174 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 4.15 Scenario spectrum with multiple scenarios
Notice that this is avalid scenario spectrumsince:
A. There is at least one scenario with a negative result.
B. The sum of the probabilities equals 1.00.
C. The scenarios within the spectrum do not overlap.
For example the stagnation scenario implies peace. However, the stagnation
scenario implies peace with zero economic growth. The peace scenario is
separate and apart from this, and implies peace with at least some economic
growth. In other words, the stagnation scenario isnotencapsulated in the
peace scenario, nor is any scenario encapsulated in another.
One last point about scenario spectrums, and this is very important:
All scenarios within a given spectrum must pertain to outcomes of a given
holding period. Again, the length of the holding period can be any length you
choose—it can be one day, one week, quarter, month, year, whatever, but
the holding period must be decided upon. Once decided upon, all scenarios
in a given spectrum must pertain to possible outcomes over thenextholding
period, and all scenario spectrums must be for the same length holding pe-
riod. This is critical. Thus, if you decide upon one day for the holding period
length, then all of your scenarios in all of your scenario spectrums must
pertain to possible outcomes for the next day.