back period for the calculation will be a little longer than desirable for a short-term
system. Remember, we strive to find a maximum trade length of no more than 10
days, because that’s how long the market will remember why it took off one way
or another, and created our trading opportunity in the first place. By the same
token, we shouldn’t use any more data than that to calculate our stops and exit
points when entering the trade. If we use more data than necessary, that data will
be obsolete and only help us arrive at a suboptimal solution. If it’s reasonable to
believe that the market will only remember what triggered a trade for five to ten
days, then it’s equally reasonable to assume that the market won’t remember the
fundamental reasons leading into the trade for more than five to ten days either.
The second way to measure volatility is the average true range method,
which is very well known in technical analysis circles. To calculate the daily true
range, simply take the highest of the previous day’s close and today’s high, and
subtract the lowest of the previous day’s close and today’s low. Most often the daily
true range simply will be the distance between today’s high and low, but on days
when the market gaps higher or lower, that gap will be accounted for by adding the
distance between yesterday’s close and whichever of today’s extremes is closest to
it. To calculate the average true range over a certain number of bars or days, sim-
ply sum up all true ranges for all bars in the lookback period and divide by the
number of bars.
The calmer the market over the lookback period, the smaller the average true
range and the closer the stops and exits will be to the entry price. For example, if
the average true range over the lookback period is 4 percent, and you’ve decided
to place a stop two average true ranges away from the entry price, then that stop
will be 8 percent away. If the price of the stock is $100, the stop will be placed $8
away, but if the price of the stock is $50, then the stop will be $4 away from the
entry price. If, on the other hand, the average true range was only 3 percent, then
a stop loss will be placed $6 away from a $100 stock and $3 away from a $50
stock. In this way, the average true range becomes a universal measure that can be
applied to all stocks, no matter the price.
The major advantage of the average true range method, compared to the stan-
dard deviation method, is that the former doesn’t need as much data to make the
calculations reliable.
The major disadvantage of the average true range method, compared to the
percentage method, is that the former needs a certain amount of historical data for
its calculations, which presents yet another optimization problem. To solve this, I
have equalized the lookback period for the average true range calculation with the
maximum allowed holding period for a trade. For example, if the maximum hold-
ing period for a trade is set to six days, then the lookback period for the average
true range calculation also will be six days. Likewise, if I test a system using vary-
ing holding periods, say from one to ten days, in steps of one day, the lookback
period for the average true range calculation will always be the same as the max-CHAPTER 19 Placing Stops 211