Optimization and portfolio selection 167
7.3 Part 2: The DTR optimizer
No matter what kind of optimizer one uses to generate an efficient frontier of
passive indexes, it is important to know if there may be some combination of
active managers and passive indexes that would lie above the efficient frontier
as shown in Figure 7.6.
Figure 7.6 depicts a hypothetical representation of what this efficient fron-
tier would look like. The numbers 4, 8, and 12 represent points on the efficient
frontier for portfolios of passive indexes that have the highest upside potential
ratio for a given level of downside risk. The points correspond to DTRs of 4%,
8%, and 12%.
To accomplish this, we begin with a quadratic optimizer developed by Bill
Sharpe. Using the Surz indexes, we can quickly identify the style blend of thou-
sands of managers. For illustrative purposes, a partial list is shown in Figure
7.7. Three years of monthly returns were used. M Capital is a fund that
attempts to track the S & P 500 while SW claims to be a large value manager.
The S & P 500 is often used as a surrogate for the market. For details on the
error of this assumption, see Chapter 2 by Ron Surz. All a manager would
have to do is change the weights to claim an enhanced index. In this case, large
cap is overweighted. If an S & P 500 index is employed, it should be evaluated
as an active manager competing with the passive indexes that more accurately
reflect the complete market of 6,000 plus stocks. HW loads almost entirely on
the midcap value index yet only has an R 2 of 0.82. In other words, 18% of the
difference in the variance in returns between the midcap index plus 1% large
value index is not being explained. Something is missing. We asked a friend
to run the data on a standard style analyzer and it came up with 54% large
cap value. The reason? He unknowingly was using quarterly data. There were
only 12 observations for 9 variables. That is totally unreliable. When he used
5 years of quarterly data, his answer was more similar to ours. The point we
wish to make is that all quantitative models that attempt to do the same thing
are not the same and even those that are the same are influenced by the period-
icity of the data.
Name R^2 U-P ratio DTRα LrgVal LrgCor LrgGro MidVal MidCor MidGro MinVal MinCor MinGro
LrgValu 1 0% 100% 0%
LrgCore 1 0% 0%
LrgGrow 1 0% 0%
MidValu 1 0% 0%
MidCore 1 0% 0%
MidGrow 1 0% 0%
MinValu 1 0% 0%
MinCore 1 0% 0%
MinGrow 11.25
0.84
0.61
1.53
1.1
0.66
1.91
0.75
0.34 0% 100%0%
0%
0%
0%
0%
0%
0%
100%
0%
Mellon Capital 0.99 1.03 –1% 43% 19% 19% 11% 8% 0% 0% 0% 0%
HW Large Value0.82 1.53 –8% 1% 0% 0% 99% 0% 0% 0% 0% 0%0%
0%
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0%Figure 7.7 DTR α efficient frontier representation.