not do because you only have a $100,000. Or, if the K value equals 0.03, the
amount to risk should be $3,000 (0.03 * 100,000), and the number of shares to buy
would be 750 (3,000 / 4), for a total value of $37,500 (750 * 50).
Therefore, the larger K is, the looser the stop loss should be, so that the sug-
gested amount to trade won’t exceed the available capital, or your maximum allot-
ted (relative) amount for one trade. The looser the stop loss, the larger K can be
without making you exceed your available capital. Again, the word relativeis
within parentheses to indicate that the maximum allotted amount can vary with the
total equity. Another hallmark of a skillful trader is the ability to find the right bal-
ance between these two variables, so that he can be in the desired number of posi-
tions simultaneously.
In the first example, we can only be in one trade at a time, given the amount
of money we have at hand [Integer(100,000 / 83,759) 1]. In the second exam-
ple, we can’t trade at all [Integer(100,000 / 167,500) 0]. In the third example,
we can be in two trades at a time [Integer(100,000 / 37,500) 2]. Obviously, as
short-term system traders, we would like to be in at least 10 to 20 trades simulta-
neously. Thus, the distance between the stop loss and the entry price must be very
large, and the more positions we want to be in simultaneously, or the less we want
to risk per trade, the larger this distance should be. We will learn how to deal with
this in a little while, given that we already have decided on where to place our
stops in Part 3.
However, even armed with the knowledge of the system’s K value, there is
no guarantee that we won’t be extremely unlucky in the future. Figure 24.1 shows
the results from 100 trade simulations using the winning and losing percentages
and average trade values we have worked with so far. The y-axis represents the
profit or loss (the starting balance was set to 100). A large number of these simu-
lations end up as losing propositions, even though we’re risking 6.7 percent of
available equity with a 60 percent chance of success. However, where and when
these winning and losing trades happen, which is determined randomly, still can
determine the overall profitability.
In the case of Figure 24.1, the best run produces an average profit per trade
of $426, while the worst run produces an average loss of 96 cents per trade, with
25 percent of all test runs ending up in negative territory. The risk–reward ratio,
calculated as the average profit per trade produced by all 100 test runs divided by
the standard deviation of all average profits, comes out to 0.41 (28.6 / 69.8), which
is not particularly good. (As already discussed earlier, preferably this value should
be above one.)
Obviously, a strategy needs to be better than this to keep the bad-luck conse-
quences to a minimum. Let’s see what happens if we increase the win–loss ratio in
Figure 24.1 from 0.75 to 0.8 (for example, by trading a strategy with an average
winner of 4 points and an average loser of 5 points), which also increases the K
value to 0.1. Figure 24.2 shows the outcome of 100 such simulations.CHAPTER 24 The Kelly Formula 291