QuantNet: transferring learning across trading strategies

Figures & data

Figure 1. QuantNet workflow: from market data to decoding/signal generation.

Figure 2. World map depicting the different clusters formed from the scores of QuantNet encoder. For visualization purposes, we have picked the market with the biggest market capitalization to represent the country in the cluster.

Figure 3. Histogram of Sharpe ratio contrasting QuantNet with baseline strategies.

Table 1. Median and mean absolute deviation (in brackets) performance on 3103 stocks across all markets analysed.

Metric	Buy and hold	Risk parity	TS Mom	CS Mom	No Transfer LSTM	No Transfer Linear	QuantNet
Ann Ret	0.000020	0.000193	0.000050	0.000042	0.002508	0.001537	0.005377
	(0.13433)	(0.00270)	(0.00019)	(0.00019)	(0.07645)	(0.08634)	(0.02898)
Ann Vol	0.287515	0.001536	0.000290	0.000270	0.008552	0.007768	0.023665
	(0.10145)	(0.00537)	(0.00036)	(0.00036)	(0.13455)	(0.14108)	(0.04540)
CR	0.000040	0.095516	0.139599	0.143195	0.158987	0.169345	0.241255
	(0.33583)	(0.29444)	(1.05288)	(1.18751)	(0.55762)	(0.57170)	(0.59968)
DownRisk	0.202361	0.001076	0.000195	0.000178	0.005656	0.005124	0.015734
	(0.07042)	(0.00361)	(0.00024)	(0.00025)	(0.09223)	(0.09553)	(0.03291)
Kurt	5.918386	6.165916	13.333863	18.112853	16.87256	15.73864	16.19961
	(10.2515)	(13.9426)	(19.2278)	(24.4672)	(30.2204)	(31.0395)	(24.7336)
MDD	−0.419984	−0.002935	−0.000488	−0.000444	−0.014564	−0.01286	−0.03847
	(0.14876)	(0.00987)	(0.00082)	(0.00081)	(0.16724)	(0.17820)	(0.07881)
SR	0.000051	0.155560	0.226471	0.234583	0.304244	0.306572	0.354776
	(0.42324)	(0.42028)	(0.40627)	(0.41547)	(0.51552)	(0.51182)	(0.57218)
Skew	−0.087282	−0.092218	0.427237	0.568364	0.256736	0.171629	0.297182
	(0.82186)	(0.96504)	(1.28365)	(1.60612)	(1.77245)	(1.74804)	(1.66854)
SortR	0.217621	0.220335	0.333685	0.349124	0.443422	0.454035	0.52196
	(0.59710)	(0.61883)	(1.02616)	(0.633953)	(0.78525)	(0.86715)	(1.02465)

TS Mom, time series momentum and CS Mom, cross-section momentum. We highlighted in bold only the metrics where a comparison can be made, like Sharpe ratios, Calmar ratios, Kurtosis, Skewness, and Sortino ratios.

Figure 4. Average Sharpe ratios of QuantNet and No Transfer across 58 equity markets.

Figure 5. (a) Average cumulative returns (%) of SPX Index, UKX Index, KOSPI Index and SASEIDX Index contrasting QuantNet and No Transfer. Average Sharpe ratio difference between QuantNet versus No Transfer, aggregated by sample size (b) and number of assets per market (c)—in both we have subtracted QuantNet SR from No Transfer SR to reduce cross-asset variance and baseline effect.

Table A1. Markets used during our experiment.

