126 EMPIRICAL RESULTS
Table 13.6 Top five (average) allocation weights of some strategies on NYSE (O)
Asset # 6 23 9 26 20 Asset # 23 6 20 9 16
BCRP 0.28 0.25 0.20 0.18 0.09 EG 0.032 0.030 0.029 0.029 0.029
Asset # 8 35 2 3 22 Asset # 23 20 26 33 9
ONS 0.25 0.17 0.13 0.07 0.06 B
K
0.21 0.11 0.08 0.07 0.06
Asset # 23 20 9 6 26 Asset # 23 9 26 6 20
B
NN
0.21 0.15 0.08 0.08 0.08 CORN 0.38 0.09 0.09 0.09 0.08
Asset # 20 23 9 26 6 Asset # 23 20 9 26 6
Anticor 0.11 0.10 0.10 0.06 0.05 PAMR 0.19 0.11 0.11 0.08 0.06
top five weighted assets, the three algorithms also have much higher volatilities on
other assets. Concerning their performance, it is possible that to achieve better per-
formance, a portfolio has to be frequently rebalanced, not only on certain assets as
the pattern matching–based algorithms do but also on all assets.
Second, most average weights of the state-of-the-art algorithms are assigned to
the assets with the highest volatilities (highest Std values). It is common knowl-
edge that high return is often associated with high risk,
∗
while the reverse is not
always true. That is, although a portfolio has to be rebalanced among volatile assets,
such that the portfolio can gain profits from market volatility, high volatility can-
not guarantee high profit. For example, on the NYSE (O) dataset, although Anticor
and PAMR have the same top five average allocation pool, their performances are
drastically different.
Third, PAMR, which systematically exploits the mean reversion property, rebal-
ances more actively than Anticor, and OLMAR rebalances even more actively.
Connecting the rebalance activities to their performance, we may conclude that even
though both are based on the same principle, more active rebalance leads to better
performance, as it can better exploit market volatility. PAMR’s concentration on asset
#23, which has the highest negative autocorrelation, sheds lights on the possible con-
nection between mean reversion algorithms and the autocorrelation among assets (Lo
and MacKinlay 1990; Conrad and Kaul 1998; Lo 2008). Moreover, from Table C.5,
we can observe that most of the top average allocation weights of the mean reversion
algorithms are assets with negative autocorrelations, except DJIA.
13.7 Summary
In this chapter, we empirically evaluated the four proposed algorithms. The empiri-
cal results clearly validate the effectiveness of the proposed algorithms. In terms of
cumulative wealth, which is the main performance metric, our proposed algorithms
sequentially beat the state-of-the-art algorithms. In terms of (volatility/drawdown)
risk-adjusted return, the proposed algorithms achieve high risk-adjusted returns,
∗
Such a statement is true in traditional finance. However, in recent years, some arbitrage strategies,
which can earn return without high risk, have emerged.
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