Optimization and portfolio selection 163
estimate of the shape of the joint distribution than assuming a bell shape (stand-
ard normal distribution). We recognize that this shape should change when the
market is undervalued in that it should be more positively skewed than normal,
and that it should be more negatively skewed when the market is overvalued.
However , when the market has been undervalued in the past, the subsequent
result is seldom, if ever, the same. This is where we call on Bradley Efron’s
bootstrap procedure to generate a distribution of returns that could have hap-
pened from all those periods in the past when the market was undervalued.
The same is done for all those periods in the past when the market was over-
valued. This saves us from saying foolish things like “ The future is going to
be like 1932 or 1990, etc. ” What we are assuming is that the distribution of
returns will be more closely approximated by bootstrapping all of the monthly
returns from all past periods when the market proved to be undervalued.
A representation of that distribution is given in Figure 7.1.
Next (see Figure 7.2 ) we allow the user to identify which part of the world
he or she is operating from. That will determine which currency the indexes
will be denominated in and which indexes to use.
Next we allow the user to select combinations of scenarios from the three buck-
ets of returns. If the user does not wish to make such a decision, the choice should
be “ unknown, ” in which case the returns from all three buckets are used.
Let us assume the choice is US and the user chooses “ Unknown ” for the sce-
nario. A distribution for each index is then presented. Figure 7.3 displays the
distribution for the MSCI Japan index with a mean of 15%.
Figure 7.1 Scenario selection screen.