Region	Index/Market	Country	# Samples	# Assets	Region	Index/Market	Country	# Samples	# Assets
Americas	IBOV	Brazil	3250	29	Europe	HEX	Finland	1882	65
Americas	MERVAL	Argentina	3055	11	Europe	IBEX	Spain	3499	23
Americas	MEXBOL	Mexico	3002	19	Europe	ISEQ	Ireland	2888	14
Americas	RTY	US	2356	554	Europe	KFX	Denmark	3345	15
Americas	SPTSX	Canada	3173	129	Europe	OBX	Norway	2812	17
Americas	SPX	US	3291	376	Europe	OMX	Sweden	3453	29
Asia and Pacific	AS51	Australia	2363	91	Europe	PX	Czechia	3374	5
Asia and Pacific	FBMKLCI	Malaysia	3131	23	Europe	SBITOP	Slovenia	2995	6
Asia and Pacific	HSI	China	2599	37	Europe	SMI	Switzerland	3948	19
Asia and Pacific	JCI	Indonesia	2007	44	Europe	SOFIX	Bulgaria	1833	5
Asia and Pacific	KOSPI	South Korea	3041	297	Europe	UKX	UK	3664	75
Asia and Pacific	KSE100	Pakistan	2036	41	Europe	VILSE	Lithuania	2765	5
Asia and Pacific	NIFTY	India	3066	38	Europe	WIG20	Poland	3449	8
Asia and Pacific	NKY	Japan	3504	186	Europe	XU100	Turkey	2545	76
Asia and Pacific	NZSE50FG	New Zealand	3258	21	MEA	DFMGI	UAE	2184	11
Asia and Pacific	PCOMP	Philippines	3013	16	MEA	DSM	Qatar	2326	16
Asia and Pacific	SHSZ300	China	2881	18	MEA	EGX30	Egypt	1790	22
Asia and Pacific	STI	Singapore	2707	27	MEA	FTN098	Namibia	1727	16
Asia and Pacific	TWSE	Taiwan	3910	227	MEA	JOSMGNFF	Jordan	2287	15
Europe	AEX	Netherlands	4083	17	MEA	KNSMIDX	Kenya	1969	14
Europe	ASE	Greece	2944	51	MEA	KWSEPM	Kuwait	2785	11
Europe	ATX	Austria	3511	13	MEA	MOSENEW	Morocco	2068	27
Europe	BEL20	Belgium	3870	14	MEA	MSM30	Oman	2069	24
Europe	BUX	Hungary	3753	8	MEA	NGSE30	Nigeria	1761	25
Europe	BVLX	Portugal	3269	17	MEA	PASISI	Palestine	1447	5
Europe	CAC	France	3591	36	MEA	SASEIDX	Saudi Arabia	1742	71
Europe	CRO	Croatia	1975	13	MEA	SEMDEX	Mauritius	2430	5
Europe	CYSMMAPA	Cyprus	2056	42	MEA	TA-35	Israel	2677	23
Europe	DAX	Germany	3616	27	MEA	TOP40	South Africa	2848	34

MEA, Middle East and Africa.

Table B1. No Transfer and QuantNet hyperparameters and configurations investigated.

	No transfer		QuantNet (encoder/decoder-transfer layer)
Hyper-parameter	Linear	LSTM	Linear-linear	Linear-LSTM	LSTM-linear	LSTM-LSTM
Batch size (L)	16-128	16-128	16-128	16-96	16-96	16-96
Sequence length (p)	21-504	21-504	21-504	21-252	21-252	21-252
Learning rate	0.0001-0.1	0.0001-0.1	0.0001-0.1	0.0001-0.5	0.0001-0.5	0.0001-0.5
E/D # layers		1-2			1-2	1-2
E/D dropout		0.1-0.9			0.1-0.9	0.1-0.9
TL # layers				1-2		1-2
TL dropout				0.1-0.9		0.1-0.9
TL dimension (N)	10, 25, 50, 100
Training steps	2000

Figure A1. Taxonomy of transfer learning sub-paradigms.

Table D1. Approaches and applications of transfer learning across finance and general domains.

Approach	Brief description	Financial applications	Other references
Instance	Re-weighting labelled data in the source domain for use in the target domain	News-rich to news-poor stocks (Li et al. 2018); mitigating class imbalance in credit scoring (Li et al. 2018, Voumard and Beydoun 2019)	Jiang et al. (2019), Qu et al. (2019)
Feature	Find a suitable feature mapping to approximate the source domain to the target domain	Sentiment feature space (Li et al. 2018); Portfolio selection factors (Hu et al. 2015)	Zhuang et al. (2015), Yang et al. (2018)
Parameter	Learn shareable parameters or priors between the source and target tasks models	BERT specialized to financial sentiment analysis (Araci 2019, Hiew et al. 2019); Stock selection, forecasting (Ghosn and Bengio 1997, Bitvai and Cohn 2015); yield curve forecasting (Nunes et al. 2019)	Devlin et al. (2018b), Chen et al. (2019)
Relational-knowledge	Learn a logical relationship or rules in the source domain and transfer it to the target domain		Park et al. (2019), Wang et al. (2016)

Figure A2. Average Sharpe (a) and Calmar (b) ratios of QuantNet and No Transfer across 58 markets.

Figure A3. World map of average relative (%) Sharpe ratio difference between QuantNet versus No Transfer. For visualisation purposes, we have averaged the metric for the USA, China, and Israel/Palestine.

