Optimalf 165
made broader so that you don’t need 10,000 scenarios to cover 99% of the
spectrum.
In making your scenarios broader, you must avoid the common pitfall
of three scenarios: an optimistic one, a pessimistic one, and a third in which
things remain the same. This is too simple, and the answers derived there-
from are often too crude to be of any value. Would you want to find your
optimalffor a trading system based on only three trades?
So, even though there may be an unknowably large number of scenarios
to cover the entire spectrum, we can cover what we believe to be about
99% of the spectrum of outcomes. If this makes for an unmanageably large
number of scenarios, we can make the scenarios broader to trim down
their number. However, by trimming down their number, we lose a certain
amount of information. When we trim down the number of scenarios (by
broadening them) to only three (a common pitfall), we have effectively
eliminated so much information that the effectiveness of this technique is
severely hampered.
What, then, is a good number of scenarios to have? As many as you can
and still manage them.
Think of the two-to-one coin toss as a spectrum of two scenarios. Each
has a probability, and that probability is .5 for each scenario, labeled heads
and tails. Each has an outcome,+2 and−1, respectively:
Scenario Probability OutcomeHeads .5 2
Tails .5 − 1Assume again that we are decision making for XYZ. We are looking
at marketing a new product of ours in a primitive, remote little country.
Assume we have five possible scenarios we are looking at (in reality, you
would have many more than this, but we’ll use five for the sake of simplicity).
These five scenarios portray what we perceive as possible futures for this
primitive remote country, their probabilities of occurrence, and the gain or
loss of investing there.
Scenario Probability ResultWar .1 −$500,000
Trouble .2 −$200,000
Stagnation .2 0
Peace .45 $500,000
Prosperity .05 $1,000,000
Sum 1.00