The Windham Portfolio Advisor 95
absolute return but underperform the competition or benchmark (Quadrant III).
These results would probably be tolerable because the investor produces supe-
rior performance along at least one dimension. However, what would likely
be very unpleasant is a situation in which an investor generates an unfavor-
able absolute result and at the same time performs poorly relative to other inves-
tors or the benchmark (Quadrant IV). It is the fear of this outcome that induces
investors to conform to the norm.
One might argue that investors are driven by a different motivation when they
constrain their portfolios to resemble normal industry portfolios; to wit, they
lack confidence in their assumptions about expected return, standard deviation,
and correlation. It may be the case that, although the optimal result calls for a
50% allocation to foreign equities, the investor lacks confidence in the relevant
inputs, and therefore is warranted in overriding the optimal recommendation.
This reasoning is a subterfuge for the true motivation, which is fear of being
wrong and alone. Consider the following thought experiment. By some form
of divine intervention we acquire secret knowledge of the true distributions and
correlations of all the assets to be included in our portfolio. With this knowl-
edge, we solve for the optimal portfolio, which again calls for a 50% allocation
to foreign equities compared to an industry norm of 10%. Would we be more
inclined to accept the recommended solution without constraints knowing that
our views about expected return, standard deviation, and correlation are une-
quivocally true? Probably not, for the following reason. Even if we have perfect
foreknowledge of the expected returns and the distributions around them, there
is about a 50% chance that the actual returns will be either above or below
the expected returns during any given period — and there is a substantial likeli-
hood for distributions with high standard deviations that the actual returns will
be significantly different from the expected returns. Thus, even though we may
be right on average over the long run, we will almost certainly be wrong (due
to high standard deviations) and alone (due to an uncommon allocation) over
some shorter periods. Most investors, owing either to career or psychological
considerations, are unwilling to risk the chance of such an unpleasant outcome.
Investors have sought protection from this unhappy consequence by con-
straining their portfolios to match typical industry allocations. Although this
approach is reasonably effective, it is not the best approach for dealing with
the fear of being wrong and alone. Chow (1995) introduced a technique that
optimally deals with absolute and relative performance. He simply augmented
the quantity to be maximized to equal expected return minus risk aversion
times variance minus tracking error aversion times tracking error squared. This
measure of investor satisfaction simultaneously addresses concerns about abso-
lute performance and relative performance. Although it includes two terms for
risk, it only includes one term for expected return. This is because absolute
return and relative return are linearly related to each other. Instead of produc-
ing an efficient frontier in two dimensions, this optimization process produces
an efficient surface in three dimensions: expected return, standard deviation,
and tracking error, as shown ( Figure 4.2 ).