EXPERIMENT 3 109
except the DJIAdataset; and OLMAR achieves excellent performance in all datasets.
These encouraging results show that the proposed methods are able to reach a good
trade-off between return and risk, even though we do not explicitly consider risk in
the method formulations.
13.3 Experiment 3: Evaluation of Parameter Sensitivity
In the following four subsections, we evaluate how different choices of parameters
affect the proposed four strategies.
13.3.1 CORN’s Parameter Sensitivity
The proposed CORN has two parameters, that is, the correlation coefﬁcient thres-
hold ρ and the window size for the experts w (or W ).
First, let us see the effects of ρ with ﬁxed W , in Figure 13.3. Clearly, the ﬁgures
validate the preliminary analysis in Section 8.4. In general, CORN achieves the best
performance when ρ is around 0, as the ﬁgures often peak around 0 or some small
positive values; and, when ρ approaches −1 or 1, CORN’s performance degrades.
Although CORN does not perform well on the TSE and DJIA datasets, on which the
cumulative wealth is often less than the BCRP strategy, it signiﬁcantly outperforms
the two benchmarks on other datasets. Based on the above observation, choosing a
satisfying ρ for CORN is straightforward, as some small positive values often give
good performance on all datasets.
We also examine the effects of W with ﬁxed ρ in Figure 13.4. Note that here CORN
denotes the CORN experts with a speciﬁed w and CORN-U denotes the uniform com-
bination of CORN experts with w from 1 to W . Although the cumulative wealth
achieved by CORN experts ﬂuctuates with different w’s, CORN-U’s cumulative
wealth is much more robust with respect to W . Such an observation validates the
effectiveness of the proposed CORN-U and eases the selection of a satisfying W.
13.3.2 PAMR’s Parameter Sensitivity
In this section, we examine PAMR’s parameters, that is, the mean reversion threshold
for the three algorithms and the aggressiveness parameter C for the two variants.
First, we examine the effect of on PAMR’s cumulative wealth. As is greater
than 1, PAMR degrades to uniform constant rebalanced portfolios (CRP) strategy, and
the wealth stabilizes at a constant value achieved by uniform CRP. Thus, we show the
effect of in the range of [0, 1.5]. Figure 13.5 shows the cumulative wealth achieved
by PAMR with varying and two benchmarks, that is, Market and BCRP. Results on
most datasets, except the DJIA dataset, show that the cumulative wealth achieved by
PAMR consistently grows as approaches 0. That is, the smaller the threshold, the
higher the cumulative wealth is, which validates that the motivating mean reversion
does exist on most stock markets. Moreover, in most cases, the cumulative wealth
tends to stabilize as crosses certain dataset-dependent thresholds. As stated before,
We will study it in future.
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