302 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 9.5 Two-to-one coin toss—40 plays
When we trade a portfolio of markets and/or systems, we simply mag-
nify the effect of missing the peak of the curve inn+1 space.
A Comparison to the Old Frameworks
Let’s take a look at a simple comparison of the results generated by this
new framework versus those of the old E-V framework.
Suppose, for the sake of simplicity, we are going to play two simultane-
ous games. Each game will be the now-familiar two-to-one coin toss. Further
assume that all of the pairwise correlations are zero. The new framework
tells us that the optimal point, the peak in the three-dimensional (n+1)
landscape is at 23% for both games.
The old framework, in addition to the zero values for the pairwise corre-
lations, has .5 as the E value, the mean, and 2.25 as the V value, the variance.
The result of this, through the old framework, generates .5 for both games.
This means that one-half of your account should be allocated toward
each game. But what does this mean in terms of leverage? How much is a
game? If a game is $1, the most I can lose, then .5 is way beyond the optimal
of .23. How do I progress my stake as I go on? The correct answer, the