Does option trading affect idiosyncratic momentum?

Figures & data

Table 1. Performance of Traditional Momentum Portfolios for 3-month Holding Period

Holding Period K=3
	January 1972 - December 2017			January 1972 - December 1995			January 1996 - December 2017
Decile	Avg Ret	CAPM Alpha	FF3 Alpha	Avg Ret	CAPM Alpha	FF3 Alpha	Avg Ret	CAPM Alpha	FF3 Alpha
Losers	0.393	-0.024	-0.022	0.358	-0.202	-0.196	0.431	0.170	0.180
2	0.523	0.184	0.191	0.554	0.015	-0.003	0.490	0.370	0.389
3	0.628	0.254	0.255	0.642	0.142	0.155	0.613	0.378	0.377
4	0.664	0.270	0.262	0.647	0.084	0.081	0.684	0.474	0.472
5	0.698	0.331	0.333	0.822	0.257	0.259	0.562	0.406	0.417
6	0.729	0.400	0.423	0.934	0.397	0.464	0.502	0.396	0.414
7	0.840	0.517	0.558	0.989	0.466	0.537	0.676	0.568	0.609
8	0.838	0.527	0.558	1.112	0.599	0.651	0.536	0.445	0.482
9	0.856	0.517	0.589	1.211	0.681	0.749	0.464	0.327	0.415
Winners	0.956	0.656	0.743	1.307	0.850	0.921	0.569	0.427	0.543
WML	0.563	0.680	0.765	0.948	1.052	1.116	0.138	0.257	0.363
T-stat	3.20	3.39	3.76	4.90	4.70	4.84	0.46	0.75	1.06

Decile portfolios are formed every month from January 1972 to December 2017. Traditional momentum portfolios are formed by sorting stocks based on past 12–2 month total stock returns. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for every decile portfolio as well as the corresponding alphas of the CAPM and Fama and French (1993) three-factor model. The last two rows show the differences in monthly returns and the differences in alphas between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat) in traditional momentum sorted portfolios. Average returns and risk-adjusted returns are given in percentage terms. The samples cover January 1972 to December 2017, January 1972 to December 1995 and January 1996 to December.

Table 2. Performance of Idiosyncratic Momentum Portfolios for 3-month Holding Period

Holding Period K = 3
	January 1972—December 2017			January 1972—December 1995			January 1996—December 2017
Decile	Avg Ret	CAPM	FF3	Avg Ret	CAPM	FF3	Avg Ret	CAPM	FF3
Losers	0.377	0.004	0.025	0.401	−0.142	−0.132	0.349	0.171	0.205
2	0.454	0.107	0.129	0.595	0.047	0.055	0.297	0.166	0.201
3	0.620	0.259	0.283	0.644	0.128	0.143	0.593	0.399	0.429
4	0.724	0.339	0.356	0.766	0.158	0.178	0.678	0.539	0.556
5	0.772	0.396	0.417	0.892	0.323	0.361	0.638	0.471	0.499
6	0.780	0.440	0.459	0.931	0.407	0.433	0.613	0.474	0.496
7	0.805	0.502	0.513	0.970	0.462	0.493	0.623	0.539	0.547
8	0.832	0.494	0.543	1.010	0.471	0.505	0.635	0.514	0.574
9	0.838	0.535	0.554	1.047	0.577	0.624	0.606	0.483	0.511
Winners	0.988	0.629	0.678	1.152	0.590	0.654	0.807	0.668	0.720
WML	0.611	0.625	0.653	0.751	0.731	0.786	0.458	0.497	0.515
T-stat	6.09	5.38	5.33	5.73	4.75	4.95	2.98	2.83	2.90

Decile portfolios are formed every month from January 1972 to December 2017. Idiosyncratic momentum portfolios are formed based on past 12–2 month volatility-scaled idiosyncratic returns estimated over past 36-month rolling windows using Fama and French (1993) three-factor model. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for every decile portfolio as well as the corresponding alphas of the CAPM and Fama and French (1993) three-factor model. The last two rows show the differences in monthly returns and the differences in alphas between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat) in idiosyncratic momentum sorted portfolios. Average returns and risk-adjusted returns are given in percentage terms. The samples cover January 1972 to December 2017, January 1972 to December 1995 and January 1996 to December 2017, respectively.

