Antinoise in U.S. equity markets

Figures & data

Figure 1. The S&P 500 index and the mean absolute signal correlations.

Notes: sample period: 1996.06–2020.08; The figure shows the relation between the S&P 500 Index and the mean absolute signal correlations between a collection of market-based and fundamental indicators. ${\rho }_{XX}$ is a correlation matrix that contains the cross-correlations between the signals. The mean of the absolute cross-correlations of the signals (the absolute of the elements of ${\rho }_{XX}$) indicates the strength of the correlations. See Section 3.2 for more detail about the signals (predictors).

Table 1. Predicted vs. realized returns (main result, out-of-sample).

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Logistic classification	Mean	0.03	0.05	0.06	0.06
	Median	0.03	0.05	0.06	0.08
	Max	0.28	0.58	0.77	0.81
	Min	−0.27	−0.55	−0.68	−0.75
	Std	0.09	0.17	0.23	0.29
Boosted trees	Mean	0.02	0.06	0.07	0.08
	Median	0.02	0.06	0.07	0.08
	Max	0.45	0.67	0.78	0.91
	Min	−0.44	−0.66	−0.76	−0.84
	Std	0.1	0.2	0.26	0.31

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Figure 2. Historical performance (main result, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Table 2. Performance indicators (main result, out-of-sample).

	Indicator	2014	2015	2016	2017	2018	2019	2020	Overall
Russell 1000 (eq w)	Return(%)	11.42	−3.15	16.32	18.66	−8.96	29.92	−2.0	8.54
	Volatility (%)	12.41	15.48	16.53	8.14	16.09	13.56	47.27	19.97
	max Drawdown	−9.53	−13.62	−12.64	−3.67	−21.54	−7.49	−41.67	−41.67
	Sharpe Ratio	0.92	−0.2	0.99	2.29	−0.56	2.21	−0.04	0.43
	Return to $|$max Drawdown$|$	1.2	−0.23	1.29	5.09	−0.42	4.0	−0.05	0.2
	Market Correlation	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
Logistic (Top 20, eq w)	Return(%)	16.99	16.65	28.55	23.5	14.97	35.65	22.62	23.78
	Volatility(%)	11.43	15.12	19.12	8.91	15.05	12.36	48.88	20.37
	max Drawdown	−7.41	−10.25	−10.34	−4.36	−12.4	−7.12	−39.17	−39.17
	Sharpe Ratio	1.49	1.1	1.49	2.64	0.99	2.88	0.46	1.17
	Return to $|$max Drawdown$|$	2.29	1.62	2.76	5.39	1.21	5.01	0.58	0.61
	Market Correlation	0.86	0.89	0.81	0.78	0.88	0.81	0.89	0.85
Boosted T (Top 20, eq w)	Return(%)	17.2	11.51	75.88	16.88	−2.24	29.37	38.83	26.22
	Volatility (%)	11.4	14.53	36.33	10.93	16.12	17.2	57.7	26.13
	max Drawdown	−7.98	−12.32	−13.57	−7.49	−20.34	−13.34	−40.42	−40.42
	Sharpe Ratio	1.51	0.79	2.09	1.55	−0.14	1.71	0.67	1.0
	Return to $|$max Drawdown$|$	2.15	0.93	5.59	2.26	−0.11	2.2	0.96	0.65
	Market Correlation	0.88	0.87	0.86	0.72	0.86	0.88	0.87	0.85

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Figure 3. Monte-Carlo correlations: varying ${\rho }_{XX}$, normal distribution.

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. Panel A shows the distribution of the empirical predictor correlations ${\rho }_{XX}$. Panel B shows the distribution of the simulated $R^2$'s. Panel C shows the distribution of the simulated predictor correlations ${\rho }_{XX}$ that yielded the lowest $R^2$. Panel D shows the distribution of the simulated predictor correlations ${\rho }_{XX}$ that yielded the highest $R^2$.

Figure 4. Monte-Carlo correlations: varying ${\rho }_{XX}$, bimodal distribution.

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. Panel A shows the distribution of the empirical predictor correlations ${\rho }_{XX}$. Panel B shows the distribution of the simulated $R^2$'s. Panel C shows the distribution of the simulated predictor correlations ${\rho }_{XX}$ that yielded the lowest $R^2$. Panel D shows the distribution of the simulated predictor correlations ${\rho }_{XX}$ that yielded the highest $R^2$.

