42 Optimizing Optimization
impact, transaction cost, etc., are easy to model and can be incorporated as
objectives in a strategy, there are others such as transfer coefficient, implied
beta, ratio of specific risk to tracking error, etc. that are not directly amena-
ble to existing optimization techniques. This latter class of metrics, referred to
as intractable metrics in the sequel, nonetheless convey important information
about a portfolio and can influence a PM’s eventual choice. The example that
follows illustrates how heatmaps can be used to gain insights into these intrac-
table metrics.
Consider the “ ActiveLongOnly ” strategy discussed above. Figure 2.12 plots
the transfer coefficient of optimal portfolios that result from combinations of
tracking error and turnover values depicted in Figure 2.10. Similar to level
curves of Figure 2.10 , the level curves in Figure 2.12 give insight into the trend
of transfer coefficients of these optimal portfolios, which can be very helpful
in portfolio construction. For instance, a PM might be indifferent to portfolios
whose expected return is more than a certain predetermined level, and among
all such portfolios he or she might be interested in choosing one with maximum
transfer coefficient. This can be easily accomplished by selecting an appropriate
level curve from Figure 2.10 and overlaying it over the heatmap in Figure 2.12.
5.5
5.45
5.4
5.35
5.3
5.25
5.2
5.15
5.1
5.05Tracking errorTu r n o v e r5
4.95
4.9
4.85
4.8
4.75
4.7
4.65
4.6
4.55
4.5
27
27.327.627.928.228.528.829.129.429.7
30
30.330.630.931.231.531.832.132.432.7
33Color keyValue0.660.69 Transfer coefficientFigure 2.12 Turnover — tracking error — transfer coefficient heatmap.