Table 3. Momentum Returns by Holding Periods K = 3, 6, 12

		K = 3			K = 6			K = 12
		Whole period	Sub 1	Sub 2	Whole period	Sub 1	Sub 2	Whole period	Sub 1	Sub 2
Panel A
Traditional Momentum	P1	0.393	0.358	0.431	0.446	0.383	0.517	0.620	0.628	0.612
	P5	0.698	0.822	0.562	0.662	0.816	0.490	0.650	0.794	0.484
	P10	0.956	1.307	0.569	0.682	1.088	0.229	0.418	0.720	0.073
	WML	0.563	0.948	0.138	0.235	0.704	−0.288	−0.202	0.092	−0.538
	T-stat	3.20	4.90	0.46	1.85	5.67	−1.27	−2.17	1.11	−3.11
Panel B
Idiosyncratic Momentum	P1	0.377	0.401	0.349	0.296	0.320	0.269	0.349	0.382	0.310
	P5	0.772	0.892	0.638	0.696	0.837	0.539	0.656	0.822	0.467
	P10	0.988	1.152	0.807	0.861	1.018	0.684	0.776	0.944	0.582
	WML	0.611	0.751	0.458	0.565	0.699	0.415	0.427	0.562	0.272
	T-stat	6.09	5.73	2.98	8.94	8.78	4.18	9.38	10.28	3.68

Decile portfolios are formed every month from January 1972 to December 2017. Panel A shows the results of traditional momentum, Panel B shows the results of idiosyncratic momentum results. Traditional momentum portfolios are formed by sorting stocks based on past 12–2 months total stock returns and idiosyncratic momentum portfolios are formed based on past 12–2 months volatility-scaled idiosyncratic returns estimated over past 36-month rolling windows using Fama and French (1993) three-factor model. Winner portfolio is denoted by P10, loser portfolio is denoted P1, P5 denotes the fifth decile, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for loser, decile 5 and winner portfolios as well as the differences in monthly returns between winners and losers portfolios with their corresponding HAC adjusted t-statistics (t-stat) in traditional momentum and idiosyncratic momentum sorted portfolios. The returns are given in percentage terms. The samples cover January 1972 to December 2017 (represented by whole period), January 1972 to December 1995 (represented by sub 1) and January 1996 to December 2017 (represented by sub 2), respectively.

Table 4. Stocks With and Without Options

Year	Total Number of Stocks	Number of Stocks with Options	% Stocks with Options	Number of Stocks without Options	% Stocks without Options
1998	4971	1022	0.206	3949	0.794
1999	4851	1066	0.220	4785	0.780
2000	4829	1374	0.285	3455	0.715
2001	3687	1394	0.378	2293	0.622
2002	3214	1477	0.460	1737	0.540
2003	3187	1477	0.463	1710	0.537
2004	3419	1619	0.474	1800	0.526
2005	3353	1666	0.497	1687	0.503
2006	3396	1769	0.521	1627	0.479
2007	3335	1934	0.580	1401	0.420
2008	2891	2095	0.725	796	0.275
2009	2499	1944	0.778	555	0.222
2010	2697	2042	0.757	655	0.243
2011	2692	2025	0.752	667	0.248
2012	2543	1987	0.781	556	0.219
2013	2641	2131	0.807	510	0.193
2014	2792	2163	0.775	629	0.225
2015	2757	2250	0.816	507	0.184
2016	2662	2098	0.788	564	0.212
2017	2684	2204	0.821	480	0.179

This table presents the numbers and percentage of stocks with and without options in our sample period from 1998 to 2017. We define a stock with options if it has option traded volume on CBOE. Due to the availability of data on CBOE, we only consider the time period from 1998 to 2017.