Table 3. Implied market volatility and signal correlations (${\rho }_{XX}$).

Predictor Correlation	Subsample	abs(${\rho }_{XX}$)	CBOE VIX	Median iVol	Mean iVol
Pred Corr (t)	1996.06–2020.08	Median	0.35	0.41	0.43
		Mean	0.39	0.46	0.49
	2013.12–2020.08	Median	0.23	0.28	0.25
		Mean	0.32	0.37	0.34
Pred Corr (t,t-20)	1996.06–2020.08	Median	0.37	0.43	0.45
		Mean	0.45	0.52	0.54
	2013.12–2020.08	Median	0.26	0.35	0.32
		Mean	0.39	0.46	0.43
Pred Corr (t,t-60)	1996.06–2020.08	Median	0.39	0.43	0.45
		Mean	0.5	0.55	0.57
	2013.12–2020.08	Median	0.31	0.29	0.26
		Mean	0.39	0.39	0.36

Notes: Sample period: 1996.06–2020.08; The figure shows the relation between implied market volatility as measured by (i) the CBOE Volatility Index (VIX), (ii) the median and (iii) the mean implied 30-days at the money volatility of stocks in the Russell 1000; the strength of the correlations across signals as measured by (a) the median and (b) the mean absolute correlation in the Signal Correlations Matrix, ${\rho }_{XX}$. There are three samples for the predictor correlations: (i) day t, (ii) day t and day t-20, and (iii) day t and day t-60.

Figure A1. Historical performance (Robustness test A, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Table B1. Performance indicators (Robustness test A, out-of-sample).

	Indicator	2014	2015	2016	2017	2018	2019	2020	Overall
Logistic (Top 10, eq w)	Return(%)	19.74	17.96	22.33	24.24	23.37	39.64	35.22	27.32
	Volatility(%)	11.4	13.67	20.81	9.37	14.61	11.38	45.74	19.63
	max Drawdown	−6.49	−12.67	−10.63	−4.05	−12.06	−5.08	−34.08	−34.08
	Sharpe Ratio	1.73	1.31	1.07	2.59	1.6	3.48	0.77	1.39
	Return to $|$max Drawdown$|$	3.04	1.42	2.1	5.99	1.94	7.8	1.03	0.8
	Market Correlation	0.8	0.86	0.76	0.7	0.79	0.73	0.83	0.78
Logistic (Top 50, eq w)	Return(%)	18.01	7.74	29.85	18.56	4.34	42.38	5.02	18.24
	Volatility(%)	11.55	15.45	18.04	8.62	15.4	12.57	47.96	20.09
	max Drawdown	−7.62	−10.58	−10.01	−3.95	−16.19	−5.6	−41.6	−41.6
	Sharpe Ratio	1.56	0.5	1.66	2.15	0.28	3.37	0.1	0.91
	Return to $|$max Drawdown$|$	2.36	0.73	2.98	4.69	0.27	7.57	0.12	0.44
	Market Correlation	0.91	0.94	0.88	0.86	0.95	0.9	0.96	0.92
Boosted T (Top 10, eq w)	Return(%)	28.21	18.81	99.26	21.9	7.7	23.39	43.67	34.1
	Volatility(%)	12.32	16.68	45.61	12.2	16.57	19.87	56.94	28.69
	max Drawdown	−5.93	−13.11	−16.95	−7.21	−17.82	−15.15	−35.49	−35.49
	Sharpe Ratio	2.29	1.13	2.18	1.8	0.46	1.18	0.77	1.19
	Return to $|$max Drawdown$|$	4.76	1.43	5.86	3.04	0.43	1.54	1.23	0.96
	Market Correlation	0.8	0.79	0.8	0.61	0.8	0.82	0.85	0.79
Boosted T (Top 50, eq w)	Return(%)	16.66	7.55	57.71	13.81	−8.42	37.07	16.53	19.59
	Volatility(%)	11.0	14.37	28.13	10.04	16.07	15.5	55.2	23.69
	max Drawdown	−7.54	−11.9	−11.56	−6.42	−20.2	−8.58	−40.29	−40.29
	Sharpe Ratio	1.51	0.53	2.05	1.38	−0.52	2.39	0.3	0.83
	Return to $|$max Drawdown$|$	2.21	0.63	4.99	2.15	−0.42	4.32	0.41	0.49
	Market Correlation	0.91	0.93	0.91	0.85	0.93	0.92	0.94	0.91

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Figure A2. Historical performance (robustness test B, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2016.12; out-of-sample period: 2016.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Table C1. Predicted vs. realized returns (robustness test B, out-of-sample).