Figure A4. Scatterplot of QuantNet and No Transfer average Sharpe (a) and Calmar (b) ratios of each market overlaid by a linear regression curve.

Table E1. Financial metrics of QuantNet and No Transfer strategies in SPX Index, UKX Index, KOSPI Index, and SASEIDX Index.

	Americas_SPX		Asia and Pacific_KOSPI		Europe_UKX		MEA_SASEIDX
Mean (SD)	No transfer	QuantNet	No transfer	QuantNet	No transfer	QuantNet	No transfer	QuantNet
Ann Ret	0.000133	0.041031	0.073337	0.054152	0.000406	0.006555	0.000642	0.026092
	(0.001259)	(0.029839)	(0.25494)	(0.046237)	(0.001395)	(0.00609)	(0.002784)	(0.012866)
Ann Vol	0.002436	0.053368	0.403113	0.07075	0.002717	0.009576	0.003598	0.01895
	(0.00064)	(0.012918)	(0.144194)	(0.025008)	(0.00111)	(0.004583)	(0.003219)	(0.004739)
CR	0.133073	0.756976	0.289853	0.822309	0.210127	0.813796	0.267246	1.783155
	(0.377186)	(0.616175)	(0.620299)	(0.785171)	(0.445449)	(0.708568)	(0.745929)	(1.133185)
DownRisk	0.001717	0.035575	0.271677	0.047184	0.001661	0.005364	0.002236	0.010502
	(0.000522)	(0.009612)	(0.098263)	(0.017854)	(0.000433)	(0.002129)	(0.000513)	(0.002464)
Kurt	33.29913	19.51515	13.87472	22.58056	95.31436	88.42658	41.8963	33.41796
	(45.57039)	(18.51033)	(19.28247)	(34.13021)	(135.1503)	(116.5215)	(87.54653)	(48.08607)
MDD	−0.00467	−0.06681	−0.50323	−0.09328	−0.00432	−0.00988	−0.00614	−0.01755
	(0.002296)	(0.028684)	(0.190464)	(0.051306)	(0.001905)	(0.005301)	(0.003198)	(0.007012)
SR	0.061702	0.783197	0.347892	0.783428	0.108635	0.627227	0.12883	1.362307
	(0.512651)	(0.49204)	(0.540274)	(0.578968)	(0.529708)	(0.486396)	(0.579286)	(0.586632)
Skew	−0.21186	0.28355	0.374017	0.277958	2.943023	3.573138	0.495534	2.469297
	(2.851112)	(1.685894)	(1.36364)	(2.239952)	(6.586847)	(5.566353)	(4.07845)	(2.360219)
SortR	0.144905	1.245084	0.564466	1.256064	0.301707	1.207481	0.359786	2.587949
	(0.760463)	(0.847215)	(0.839065)	(0.979779)	(0.898402)	(0.979499)	(1.206481)	(1.344404)
	Americas_SPX		Asia and Pacific_KOSPI		Europe_UKX		MEA_SASEIDX
Median (MAD)	No transfer	QuantNet	No transfer	QuantNet	No transfer	QuantNet	No transfer	QuantNet
Ann Ret	0.000197	0.038476	0.059234	0.052772	0.000326	0.005321	0.000508	0.023614
	(0.000982)	(0.023214)	(0.188703)	(0.036438)	(0.00108)	(0.004778)	(0.001666)	(0.009858)
Ann Vol	0.002399	0.053732	0.380229	0.066449	0.002495	0.008573	0.003128	0.01865
	(0.000497)	(0.010269)	(0.111283)	(0.01968)	(0.000695)	(0.003598)	(0.001038)	(0.002928)
CR	0.045842	0.626018	0.133249	0.657845	0.092861	0.654498	0.091411	1.676411
	(0.271252)	(0.479759)	(0.470007)	(0.605487)	(0.328843)	(0.584447)	(0.410032)	(0.912643)
DownRisk	0.001648	0.035679	0.254761	0.044209	0.00157	0.004724	0.002257	0.009973
	(0.000395)	(0.007424)	(0.076679)	(0.013787)	(0.000333)	(0.00173)	(0.000405)	(0.001975)
Kurt	20.43113	14.44403	8.225536	13.04102	35.86203	30.40254	25.0625	28.02965
	(23.64829)	(10.23454)	(10.6417)	(17.31602)	(96.22141)	(86.32176)	(30.82765)	(15.90609)
MDD	−0.00419	−0.06071	-0.49819	−0.08132	−0.00393	−0.00841	−0.00578	−0.01573
	(0.001741)	(0.020741)	(0.157264)	(0.039347)	(0.001549)	(0.003937)	(0.002449)	(0.005458)
SR	0.085695	0.79579	0.366404	0.818361	0.154884	0.628875	0.184811	1.382302
	(0.406313)	(0.400688)	(0.437163)	(0.465154)	(0.407551)	(0.379645)	(0.451943)	(0.4808)
Skew	0.044563	0.407357	0.271776	0.148158	0.360259	1.385536	−0.06615	2.559821
	(1.742953)	(1.110312)	(0.811512)	(1.318841)	(4.960393)	(4.198536)	(2.102935)	(1.412129)
SortR	0.112332	1.205009	0.55375	1.235756	0.203793	1.128096	0.26026	2.315208
	(0.595473)	(0.690404)	(0.675314)	(0.779847)	(0.701329)	(0.793781)	(0.764835)	(1.124332)

