The Windham Portfolio Advisor 97
4.2.3 Summary
Investors care about both absolute and relative performance, as revealed by
their reluctance to depart significantly from normal industry portfolios. To
date, the investment community has addressed aversion to being wrong and
alone in an ad hoc fashion by imposing allocation constraints on the mean –
variance optimization process. The WPA, by contrast, encompasses both abso-
lute and relative measures of risk in an unconstrained optimization process,
which is almost always superior to constrained mean – variance optimization.
4.3 Within -horizon risk measurement
4.3.1 The problem
Investors measure risk incorrectly by focusing exclusively on the distributions of
outcomes at the end of their investment horizons. Their investments are exposed
to risk during the investment horizon as well. This approach to risk measure-
ment ignores intolerable losses that might occur throughout an investment
period, either as an accumulation of many small losses or from a significant loss
that later — too late, perhaps — would otherwise recover.
4.3.2 The WPA solution
The WPA provides two related risk measures that enable investors to evaluate
a portfolio’s exposure to loss all throughout the investment horizon: within-
horizon probability of loss and continuous value at risk.
Exhibit 3 illustrates the distinction between risk based on ending outcomes
and risk based on outcomes that might occur along the way. Each line repre-
sents the path of a hypothetical investment through four periods. The horizon-
tal line represents a loss threshold, which in this example equals 10%. Exhibit
3 reveals that only one of the five paths breaches the loss threshold at the end
of the horizon; hence we might conclude that the likelihood of a 10% loss
equals 20%. However, four of the five paths at some point during the invest-
ment horizon breach the loss threshold, although three of the four paths subse-
quently recover. If we also care about the investment’s performance along the
way to the end of the horizon, we would instead conclude that the likelihood
of a 10% loss equals 80% ( Figure 4.3 ).
One might argue that calculation of daily value at risk measures a strategy’s
exposure to loss within an investment horizon, but this is not true. Knowledge of
the value at risk on a daily basis does not reveal the extent to which losses may
accumulate over time. Moreover, even if daily value at risk is adjusted to account
for prior gains and losses, the investor still has no way to know at the inception
of the strategy, or at any other point, the cumulative value at risk to any future
point throughout the horizon, including interim losses that later recover.