On the other hand, when the trader drops down to trading a 15-minute bar chart, analysis in Figure 12.8 shows the risk is just under 4 cents per bushel or $200 per contract. Therefore, our trader would need to trade a 15-minute chart or smaller to stay within his risk limit.

Using the VAR model, we come up with similar average risk of a little over 4 cents for the 15-minute chart but jump to 8.6 cents at the second standard deviation on the 45-minute chart. We can see also that the maximum amount of risk we have to