The Risk of Individual Stocks’ Tail Dependence with the Market and Its Effect on Stock Returns

Table 6

(a) Regression of portfolio returns on the proxy for tail dependence and Fama-French factors. This table shows results from regressing each of the nine size and book-to-market value sorted portfolios’ excess returns on three factors in Fama-French model and the proxy for tail dependence; that is, + , where represent each portfolio’s returns, represent market returns, and are risk-free rates. SML, HML, and MP_TDC are the proxies for size, book-to-market value, and tail dependence, respectively. “” denotes the fact that the corresponding coefficients are significantly different from zero at the confidence level of 5%. (b) Regression of portfolio returns on the proxies for tail dependence and all the other factors. This table shows results from regressing each of the nine size and book-to-market value sorted portfolios’ excess returns on three factors in Fama-French model, the proxy for tail dependence, and the proxies for other factors; that is, + + + + , where represent each portfolio’s returns, represent market returns, and are risk-free rates. SML, HML, MP_LEV, MP_E/P, MP_ASQT, MP_TURN, MP_MTM, MP_VOL, and MP_TDC are, respectively, the proxies for size, book-to-market value, leverage, earning-price ratio, square root of Amihud’s measure, Turnover, momentum, volatility, and tail dependence. “” denotes the fact that the corresponding coefficients are significantly different from zero at the confidence level of 5%.

(a)

	Low	Median	High	Low	Median	High
Small	−0.428	−0.221	−0.254	−1.688	−0.866	−1.069
Median	−0.381	−0.509	−0.315	−1.484	−1.960	−1.310
Large	−0.327	−0.450	−0.457	−1.341	−1.804	−1.962
Small	0.998	0.962	1.010	20.105	18.978	21.544
Median	0.963	1.018	0.966	19.332	19.998	20.470
Large	0.946	1.027	0.994	19.822	20.674	21.389
Small	0.544	0.435	0.439	4.539	3.553	3.881
Median	0.040	0.079	0.074	0.334	0.645	0.648
Large	−0.386	−0.072	−0.106	−3.352	−0.604	−0.946
Small	−0.212	0.214	0.418	−1.723	1.710	3.608
Median	−0.115	0.132	0.461	−0.937	1.048	3.947
Large	−0.307	0.253	0.473	−2.604	2.061	4.116
Small	0.548	0.677	0.715	4.546	5.501	6.288
Median	0.570	0.616	0.678	4.713	4.985	5.917
Large	0.556	0.418	0.509	5.797	3.468	4.508
				Increase of by adding proxy for TDC
Small	84.3%	82.8%	86.1%	2.6%	4.3%	4.7%
Median	80.0%	81.1%	82.7%	3.7%	3.9%	5.1%
Large	80.7%	80.6%	82.4%	3.7%	1.8%	2.9%

(b)

	Low	Median	High	Low	Median	High
Small	−0.075	−0.084	−0.051	−0.189	−0.216	−0.129
Median	−0.140	−0.124	−0.049	−0.360	−0.304	−0.128
Large	−0.065	−0.118	−0.062	−0.170	−0.290	−0.157
Small	0.965	0.922	0.978	18.906	17.960	20.470
Median	0.931	0.988	0.933	18.016	18.893	19.273
Large	0.912	0.991	0.957	18.579	19.756	20.408
Small	0.464	0.303	0.304	2.056	1.335	1.439
Median	0.091	0.024	−0.009	0.398	0.102	−0.040
Large	−0.246	−0.117	−0.018	−1.135	−0.527	−0.089
Small	−0.199	0.253	0.537	−1.356	1.707	3.896
Median	−0.056	0.076	0.421	−0.375	0.504	3.022
Large	−0.212	0.223	0.478	−1.500	1.546	3.537
Small	0.152	0.156	0.029	0.753	0.736	0.148
Median	0.215	0.144	0.265	1.010	0.669	1.331
Large	0.219	0.077	0.102	1.081	0.372	0.529
Small	−0.012	−0.214	−0.113	−0.088	−1.528	−0.869
Median	−0.234	0.061	−0.077	−1.664	0.429	−0.582
Large	−0.048	0.057	−0.015	−0.360	0.418	−0.116
Small	0.015	−0.009	0.107	0.058	−0.036	0.454
Median	−0.154	−0.008	0.019	−0.607	−0.031	0.080
Large	−0.110	−0.057	−0.239	−0.456	−0.231	−1.037
Small	−0.087	−0.057	−0.132	−0.535	−0.345	−0.864
Median	0.122	−0.173	−0.143	0.737	−1.032	−0.928
Large	−0.022	−0.166	0.094	−0.142	−1.036	0.625
Small	0.187	0.168	−0.004	1.545	1.376	−0.031
Median	0.040	0.244	0.212	0.323	1.967	1.849
Large	−0.065	0.247	0.205	−0.560	2.078	1.845
Small	0.341	0.304	0.303	2.033	1.803	1.927
Median	0.232	0.259	0.223	1.365	1.508	1.401
Large	0.298	0.342	0.397	1.846	2.076	2.575
Small	0.343	0.383	0.490	2.241	2.485	3.418
Median	0.403	0.424	0.448	2.603	2.701	3.089
Large	0.438	0.190	0.345	2.977	1.260	2.456
				Increase of by adding proxy for TDC
Small	84.7%	83.7%	86.6%	0.6%	0.7%	1.3%
Median	80.1%	81.5%	83.2%	1.1%	1.0%	1.3%
Large	81.1%	81.7%	83.4%	1.3%	0.1%	0.7%