Characteristics of Optimalf 185
discussing multiple simultaneous plays (i.e., “portfolios”), we invoke them
here to illuminate the point. The same principle applies to trading a portfolio
where not all components of the portfolio are in the market all the time.
You should trade at the optimal levels for the combination of components
(or single component) that results in the optimal growth as though that
combination of components (or single component) were to be traded an
infinite number of times in the future.
EFFICIENCY LOSS IN SIMULTANEOUS
WAGERING OR PORTFOLIO TRADING
Let’s again return to our 2:1 coin-toss game. Let’s again assume that we are
going to play two of these games, which we’ll call System A and System B,
simultaneously and that there is zero correlation between the outcomes of
the two games. We can determine our optimalfs for such a case as betting
one unit for every 4.347826 in account equity when the games are played
simultaneously. When starting with a bank of 100 units, notice that we finish
with a bank of 156.86 units:
System A System BTrade P&L Trade P&L BankOptimalfis 1 unit for every
4.347826 in equity:
100.00
− 1 −23.00 − 1 −23.00 54.00
2 24.84 − 1 −12.42 66.42
− 1 −15.28 2 30.55 81.70
2 37.58 2 37.58 156.86
Now let’s consider System C. This would be the same as Systems A and
B, only we’re going to play this game alone, without another game going
simultaneously. We’re also going to play it for eight plays—as opposed to
the previous endeavor, where we played two games for four simultaneous
plays. Now our optimal fis to bet one unit for every four units in equity.
What we have is the same eight outcomes as before, but a different, better
end result: