EXPERIMENT 2 105
This observation supports the effectiveness of proposed algorithms, and, to the best
of our knowledge, no one has ever claimed such a fantastic performance.
Fourthly, it is promising to see that all pattern matching–based algorithms, espe-
cially CORN, have better performance than the benchmarks on most datasets. And
the proposed CORN signiﬁcantly outperforms the existing pattern matching–based
algorithms, including B
, validating its motivating idea of improving the
matching process. Fifthly, the encouraging results achieved by the last three strategies
(PAMR, CWMR, and OLMAR) validate the importance of exploiting mean reversion
in ﬁnancial markets via an effective learning algorithm.
In addition, we can see that most algorithms perform poorly on the DJIA
dataset, including CORN, PAMR, and CWMR. While the failure of CORN is still
unexplainable, the failure of the two mean reversion algorithms indicates that the
motivating (single-period) mean reversion may not exist in the dataset, as analyzed in
Sections 10.1 and 11.1.2. While OLMAR is proposed to explore (multiple-period)
moving average reversion, it can achieve much better performance, which thus
validates its motivating idea.
On the reversed datasets, though not as shiny as the original datasets, the pro-
posed algorithms also perform excellently. In all cases, the proposed algorithms not
only beat the benchmarks, including the market and BCRP, but also achieve the best
performance. Note that these reversed datasets are artiﬁcial datasets, which never
exist in real markets. However, algorithms’ behaviors on these datasets still provide
strong evidence that the proposed algorithms can effectively exploit the markets and
outperform the benchmarks and the state of the art.
Besides the ﬁnal cumulative wealth, we are also interested in examining how the
cumulative wealth changes over the entire trading periods. Figure 13.1 shows the
trends of cumulative wealth by the proposed algorithms and four existing algorithms
(two benchmarks and two state-of-the-art algorithms). Note that PAMR and CWMR
almost overlap on the ﬁgures; thus, we only present the trends of PAMR. Clearly, the
proposed strategies consistently surpass the benchmarks and the competing strategies
over the entire trading periods on most datasets (except DJIA dataset), which again
validates the efﬁcacy of the proposed techniques.
Finally, to measure whether such excess returns can be obtained by simple luck,
we conduct a statistical t-test as described in Section 12.4. Table 13.2 shows the
statistical results on the four proposed algorithms. The results clearly show that the
observed excess return is impossible to obtain by simple luck on most datasets. To be
speciﬁc, on datasets except DJIA, the probabilities for achieving the excess return by
luck are almost 0. On the DJIA dataset, though PAMR and CWMR have a probability
of 40% to achieve the excess return by luck, OLMAR has a probability of only 1.69%.
Nevertheless, the results show that the proposed strategies are promising and reliable
to achieve high returns with high conﬁdence.
13.2 Experiment 2: Evaluation of Risk and Risk-Adjusted Return
We now evaluate the volatility risk and drawdown risk, and the risk-adjusted return in
terms of an annualized Sharpe ratio (SR) and Calmar ratio (CR). Figure 13.2 shows
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