168 Optimizing Optimization
Following the style analysis, the DTR optimizer solves for that combination
of active and passive managers that fulfills the desired asset allocation shown
at the bottom of Figure 7.9 and provides the highest overall added value as
measured by DTR α (^) ·
Portfolio 3 shown in Figure 7.9 is for the DTR 8 portfolio. Seventy-eight per-
cent of the portfolio is in US securities and 48% of the portfolio is in US equity.
That leaves 30% in US fixed income (30 48 78). The mean of this joint dis-
tribution is 8.5%, which is approximately equal to the DTR of 8%. If one were
making decisions on the basis of probabilities, there is about the same chance of
returns being higher than the mean as there is of being lower. However, this port-
folio has the potential for returning 12.7% in any given year and the downside
risk of achieving that is only 7.3%. Dividing the upside potential by the down-
side risk (see arrows) yields an upside potential ratio of 1.74, indicating 74%
more upside potential than downside risk. Expected Utility Theory, explained in
the Appendix, would claim that risk averse investors should make decisions on
the basis of the upside potential ratio instead of mere probabilities. We further
claim that the proper focus is the DTR and not the mean.
What is actually taking place is a shift in the joint distribution of the portfolio.
Figure 7.9 depicts a 500 basis point shift from left to right for a DTR α of 5%.
Figure 7.10 shows the final output of the SIA optimizer. At the bottom is the
asset allocation that was stipulated as input to the optimizer. At the top is the
combination of active managers and passive indexes that fulfills the asset allo-
cation and adds value in terms of DTR α while reducing costs by using indexes.
To reiterate, the first requirement is to ensure that the asset allocation that was
Figure 7.8 Style analyzer.