Figure A5. Average cumulative returns (%) of SPX Index, UKX Index, KOSPI Index and SASEIDX Index contrasting QuantNet and No Transfer strategies. Before aggregation, each underlying asset was volatility-weighted to 10%.

Figure A6. Histogram of Sharpe ratio of SPX Index, UKX Index, KOSPI Index, and SASEIDX Index contrasting QuantNet and No Transfer strategies.

Figure A7. Scatterplot of Sharpe ratio of SPX Index, UKX Index, KOSPI Index, and SASEIDX Index contrasting QuantNet and No Transfer strategies.

Table F1. Models coefficients and t-stats for the different markets and factors.

	SPX		UKX		SASEIDX		KOSPI
	Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat
Alpha	0.0003${}^{\ast }$	2.554	0.0002${}^{\ast }$	2.258	0.0006${}^{\ast }$	3.856	0.0003${}^{\ast }$	4.034
Beta	−0.0004${}^{\ast }$	−2.367	−0.0002	−1.558	−0.0006${}^{\ast }$	−2.804	−0.0001	−0.213
Small minus Big	0.0003	1.158	0.0002	1.075	0.0006	1.856	0.0001	0.182
High minus Low	−0.0005	−1.778	−0.0006${}^{\ast }$	−2.813	−0.0002	−0.781	−0.0001	−0.148
Momentum	−0.0002	−1.042	0.0001	0.08	−0.0002	−0.918	−0.0001	−0.538

${}^{\ast }$p-value < 0.05.

Figure A8. Dendrogram of hierarchical clustering using the scores from QuantNet encoder layer.

Table H1. Average Sharpe ratio per different dimensions and configurations of QuantNet and No Transfer strategies.

		No transfer		QuantNet (encoder/decoder-transfer layer)
Sharpe ratio	Dimension	Linear	LSTM	Linear–Linear	Linear–LSTM	LSTM–Linear	LSTM–LSTM
Mean (SD)	10	0.324257	0.311424	0.355600	0.361986	0.370918	0.279758
		(0.6541)	(0.665251)	(0.704641)	(0.711988)	(0.715636)	(0.70962)
	25	0.324257	0.311424	0.333565	0.324842	0.325667	0.275786
		(0.6541)	(0.665251)	(0.702325)	(0.755392)	(0.707544)	(0.699151)
	50	0.324257	0.311424	0.319009	0.320583	0.234741	0.258272
		(0.6541)	(0.665251)	(0.698568)	(0.725952)	(0.752143)	(0.706733)
	100	0.324257	0.311424	0.326090	0.353448	0.228464	0.298445
		(0.6541)	(0.665251)	(0.695066)	(0.730362)	(0.722084)	(0.702126)
Median (MAD)	10	0.306572	0.304244	0.338981	0.345072	0.354776	0.275548
		(0.51182)	(0.515521)	(0.559216)	(0.533789)	(0.572184)	(0.562)
	25	0.306572	0.304244	0.314084	0.301769	0.273791	0.227461
		(0.51182)	(0.515521)	(0.552154)	(0.570677)	(0.555298)	(0.552615)
	50	0.306572	0.304244	0.302167	0.303684	0.205637	0.219550
		(0.51182)	(0.515521)	(0.546099)	(0.537824)	(0.583648)	(0.554146)
	100	0.306572	0.304244	0.307922	0.330039	0.188830	0.243308
		(0.51182)	(0.515521)	(0.540111)	(0.549627)	(0.573707)	(0.557717)

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