One implication of the strategies we implement is that they seem to have higher daily turnover than we initially expected. For future work, it would be a great idea to somehow reduce the daily turnover.
One idea might be to limit the strategies’ ability to buy once a month instead of once per week. This would fit naturally with the prediction timeline of 20-days for the LSTM and XGBoost strategies and would simultaneously reduce the daily turnover due to less frequent trading.
Likewise, the current implementation assumes 0-cost commissions which is only realistic as a US-resident through brokers like Robinhood67 and Interactive Brokers68, but in any other setting this is not necessarily the case. As such, reducing the turnover and increasing the cost of commission would be a natural step for future work and research.
Another obvious candidate for future research would be to introduce shorting in the strategies. Cur-rently the strategies are limited to long-only which is potentially limiting to the overall performance.
Lastly, GRU-cells compared to LSTM-cells in Recurrent Neural Networks shows some promise of being faster at convergence while maintaining similar performance, this could also be interesting to research further. Longer time-series frequencies could also be considered as input for the RNN model using 1D-Convolutional layers to ”down-sample” the frequencies to manageable sizes.
67Robinhood
68Interactive Brokers
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10 Appendix
1 - Overview of monthly and yearly returns for 4 strategies with HRP
Figure 60: Momentum HRP monthly and yearly returns
Figure 61: XGBoost HRP monthly and yearly returns
Figure 62: LSTM HRP monthly and yearly returns
Figure 63: 2/3 ensemble HRP monthly and yearly returns
2 - Overview of top 5 drawdown periods for all strategies Table 11: Momentum top 5 drawdown periods Asset Allocation Hierarchical Risk Parity Worst drawdown
periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 17.45 2018-01-22 2018-05-02 2019-04-01 311
2 15.34 2015-04-10 2016-11-04 2016-11-17 420
3 8.26 2014-03-04 2014-05-19 2014-08-18 120
4 7.77 2014-09-19 2014-10-29 2014-11-28 51
5 7.36 2017-06-22 2017-08-29 2017-10-26 91
Asset Allocation Naive 1/N
Worst drawdown periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 17.67 2015-04-10 2015-12-14 2016-11-14 417
2 12.11 2018-01-22 2018-05-02 2019-04-02 312
3 10.19 2014-02-27 2014-04-11 2014-08-22 127
4 8.04 2019-04-24 2019-08-05 2019-09-02 94
5 7.37 2014-10-03 2014-10-29 2014-12-03 44
Table 12: XGBoost top 5 drawdown periods Asset Allocation Hierarchical Risk Parity Worst drawdown
periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 21.90 2015-04-10 2015-08-25 2016-06-29 319
2 16.80 2018-10-08 2018-12-25 2019-02-15 95
3 11.46 2017-03-02 2018-03-23 2018-06-18 338
4 10.51 2014-12-03 2014-12-15 2014-12-23 15
5 9.87 2014-09-05 2014-10-15 2014-11-21 56
Asset Allocation Naive 1/N
Worst drawdown periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 22.72 2015-03-18 2015-08-25 2016-06-02 317
2 18.62 2018-09-21 2018-12-25 2019-05-03 161
3 13.18 2014-09-05 2014-12-15 2015-01-16 96
4 10.05 2017-03-01 2017-08-29 2018-06-14 337
5 9.98 2019-07-26 2019-08-15 2019-09-10 33
Table 13: LSTM top 5 drawdown periods Asset Allocation Hierarchical Risk Parity Worst drawdown
periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 26.47 2015-04-15 2015-09-28 2017-12-08 693
2 13.57 2018-12-03 2018-12-25 2019-02-04 46
3 12.66 2018-01-29 2018-04-02 2018-06-15 100
4 11.17 2019-09-16 2019-10-18 NaN NaN
5 10.93 2014-11-21 2014-12-16 2015-01-21 44
Asset Allocation Naive 1/N
Worst drawdown periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 30.86 2015-04-15 2016-02-11 2019-07-05 1103
2 10.35 2014-11-07 2014-12-16 2014-12-19 31
3 7.20 2019-09-16 2019-10-08 2019-12-20 70
4 6.75 2014-09-05 2014-10-13 2014-10-31 41
5 5.39 2014-12-23 2015-01-12 2015-01-22 23
Table 14: 2/3 Ensemble top 5 drawdown periods Asset Allocation Hierarchical Risk Parity Worst drawdown
periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 18.30 2015-03-16 2015-09-28 2016-06-29 338
2 15.89 2018-12-03 2018-12-25 2019-02-21 59
3 10.21 2017-03-02 2017-08-29 2017-12-07 201
4 9.32 2016-07-22 2016-11-04 2016-11-22 88
5 9.17 2018-01-23 2018-03-23 2018-05-25 89
Asset Allocation Naive 1/N
Worst drawdown periods
Net drawdown
in % Peak Date Valley Date Recovery Duration in days
1 16.79 2015-03-18 2015-08-25 2016-07-08 343
2 15.45 2018-12-03 2018-12-25 2019-02-14 54
3 10.70 2017-03-02 2017-08-29 2017-12-22 212
4 8.58 2018-01-23 2018-03-23 2018-05-25 89
5 8.49 2019-05-03 2019-05-31 2019-07-24 59
3 - Fama-French Small Minus Big individual portfolios used for construction:
SMBB/M = 1/3(Small V alue+Small N eutral+Small Growth)
−1/3(Big V alue+Big N eutral+Big Growth) SMBOP = 1/3(Small Robust+Small N eutral+Small W eak)
−1/3(Big Robust+Big N eutral+Big W eak)
SMBIN V = 1/3(Small Conservative+Small N eutral+Small Aggressive)
−1/3(Big Conservative+Big N eutral+Big Aggressive)
4 - Fundamentals:
FEATURE NAMES 0 EQ RETURNS 1 EQ ADR CHECK 2 EQ ASSETS SHARE 3 EQ AVAIL CHECK 4 EQ BOOKVAL SHARE 5 EQ CAPEX SHARE 6 EQ CAPEX SHARE 1Y 7 EQ CAPEX SHARE 2Y 8 EQ CASH EQUIV SHARE 9 EQ CASH SHARE
10 EQ CASH TAXES SHARE 11 EQ CLOSEPRICE
12 EQ COMMON SHARE OUT 13 EQ COMMON SHARE OUT 1Y 14 EQ COMMON SHARE OUT 2Y 15 EQ COMMON SHARE OUT LESS 16 EQ COUNTRY NUM
17 EQ CURR ASSETS SHARE 18 EQ CURR ASSETS SHARE 1Y
19 EQ DEFTAXES INV CREDITS SHARE 20 EQ DEFTAXLIAB SHARE
21 EQ DEPREC AMOR SHARE
22 EQ DEPREC DEPLET AMORT CF SHARE 23 EQ DEPREC DEPLET AMORT SHARE 24 EQ DEPREC DEPLET AMORT SHARE 1Y 25 EQ DEPREC DEPLET AMORT SHARE 2Y 26 EQ DILUTEDSHARES SHARE
27 EQ DIV SHARE
28 EQ DOWN REVISIONS 29 EQ EARN SHARE
30 EQ EARN SHARE BASE 31 EQ EARN SHARE DILUTED 32 EQ EBITDA SHARE
33 EQ EBIT SHARE
FEATURE NAMES
34 EQ ENTERPRISEVALUE
35 EQ ENTERPRISEVALUE SHARE 36 EQ EQUITY AFFIL EARN SHARE 37 EQ FREECF SHARE
38 EQ FREECF SHARE 1Y 39 EQ FREECF SHARE 2Y 40 EQ GICS CODE
41 EQ GROSSINCOME SHARE 42 EQ GROSS PP E SHARE 43 EQ GROSS PP E SHARE 1Y
44 EQ GROSS RECEIVABLES SHARE 45 EQ GROSS RECEIVABLES SHARE 1Y 46 EQ INCOMETAXPAYABLES SHARE 47 EQ INCOMETAX SHARE
48 EQ INTANGIBLES SHARE 49 EQ INTANGIBLES SHARE 1Y 50 EQ INTERESTEXPENSE SHARE 51 EQ INVENTORIES SHARE 52 EQ INVENTORIES SHARE 1Y 53 EQ INVESTEDCAPITAL SHARE 54 EQ INV IN AFFIL SHARE
55 EQ INV IN AFFIL SHARE 1Y 56 EQ IS COMPANY
57 EQ LONGTERMDEBT SHARE 58 EQ MARKETCAP USD
59 EQ MINORITIES SHARE 60 EQ MV PER SHARE 61 EQ NETCF SHARE 62 EQ NETDEBT SHARE 63 EQ NETINCOME SHARE
64 EQ NETINTEREST EXPENSE SHARE 65 EQ NETNON OPERATING INC SHARE 66 EQ OTHERCURRLIAB SHARE
67 EQ OTHERLIAB SHARE