266 Optimizing Optimization
rules for each of these choices and so, for illustrative purposes, we apply our
ideas to a real-world dataset involving the FTSE 100 list of companies. 23 Our
sample begins on 2 January 2003 and ends on 23 December 2008, and there-
fore includes the recent period of financial turmoil linked to the credit crunch.
11.7.1 The decay factor, ρ
In order to operationalize the idea of data reweighting, it remains to choose
an optimal value of ρ. Although cross-validation is arguably the most natural
method of estimating ρ * ( Stone, 1974 ; Fan & Yao, 2000 ), the relative abun-
dance of FTSE 100 data in both the time and cross-sectional dimensions leads
us to consider an alternative strategy.
We start by creating an asset universe that comprises 6 months of daily
FTSE 100 data from U 1 ~ Uniform[3, 10] randomly selected equities between
2 January 2003 and 23 December 2008. The optimization algorithm is then
applied to the data and the optimal portfolio weights are obtained for vari-
ous values of ρ (0, 1]. One-month out-of-sample expected utility is recorded
and the entire process is repeated N 250 times for different combinations of
equities and time periods in order to deliver an optimal ρ that is robust under
a variety of circumstances. For both geometric and hyperbolic weight schemes,
we find that the optimal value of ρ is strictly less than unity, which confirms
our earlier suspicions surrounding the superior information content of the most
recent data (see Figure 11.5 for the hyperbolic case).
0.75 0.8 0.85 0.9 0.95 1–0.9998–0.9998–0.9997–0.9997Decay coefficient, RhoExpected utilityFigure 11.5 Optimal hyperbolic decay coefficient, ρ , for 6 months of data.
23 All data are from Yahoo! Finance, sampled at a daily frequency and measured in Pounds Sterling ( £ ).