Table 5. Returns for Stocks with and without Options in Traditional Momentum Portfolios with 3-month Holding Period

Holding Period K = 3
	Stocks with Options			Stocks without Options
Decile	Avg Ret	CAPM	FF3	Avg Ret	CAPM	FF3
Losers	0.390	0.168	0.210	0.613	0.155	0.136
2	0.353	0.255	0.263	0.556	0.188	0.190
3	0.550	0.437	0.469	0.644	0.262	0.249
4	0.422	0.227	0.224	0.704	0.345	0.338
5	0.409	0.261	0.280	0.816	0.429	0.424
6	0.399	0.341	0.356	0.882	0.526	0.537
7	0.336	0.210	0.268	0.887	0.496	0.509
8	0.583	0.548	0.571	0.840	0.537	0.542
9	0.398	0.256	0.312	0.914	0.608	0.660
Winners	0.432	0.379	0.497	1.022	0.635	0.695
WML	0.042	0.212	0.287	0.408	0.480	0.559
t-stat	0.13	0.58	0.79	2.22	2.25	2.58

Decile portfolios are formed every month from January 1998 to December 2017. Traditional momentum portfolios are formed by sorting stocks based on past 12–2 month total stock returns. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for every decile portfolio as well as the corresponding alphas of the CAPM and Fama and French (1993) three-factor model. The last two rows show the differences in monthly returns and the differences in alphas between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat) in traditional momentum sorted portfolios. Average returns and risk-adjusted returns are given in percentage terms. The samples are categorized into two groups, one is stocks with options another is stocks without options.

Table 6. Returns for Stocks With and Without Options in Idiosyncratic Momentum Portfolios with 3-month Holding Period

Holding Period K = 3
	Stocks with Options			Stocks without Options
Decile	Avg Ret	CAPM Alpha	FF3 Alpha	Avg Ret	CAPM Alpha	FF3 Alpha
Losers	0.215	0.101	0.135	0.442	0.027	0.034
2	0.089	0.018	0.043	0.527	0.167	0.173
3	0.453	0.244	0.282	0.713	0.393	0.399
4	0.522	0.418	0.441	0.770	0.365	0.372
5	0.615	0.465	0.503	0.767	0.403	0.424
6	0.570	0.405	0.440	0.818	0.468	0.460
7	0.469	0.404	0.418	0.928	0.641	0.635
8	0.535	0.463	0.508	0.830	0.456	0.497
9	0.407	0.268	0.316	0.882	0.546	0.555
Winners	0.691	0.585	0.645	0.981	0.635	0.680
WML	0.476	0.484	0.510	0.539	0.608	0.646
t-stat	2.62	2.41	2.52	4.51	4.38	4.60

Decile portfolios are formed every month from January 1998 to December 2017. Idiosyncratic momentum portfolios are formed based on past 12–2 month volatility-scaled idiosyncratic returns estimated over past 36-month rolling windows using Fama and French (1993) three-factor model. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for every decile portfolio as well as the corresponding alphas of the CAPM and Fama and French (1993) three-factor model. The last two rows show the differences in monthly returns and the differences in alphas between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat) in idiosyncratic momentum sorted portfolios. Average returns and risk-adjusted returns are given in percentage terms. The samples are categorized into two groups, one is stocks with options another is stocks without options.

Table 7. Returns for Stocks with and without Options in Momentum Portfolios

		K = 3		K = 6		K = 12
		With Opt	without Opt	With Opt	Without Opt	With Opt	Without Opt
Panel A
Traditional Momentum	P1	0.390	0.613	0.441	0.551	0.575	0.701
	P5	0.409	0.816	0.297	0.823	0.340	0.740
	P10	0.432	1.022	0.192	0.677	0.063	0.409
	WML	0.042	0.408	−0.249	0.126	−0.511	−0.293
	T-stat	0.13	2.22	−1.00	0.88	−2.67	−2.86
Panel B
Idiosyncratic Momentum	P1	0.215	0.442	0.187	0.329	0.213	0.363
	P5	0.615	0.767	0.486	0.726	0.362	0.746
	P10	0.691	0.981	0.555	0.819	0.476	0.715
	WML	0.476	0.539	0.368	0.490	0.263	0.352
	T-stat	2.62	4.51	3.23	6.11	3.20	5.58

Decile portfolios are formed every month from January 1998 to December 2017. Panel A shows the results of traditional momentum, Panel B shows the results of idiosyncratic momentum results. Traditional momentum portfolios are formed by sorting stocks based on past 12–2 month total stock returns and idiosyncratic momentum portfolios are formed based on past 12–2 month volatility-scaled idiosyncratic returns estimated over past 36-month rolling windows using Fama and French (1993) three-factor model. Winner portfolio is denoted by P10, loser portfolio is denoted by P1, P5 denotes decile 5, WML denotes winner-minus-loser portfolio. K is the number of months in holding period. The table reports the value weighted average excess monthly returns for loser, decile 5 and winner portfolios as well as the differences in monthly returns between winners and losers portfolios with their corresponding HAC adjusted t-statistics (t-stat) in traditional momentum and idiosyncratic momentum sorted portfolios. The returns are given in percentage terms. The samples are categorized into two groups, one is stocks with options another is stocks without options.