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Logistic classification	Mean	0.04	0.07	0.08	0.1
	Median	0.04	0.08	0.09	0.1
	Max	0.34	0.58	0.71	0.81
	Min	−0.31	−0.57	−0.66	−0.8
	Std	0.11	0.18	0.22	0.27
Boosted trees	Mean	0.02	0.05	0.05	0.06
	Median	0.0	0.03	0.07	0.07
	Max	0.44	0.66	0.8	0.88
	Min	−0.24	−0.49	−0.64	−0.74
	Std	0.1	0.2	0.25	0.31

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2016.12; out-of-sample period: 2016.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Table C2. Performance indicators (robustness test B, out-of-sample).

	Indicator	2017	2018	2019	2020	Overall
Russell 1000 (eq w)	Return(%)	18.66	−8.96	29.92	−2.0	9.1
	Volatility(%)	8.14	16.09	13.56	47.27	23.32
	max Drawdown	−3.67	−21.54	−7.49	−41.67	−41.67
	Sharpe Ratio	2.29	−0.56	2.21	−0.04	0.39
	Return to $|$max Drawdown$|$	5.09	−0.42	4.0	−0.05	0.22
	Market Correlation	1.0	1.0	1.0	1.0	1.0
Logistic (Top 20, eq w)	Return(%)	25.57	9.61	32.78	9.38	20.82
	Volatility(%)	8.21	16.13	11.7	38.32	19.81
	max Drawdown	−2.52	−15.16	−5.23	−36.68	−36.68
	Sharpe Ratio	3.11	0.6	2.8	0.24	1.05
	Return to $|$max Drawdown$|$	10.14	0.63	6.27	0.26	0.57
	Market Correlation	0.8	0.91	0.82	0.92	0.86
Boosted T (Top 20, eq w)	Return(%)	31.84	−10.03	40.68	17.03	20.05
	Volatility(%)	10.17	16.18	14.7	54.72	26.49
	max Drawdown	−4.55	−18.06	−8.91	−39.66	−39.66
	Sharpe Ratio	3.13	−0.62	2.77	0.31	0.76
	Return to $|$max Drawdown$|$	7.0	−0.56	4.57	0.43	0.51
	Market Correlation	0.68	0.79	0.88	0.88	0.81

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2016.12; out-of-sample period: 2016.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Figure A3. Historical performance (robustness test C, out-of-sample, monthly).

Notes: monthly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Figure A4. Performance indicators (robustness test C, out-of-sample, weekly).

Notes: weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Table D1. Predicted vs. realized returns (robustness test C, out-of-sample, monthly.

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Logistic classification	Mean	0.03	0.04	0.04	0.04
	Median	0.03	0.04	0.05	0.04
	Max	0.29	0.52	0.72	0.81
	Min	−0.28	−0.48	−0.69	−0.79
	Std	0.09	0.18	0.24	0.3
Boosted trees	Mean	0.02	0.05	0.06	0.07
	Median	0.02	0.06	0.06	0.07
	Max	0.38	0.67	0.81	0.93
	Min	−0.38	−0.6	−0.71	−0.88
	Std	0.09	0.2	0.25	0.31

Notes: monthly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Table D2. Predicted vs. realized returns (robustness test C, out-of-sample, weekly).

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Logistic classification	Mean	0.02	0.04	0.05	0.05
	Median	0.02	0.04	0.05	0.06
	Max	0.31	0.56	0.7	0.89
	Min	−0.27	−0.49	−0.62	−0.77
	Std	0.09	0.17	0.23	0.29
Boosted trees	Mean	0.03	0.06	0.06	0.06
	Median	0.02	0.05	0.06	0.07
	Max	0.44	0.68	0.82	0.89
	Min	−0.36	−0.63	−0.72	−0.76
	Std	0.09	0.2	0.26	0.31

Notes: weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Table D3. Historical performance (robustness test C, out-of-sample, monthly).

	Indicator	2014	2015	2016	2017	2018	2019	2020	Overall
Russell 1000 (eq w)	Return(%)	11.2	−3.18	15.93	18.64	−9.01	29.78	−2.09	8.41
	Volatility(%)	12.35	15.44	16.44	8.13	16.04	13.53	46.75	19.81
	max Drawdown	−9.51	−13.48	−12.67	−3.68	−21.48	−7.44	−41.41	−41.41
	Sharpe Ratio	0.91	−0.21	0.97	2.29	−0.56	2.2	−0.04	0.42
	Return to $|$max Drawdown$|$	1.18	−0.24	1.26	5.07	−0.42	4.0	−0.05	0.2
	Market Correlation	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
Logistic (Top 20, eq w)	Return(%)	15.81	17.32	24.94	18.92	0.23	27.8	2.1	15.69
	Volatility(%)	11.69	14.51	16.87	9.71	14.88	9.8	42.79	18.39
	max Drawdown	−7.74	−7.51	−10.75	−5.24	−14.77	−4.45	−36.87	−37.14
	Sharpe Ratio	1.35	1.19	1.48	1.95	0.02	2.84	0.05	0.85
	Return to $|$max Drawdown$|$	2.04	2.31	2.32	3.61	0.02	6.25	0.06	0.42
	Market Correlation	0.86	0.89	0.86	0.81	0.87	0.81	0.87	0.85
Boosted T (Top 20, eq w)	Return(%)	31.82	12.35	63.99	17.54	−1.27	33.08	10.68	23.82
	Volatility(%)	11.54	15.25	33.12	12.08	16.64	15.65	50.19	23.88
	max Drawdown	−5.33	−9.64	−11.8	−10.05	−19.69	−8.84	−44.99	−44.99
	Sharpe Ratio	2.76	0.81	1.93	1.45	−0.08	2.11	0.21	1.0
	Return to $|$max Drawdown$|$	5.97	1.28	5.42	1.75	−0.06	3.74	0.24	0.53
	Market Correlation	0.87	0.89	0.85	0.73	0.89	0.89	0.85	0.85

Notes: monthly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Table D4. Performance indicators (robustness test C, out-of-sample, weekly).

	Indicator	2014	2015	2016	2017	2018	2019	2020	Overall
Russell 1000 (eq w)	Return(%)	11.46	−3.18	16.69	18.85	−8.77	29.73	−1.44	8.72
	Volatility(%)	12.42	15.52	16.47	8.14	16.12	13.59	47.63	20.06
	max Drawdown	−9.59	−13.63	−12.7	−3.68	−21.52	−7.55	−41.88	−41.88
	Sharpe Ratio	0.92	−0.2	1.01	2.31	−0.54	2.19	−0.03	0.43
	Return to $|$max Drawdown$|$	1.19	−0.23	1.31	5.13	−0.41	3.94	−0.03	0.21
	Market Correlation	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
Logistic (Top 20, eq w)	Return(%)	10.9	15.03	36.14	17.41	6.14	30.61	35.15	22.28
	Volatility(%)	11.96	15.89	18.18	10.04	15.96	13.41	49.58	20.83
	max Drawdown	−10.53	−12.25	−9.66	−5.56	−15.38	−6.52	−43.95	−43.95
	Sharpe Ratio	0.91	0.95	1.99	1.73	0.38	2.28	0.71	1.07
	Return to $|$max Drawdown$|$	1.03	1.23	3.74	3.13	0.4	4.69	0.8	0.51
	Market Correlation	0.86	0.86	0.81	0.77	0.89	0.78	0.9	0.84
Boosted T (Top 20, eq w)	Return(%)	31.67	0.31	109.82	30.52	2.2	36.55	6.83	28.78
	Volatility(%)	14.75	14.26	40.49	9.88	18.27	16.77	63.42	28.59
	max Drawdown	−9.38	−10.71	−12.84	−5.3	−17.43	−9.26	−52.02	−52.02
	Sharpe Ratio	2.15	0.02	2.71	3.09	0.12	2.18	0.11	1.01
	Return to $|$max Drawdown$|$	3.38	0.03	8.55	5.76	0.13	3.95	0.13	0.55
	Market Correlation	0.84	0.85	0.79	0.73	0.87	0.81	0.85	0.82

Notes: weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Figure A5. Historical performance (robustness test D, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Figure A6. Performance indicators (robustness test D, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.

Table E1. Predicted vs. realized returns (robustness test D, out-of-sample).

