180 THE HANDBOOK OF PORTFOLIO MATHEMATICS
lowest denomination of bet size (one contract) and advancing to two, and
it is a benefit only if the arithmetic average trade is more than twice the
size of the geometric average trade. Furthermore, it is beneficial to use only
when you cannot trade fractional units. In Chapter 10 we will see that the
concept of a “Threshold” to the geometric is a precursor to the larger notion
of Continuous Dominance.
One Combined Bankroll versus Separate Bankrolls
SEPARATE BANKROLLS
Some very important points regarding fixed fractional trading must be cov-
ered before we discuss the parametric techniques. First, when trading more
than one market system simultaneously, you will generally do better in an
asymptotic sense using only one combined bankroll from which to figure
your contract sizes, rather than separate bankrolls for each.
It is for this reason that we “recapitalize” the subaccounts on a daily
basis as the equity in an account fluctuates. What follows is a run of two
similar systems, System A and System B. Both have a 50% chance of winning,
and both have a payoff ratio of 2:1. Therefore, the optimalfdictates that
we bet $1 for every $4 units in equity. The first run we see shows these
two systems with positive correlation to each other. We start out with $100,
splitting it into two subaccount units of $50 each. After a trade is registered,
it affects only the cumulative column for that system, as each system has its
own separate bankroll. The size of each system’s separate bankroll is used
to determine bet size on the subsequent play:
System A System B
Trade P&L Cumulative Trade P&L Cumulative
50.00 50.00
2 25.00 75.00 2 25.00 75.00
− 1 −18.75 56.25 − 1 −18.75 56.25
2 28.13 84.38 2 28.13 84.38
− 1 −21.09 63.28 − 1 −21.09 63.28
2 31.64 94.92 2 31.64 94.92
− 1 −23.73 71.19 − 1 −23.73 71.19
−50.00 −50.00
Net Profit 21.19140 21.19140
Total net profit of the two banks= $42.38
