120 EMPIRICAL RESULTS
and OLMAR) and ignore the results of CWMR, whose curves often overlap that
of PAMR. For comparison, we also plot the results achieved by two state-of-the-art
strategies (Anticor and B
) and two benchmarks (BCRP and Market). Since most
follow the winner approaches try to approach BCRP, we ignore their ﬁgures.
From the ﬁgures, we can observe that the proposed algorithms can withstand
reasonable transaction cost rates, on most datasets. For example, the break-even rates
with respect to the market index vary from 0.2% to 0.8%, except DJIA, on which only
OLMAR can withstand around 0.3%. As CORN and PAMR/CWMR fail to beat the
markets on the DJIA dataset without transaction costs, their failures with transaction
costs can be naturally expected. On the other hand, the behaviors of the proposed
algorithms diverge. With a similar pattern-matching principle, CORN often performs
similar to B
, while both of them generally underperform the mean reversion algo-
rithms. Since the three mean reversion algorithms (PAMR, CWMR, and OLMAR)
revert to the mean more actively than Anticor and thus result in more drastic portfolio
rebalances, they surpass Anticor with low or medium transaction costs and underper-
form Anticor with high transaction costs. Note that the transaction cost rate in the
real market is low
; thus, the results clearly indicate the practical applicability of the
proposed strategies even when we consider reasonable transaction costs.
Second, margin buying is another practical concern for a real-world portfo-
lio selection task. To evaluate the impact of margin buying, we adopt the model
described in Section 2.2 and present the cumulative wealth achieved by the com-
peting approaches with or without margin buying in Table 13.3. The results clearly
show that if margin buying is allowed, the proﬁtability of the proposed algorithms
on most datasets increases. Similar to the results without margin buying, certain pro-
posed algorithms often achieve the best results with margin buying. In summary, the
proposed strategies can be extended to handle the margin-buying issue and beneﬁt
from it, and thus are practically applicable.
13.5 Experiment 5: Evaluation of Computational Time
Our next experiment is to evaluate the computational time costs of different
approaches, which is also an important issue in developing a practical trading strategy.
As previously analyzed, CORN has a batch-learning step on each period and is time
consuming in both its sample selection step and portfolio optimization step,
PAMR, CWMR, and OLMAR are online learning algorithms and cost linear time
per iteration. Table 13.4 presents the computational time cost (in seconds) of three
performance-comparable approaches (Anticor, B
, and B
) on the six datasets. All
the experiments were conducted on an Intel Core 2 Quad 2.66 GHz processor with
4 GB RAM, using MATLAB
2009b on Windows XP.
For example, without considering taxesand bid–ask, Interactive Broker(www.interactivebrokers.com)
charges $0.005 per share. Since the average price of Dow Jones Composites is around $50.00 (as of June
2011), the transaction cost rate is about 0.01%.
In its MATLAB implementation, the latter step costs more than 80% of the total time.
We use MATLAB function tic/toc to measure the time. There are preprocessing (such as data loader,
variable initialization, etc.) and postprocessing (such as result analysis, etc.), whose time is all excluded
from the time statistics in Table 13.4.
T&F Cat #K23731 — K23731_C013 — page 120 — 9/28/2015 — 21:35