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Boosted trees Param 1	Mean	0.03	0.06	0.08	0.09
	Median	0.02	0.06	0.08	0.1
	Max	0.46	0.64	0.81	0.93
	Min	−0.44	−0.62	−0.79	−0.82
	Std	0.1	0.2	0.26	0.32
Boosted trees Param 2	Mean	0.03	0.06	0.07	0.07
	Median	0.03	0.07	0.08	0.08
	Max	0.43	0.7	0.84	0.88
	Min	−0.49	−0.65	−0.76	−0.87
	Std	0.12	0.24	0.3	0.36
Boosted trees Param 3	Mean	0.02	0.04	0.04	0.04
	Median	0.02	0.04	0.04	0.03
	Max	0.41	0.67	0.82	0.83
	Min	−0.45	−0.62	−0.8	−0.83
	Std	0.12	0.25	0.3	0.37
Boosted trees Sample NAN	Mean	0.02	0.03	0.04	0.04
	Median	0.02	0.03	0.04	0.03
	Max	0.42	0.59	0.71	0.88
	Min	−0.27	−0.54	−0.58	−0.78
	Std	0.1	0.19	0.25	0.31

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Figure A7. Historical performance (robustness test E, out-of-sample).

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This figure compares the performance of the different trading strategies.

Table F1. Predicted vs. realized returns (robustness test E, out-of-sample).

Method	Measure	Entire sample	Top/Bottom 50	Top/Bottom 20	Top/Bottom 10
Logistic classification	Mean	0.01	0.02	0.03	0.03
	Median	0.01	0.02	0.03	0.04
	Max	0.37	0.72	0.81	0.87
	Min	−0.37	−0.67	−0.69	−0.84
	Std	0.12	0.23	0.27	0.31
Boosted trees	Mean	0.02	0.06	0.07	0.07
	Median	0.02	0.06	0.07	0.08
	Max	0.45	0.66	0.78	0.9
	Min	−0.44	−0.67	−0.78	−0.88
	Std	0.1	0.2	0.26	0.32

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows the pooled correlations (across stocks and points in time) between predicted and subsequently realized returns.

Table F2. Performance indicators (robustness test E, out-of-sample).

	Indicator	2014	2015	2016	2017	2018	2019	2020	Overall
Russell 1000 (eq w)	Return(%)	11.42	−3.15	16.32	18.66	−8.96	29.92	−2.0	8.54
	Volatility(%)	12.41	15.48	16.53	8.14	16.09	13.56	47.27	19.97
	max Drawdown	−9.53	−13.62	−12.64	−3.67	−21.54	−7.49	−41.67	−41.67
	Sharpe Ratio	0.92	−0.2	0.99	2.29	−0.56	2.21	−0.04	0.43
	Return to $|$max Drawdown$|$	1.2	−0.23	1.29	5.09	−0.42	4.0	−0.05	0.2
	Market Correlation	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
Logistic (Top 20, eq w)	Return(%)	24.0	−4.91	22.15	13.65	3.17	30.96	7.4	13.87
	Volatility(%)	12.31	15.6	15.02	7.88	17.27	14.27	40.98	18.56
	max Drawdown	−6.45	−15.1	−7.0	−5.98	−17.01	−10.18	−31.29	−31.29
	Sharpe Ratio	1.95	−0.31	1.48	1.73	0.18	2.17	0.18	0.75
	Return to $|$max Drawdown$|$	3.72	−0.33	3.16	2.28	0.19	3.04	0.24	0.44
	Market Correlation	0.75	0.82	0.79	0.54	0.83	0.75	0.81	0.76
Boosted T (Top 20, eq w)	Return(%)	17.65	11.24	81.64	13.71	−0.76	24.63	20.77	23.3
	Volatility(%)	11.37	14.39	36.33	11.49	15.96	16.81	54.75	25.45
	max Drawdown	−7.22	−11.32	−13.92	−8.34	−19.62	−12.81	−40.65	−40.65
	Sharpe Ratio	1.55	0.78	2.25	1.19	−0.05	1.47	0.38	0.92
	Return to $|$max Drawdown$|$	2.44	0.99	5.87	1.64	−0.04	1.92	0.51	0.57
	Market Correlation	0.87	0.85	0.86	0.7	0.88	0.87	0.86	0.84

Notes: bi-weekly forecast horizon and rebalancing; in-sample period: 1995.12–2013.12; out-of-sample period: 2013.12–2020.08; Stock Sample: Russell 1000. This table shows a variety of performance measures for different trading strategies.