Table 8. Short Interest of Traditional Momentum Portfolios

Panel A: All Firms
Decile	All stocks	Stocks with Options	Stocks without Options
Average	0.058	0.067	0.041
t-stat	455.46	409.90	218.91
Panel B: Momentum Portfolios
Decile	All stocks	Stocks with Options	Stocks without Options
Losers	0.088	0.105	0.056
2	0.067	0.078	0.045
3	0.058	0.067	0.042
4	0.053	0.060	0.039
5	0.049	0.055	0.036
6	0.047	0.053	0.036
7	0.048	0.054	0.036
8	0.050	0.056	0.037
9	0.054	0.062	0.038
Winners	0.066	0.081	0.041
WML	−0.021	−0.023	−0.015
t-stat	−32.05	−26.81	−17.99
Difference in WML = −0.008 t-stat = −5.94

Decile portfolios are formed every month from January 1998 to December 2017. Traditional momentum portfolios are formed by sorting stocks based on past 12–2 month total stock returns. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. The table reports the time-series average of short interest and the differences in between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat).This table also represents the difference in spread portfolios between stocks with options and stocks without options as well as its corresponding t-statistics.

Table 9. Short Interest of Idiosyncratic Momentum Portfolios

Panel A: All Firms
Decile	All stocks	Stocks with Options	Stocks without Options
Average	0.056	0.062	0.043
t-stat	380.11	341.33	176.98
Panel B: Momentum Portfolios
Decile	All stocks	Stocks with Options	Stocks without Options
Losers	0.067	0.074	0.050
2	0.061	0.067	0.047
3	0.059	0.064	0.045
4	0.057	0.063	0.044
5	0.055	0.061	0.041
6	0.054	0.061	0.041
7	0.053	0.058	0.042
8	0.053	0.059	0.041
9	0.051	0.057	0.038
Winners	0.052	0.058	0.039
WML	−0.015	−0.016	−0.011
t-stat	−22.03	−20.06	−10.26
Difference in WML = −0.005 t-stat = −3.71

Decile portfolios are formed every month from January 1998 to December 2017. Idiosyncratic momentum portfolios are formed based on past 12–2 month volatility-scaled idiosyncratic returns estimated over past 36-month rolling windows using Fama and French (1993) three-factor model. Winner portfolio denotes decile 10, loser portfolio denotes decile 1, WML denotes winner-minus-loser portfolio. The table reports the time-series average of short interest and the differences in between winners and losers portfolios with their associated HAC adjusted t-statistics (t-stat).This table also represents the difference in spread portfolios between stocks with options and stocks without options as well as its corresponding t-statistics.

Table 10. Summary of Results

Panel A. Performances of returns during the period of 1996 to 2017
Holding Months	Traditional Momentum		Idiosyncratic Momentum
K = 3	Positive	Insignificant	Positive	Significant
K = 6	Negative	Insignificant	Positive	Significant
K = 12	Negative	Significant	Positive	Significant
Panel B. Performances stocks with options during the period of 1996 to 2017
Holding Months	Traditional Momentum		Idiosyncratic Momentum
K = 3	Positive	Insignificant	Positive	Significant
K = 6	Negative	Insignificant	Positive	Significant
K = 12	Negative	Significant	Positive	Significant

This table shows the summary of results. Panel A shows the comparison of momentum return performances between the traditional momentum strategy and the idiosyncratic momentum strategy during the period from 1996 to 2017. Panel B shows the comparison of momentum return performances between the traditional momentum strategy and the idiosyncratic momentum strategy for stock with options.

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56. https://doi.org/10.1016/0304-405X(93)90023-5

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