Ralph Vince - Portfolio Mathematics

170 THE HANDBOOK OF PORTFOLIO MATHEMATICS

is using, let’s say he can discern the following scenarios for this potential
trade:

Scenario Probability Result

Best-case outcome .05 150/cent bushel (profit)

Quite likely .4 10/cent bushel (profit)

Typical .45 −5/cent bushel (loss)

Not good .05 −30/cent bushel (loss)

Disastrous .05 −150/cent bushel (loss)

Now, when our Elliot Wave soybean trader (or weather forecaster soy-
bean trader) paints this set of scenarios, this set of possible outcomes to
this trade, and, in order to maximize his long-run growth (and survival),
assumes that he must make this same trading decision an infinite number
of times into the future, he will find, using this scenario planning approach,
that optimally he should bet .02 (2%) of his stake on this trade. This trans-
lates into putting on one soybean contract for every $375,000 in equity, since
the scenario with the largest loss,−150/cent bushel, divided by the optimal
ffor this scenario set, .02, results in $7, 500/. 02 =$375, 000. Thus, at one
contract for every $375,000 in equity, the trader can be said to be risking 2%
of his stake on the next trade.
For each trade, regardless of the basis the trader uses for making the
trade (i.e., Elliot Wave, weather, etc.), the scenario parameters may change.
Yet the trader must maximize the long-run geometric growth of his account
by assuming that the same scenario parameters will be infinitely repeated.
Otherwise, the trader pays a severe price. Notice in our soybean trader
example, if the trader were to goto the right of the peak of the f curve(that
is, have slightly too many contracts), he gains no benefit. In other words,
if our soybean trader were to put on one contract for every $300,000 in
account equity, he would actually make less money in the long run than
putting on one contract for every $375,000.
When we are presented with a decision in which there is a different set
of scenarios for each facet of the decision, selecting the scenario whose
geometric mean corresponding to its optimalfis greatest will maximize
our decision in an asymptotic sense.
For example, suppose we are presented with a decision that involves
two possible choices. It could have many possible choices, but for the sake
of simplicity we will say it has two possible choices, which we will call
“white” and “black.” If we choose the decision labeled white, we determine
that it will present the possible future scenarios to us: