Too Connected to Fail? Inferring Network Ties From Price Co-Movements

Figures & data

Table 1. Descriptive statistics: CDS spreads and stock price returns

Sector/Region	Mean	Std. Dev.	Obs.	N. of inst.	Min	25th pct.	Median	75th pct.	Max
CDS spreads (bp)
Sector
Banks	18.4	16.1	106,479	118	3.3	10.1	14.0	21.2	417.3
Insurance	46.4	88.3	30,441	33	4.8	15.1	24.3	38.2	981.5
Investment Trusts	41.6	22.9	19,041	21	5.7	29.0	38.2	49.2	353.2
Other institutions	46.0	73.0	12,707	14	6.4	18.7	28.2	40.3	540.0
Region
U.S.	35.7	31.1	52,547	57	4.8	19.8	28.5	41.1	512.2
Europe	19.4	32.0	83,173	92	3.3	10.0	13.6	19.8	540.0
O.D.	38.3	91.0	26,280	29	3.9	10.2	15.8	32.5	981.5
E.M.	38.1	24.6	6,668	8	10.9	22.5	30.0	44.6	207.0
Total	28.1	46.9	168,668	186	3.3	11.3	17.7	30.3	981.5
Stock price returns (%)
Sector
Banks	−0.1	1.5	95,772	109	−28.2	−0.8	0.0	0.7	27.0
Insurance	−0.0	1.4	23,632	27	−16.3	−0.7	0.0	0.7	18.2
Investment Trusts	−0.1	1.4	17,595	20	−8.8	−0.9	−0.1	0.7	18.4
Other institutions	−0.1	1.5	6,908	8	−20.0	−0.9	−0.1	0.7	16.9
Region
U.S.	−0.0	1.3	41,710	48	−20.0	−0.7	−0.0	0.6	18.2
Europe	−0.1	1.3	61,741	69	−23.9	−0.7	0.0	0.6	27.0
O.D.	−0.0	1.5	19,852	23	−16.3	−0.7	0.0	0.7	17.7
E.M.	−0.1	2.2	20,604	24	−18.2	−1.2	0.0	1.0	22.2
Total	−0.1	1.5	143,907	164	−28.2	−0.8	0.0	0.7	27.0
Market index returns (%)
MSCI World index	0.01	1.1	910	1	−7.3	−0.5	0.1	0.5	9.1

NOTES: Descriptive statistics of daily CDS spreads in basis points and stock price percentage returns are reported for the period January 1, 2004, through August 8, 2007. CDS spreads are obtained from the Markit Group databases. Stock prices are obtained from the Bloomberg databases. “Investment Trusts” consists of real estate investment trusts and private equity investment trusts. “Other institutions” consist of financial services institutions, investment and lease firms, and subsidiary firms. “U.S,” stands for United States. “Europe” for the developed countries in Europe. “O.D” stands for developed countries other than the U.S. and the countries in Europe. “E.M.” stands for emerging markets. The specific countries within these four groups are listed in Table 2.

Table 2. Countries within regions

U.S.	Europe	O.D.	E.M.
United	Austria (AT)	Australia (AU)	Argentina (AR)
States	Belgium (BE)	Canada (CA)	Brazil (BR)
(US)	Denmark (DK)	Hong Kong (HK)	China (CN)
	France (FR)	Japan (JP)	India (IN)
	Germany (DE)	Singapore (SG)	Indonesia (ID)
	Greece (GR)		Kazakhstan (KZ)
	Iceland (IS)		Korea (KR)
	Ireland (IE)		Malaysia (MY)
	Italy (IT)		Russia (RU)
	Luxembourg (LU)		South Africa (ZA)
	Netherlands (NL)		Taiwan (TW)
	Norway (NO)		Thailand (TH)
	Portugal (PT)		Turkey (TR)
	Spain (ES)		Ukraine (UA)
	Sweden (SE)
	Switzerland (CH)
	United Kingdom (GB)

NOTES: ISO 3166 country codes reported in parentheses. In the classification of “Other Developed” and “Emerging Markets,” we follow the MSCI country classification.

Table 3. Descriptive statistics: Extreme percentage changes in CDS spreads and stock prices

CDS changes in
percentages/percentiles	Mean	Std. Dev.	Obs.	Min	25th pct.	Median	75th pct.	Max
CDS spread percentage changes (%)
Overall sample	0.15	4.58	158,695	−69.93	−0.59	0.00	0.51	211.95
Critical changes only	2.29	4.68	71,361	0.00	0.26	0.93	2.45	209.58
Percentiles of critical changes	87.91	7.74	17,561	39.88	81.86	88.46	94.72	100.00
Stock price returns (%)
Overall sample	−0.12	1.51	143,907	−28.20	−0.83	0.02	0.70	27.02
Critical changes only	−0.93	1.07	72,188	−28.20	−2.12	−0.65	−0.12	−0.05
Percentiles of critical changes	86.73	8.85	13,809	63.74	80.35	88.41	94.15	100.00

NOTES: Top two rows of the two categories report descriptive statistics on percentage changes in CDS spreads, both for the overall sample and for the critical changes that are included in the calculation of the Hill estimator (5(5) $$\begin{array}{c}\hfill \widehat{\eta }\left(k\right):=\frac{1}{k}\sum _{m=1}^k\ln \left[\frac{Z(n-m+1)}{Z(n-k)}\right].\end{array}$$(5) ). The total number of observations differ from Table 1 due to an unbalanced panel. The last row of each category reports statistics of the percentiles of the minimum percentage change in CDS spreads included in the computation of the tail index estimate, outlined in Section 3. The considered sample period runs from January 1, 2004, through August 8, 2007.

Table 4. Descriptive statistics: Co-crash probabilities

Co-crash prob.	Mean	Std. Dev.	Obs.	Min	25th pct.	Median	75th pct.	Max
CDS spread-based CCPs (bp)
Overall sample	5.47	5.58	17,205	0.00	2.20	4.21	7.43	71.75
Only significant co-crash probabilities^*	7.19	5.88	11,785	0.00	3.69	5.90	9.15	71.75
Stock price-based CCPs (bp)
Overall sample	2.21	2.18	13,366	0.00	0.93	1.73	2.94	27.67
Only significant co-crash probabilities^*	5.32	2.61	2,595	0.00	3.54	4.77	6.59	27.67

NOTES: Co-crash probabilities are reported in basis points. “^*” indicates that only statistics are reported for co-crash probabilities between two institutions that share a common “credit-risk link.” For these co-crash probabilities, the tail index is not significantly different from one at the 1% significance level. The number of observations reflect the number of co-crash probabilities estimates for any possible combination of two institutions in the sample. Since 186 institutions are investigated with respect to the CDS spread-based CCPs, the total number of co-crash probabilities per period amounts to 186(186 − 1)/2 = 17,205. Likewise, the total number of possible ties for the Stock price-based CCPs amounts to 13,366, based on 164 institutions.

Figure 1. Differences in centrality. Figure displays 14 hypothetical financial institutions as nodes, which share significant credit links. Significant credit links are displayed as edges. Degree centrality denotes the proportion of institutions with which the subject institution shares a significant credit link. Betweenness centrality represents the number of times an institution acts as key link that connects two institutions along the shortest path (Bonacich 1972). The betweenness centrality measure is rescaled to a percentage of the total number of times an institution connects two other institutions along the shortest path.

Figure 2. Capital injections and asset guarantee schemes. Figure represents a graphical depiction of the first time capital injections and asset guarantee have been implemented for the support of sampled financial institutions. The figure is based on the data presented in Table A3 in the online appendix. Contributions to the bar are derived from the first date in the period 2007–2011 that a financial institutions received one of the two respective support measures.

Table 5. Descriptive statistics of bailout determinants: Centrality indicators and firm-specific factors

Variables	Values in	Mean	Std. Dev.	Obs.	Min	25th pct.	Median	75th pct.	Max
CDS-based centrality
Degree, bootstrap	(%)	68.94	23.51	186	9.19	62.16	75.14	86.49	99.46
Degree, parametric	(%)	51.37	20.39	186	4.32	37.03	56.49	65.95	83.24
Bonacich, CCP	(%)	42.62	24.76	186	0.00	23.08	38.94	58.79	99.43
Bonacich, bootstrap	(%)	65.47	25.14	186	0.00	60.12	73.58	84.57	90.03
Bonacich, parametric	(%)	57.89	25.00	186	0.00	42.10	65.06	76.91	93.44
Equity-based centrality
Degree, bootstrap	(%)	20.03	13.60	164	0.61	8.59	16.56	30.06	53.37
Degree, parametric	(%)	23.82	9.43	164	5.52	17.79	23.93	30.06	48.47
Bonacich, CCP	(%)	41.78	20.36	164	0.00	27.46	38.89	57.12	98.46
Bonacich, bootstrap	(%)	35.73	28.78	164	0.00	10.07	26.70	60.71	100.00
Bonacich, parametric	(%)	38.71	20.08	164	0.00	24.80	37.52	51.39	90.16
Rescue measures
Total capital injections	(B USD)	12.43	17.69	50	0.53	2.84	5.02	18.2	88.62
Total asset guarantees	(B USD)	50.91	78.44	21	0.26	6.33	15.12	41.15	283
Control variables
Total Assets, book value	(B USD)	328.62	499.35	138	0.02	20.91	104.77	337.49	2,070.02
SRISK	(%)	0.39	2.23	164	0.00	0.00	0.03	0.15	12.40
CCP market	(bp)	21.39	3.85	164	7.89	19.50	21.49	23.91	31.42
CAPM Beta		0.26	0.16	164	−0.09	0.14	0.25	0.33	1.01
Solvency ratio	(%)	15.54	19.07	138	1.25	4.75	6.88	18.12	99.14
RoA	(%)	2.04	4.79	138	−27.59	0.86	1.43	2.48	22.10

NOTES: Centrality measures are reported in percentages. Degree centrality reflects the proportion of members with which the institution shares a significant co-crash probability, that is, a co-crash probability for which the null of unit tail index could not be rejected at the 1% significance level. The Bonacich centrality measures are rescaled to percentages where 0% indicates that the institution is not connected to institutions that are highly connected with other members but not to other highly connected institutions. Higher values indicate that the institution acts as a gatekeeper in the sense of sharing a significant co-crash probability with multiple independent institutions that are themselves highly connected with others. “bootstrap” indicates that the links for the centrality measure were established with the test for asymptotic dependence with the bootstrap standard error for the tail index estimate. “parametric” indicates the same but instead the use of the parametric standard error estimate of Draisma et al. (2004). “CCP” after Bonacich indicates that the CCP estimate is used as the intensity measure of the link between two institutions. All variables cover the period January 2004, through August 2007, except for total assets, solvency ratio, and RoA, which are obtained for the fiscal year of 2006.

Table 6. Rescue measures explained by precrisis degree centrality

Received government support during the Global Financial Crisis
		Equity-based degree centrality in nat. logs				CDS-based degree centrality in nat. logs
					Country/				Country/
Precrisis		Overall	Industry	Country	industry	Overall	Industry	Country	industry
regressors	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Centrality		0.072	0.049	−0.015	0.011	0.054^***	0.051^***	0.046^***	0.039^**
		[0.049]	[0.044]	[0.018]	[0.017]	[0.018]	[0.019]	[0.017]	[0.017]
Controls
ln(Total Assets)	0.100^***	0.093^***	0.100^***	0.105^***	0.095^***	0.106^***	0.108^***	0.108^***	0.108^***
	[0.022]	[0.023]	[0.022]	[0.021]	[0.022]	[0.027]	[0.027]	[0.026]	[0.027]
SRISK	0.014	0.011	0.017	−0.045	0.048	−0.036	−0.034	−0.013	0.022
	[0.147]	[0.121]	[0.124]	[0.133]	[0.117]	[0.115]	[0.151]	[0.110]	[0.145]
CCP market	−0.007	−0.010	−0.009	−0.007	−0.007	−0.000	−0.000	−0.001	−0.001
	[0.009]	[0.009]	[0.009]	[0.008]	[0.009]	[0.009]	[0.011]	[0.009]	[0.011]
CAPM Beta	−0.108	−0.193	−0.166	−0.133	−0.079	−0.090	−0.097	−0.095	−0.095
	[0.207]	[0.214]	[0.222]	[0.196]	[0.215]	[0.166]	[0.179]	[0.174]	[0.190]
Solvency ratio	−0.033^*	−0.032^**	−0.034^**	−0.033^**	−0.031^**	−0.028	−0.028	−0.032	−0.034
	[0.018]	[0.013]	[0.014]	[0.014]	[0.015]	[0.022]	[0.024]	[0.022]	[0.024]
RoA	0.046^*	0.042^**	0.046^**	0.047^**	0.045^**	0.036	0.037	0.043	0.048
	[0.027]	[0.020]	[0.021]	[0.021]	[0.021]	[0.031]	[0.035]	[0.031]	[0.035]
Observations	124	124	124	124	124	112	112	112	112
log-likelihood	−52.066	−50.636	−51.416	−51.750	−51.851	−38.363	−38.638	−39.735	−40.632
Pseudo R^2	0.241	0.262	0.251	0.246	0.244	0.411	0.406	0.389	0.376
Area under ROC curve	0.822	0.840	0.831	0.826	0.825	0.904^*	0.902^*	0.892	0.888

NOTES: Table reports the marginal effect of variables derived from logit regressions on whether an institution received financial support or guarantees from central regulators during the Global Financial Crisis, see Table A3. Columns (2) through (9) differ in whether stock returns or CDS spreads are at the basis of the centrality measure, and between regional and industry link restrictions between institutions. A link between two institutions is found if we fail to reject the null of asymptotic dependence between two institutions’ stock or CDS spread return series and the test uses of the bootstrap standard error estimate of the tail index, see Section 3.4. The regressors are obtained in the precrisis period from January 2004 through August 2007. Bootstrap standard errors are reported in brackets, 1000 replications. “^***,” “^**,” and “^*” denote, respectively, significantly different from zero at the 1%, 5%, and 10% level. “Area under ROC curve” reports the coefficient of concordance and whether it differs significantly relative to the value obtained where Bonacich centrality measures are excluded, column (1).

Table 7. Rescue measures explained by precrisis Bonacich centrality

Received government support during the Global Financial Crisis
		Equity-based Bonacich centrality in nat. logs				CDS-based Bonacich centrality in nat. logs
					Country/				Country/
Precrisis		Overall	Industry	Country	industry	Overall	Industry	Country	industry
regressors	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Centrality		0.201^**	0.134^***	0.073^***	0.132^***	0.101^***	0.151^***	0.042	0.086^*
		[0.090]	[0.039]	[0.024]	[0.048]	[0.035]	[0.052]	[0.029]	[0.048]
Controls
ln(Total Assets)	0.100^***	0.086^***	0.046	0.098^***	0.077^***	0.104^***	0.088^***	0.112^***	0.103^***
	[0.022]	[0.022]	[0.030]	[0.021]	[0.020]	[0.026]	[0.026]	[0.027]	[0.027]
SRISK	0.014	0.024	0.039	0.014	−0.020	−0.025	−0.071	−0.014	−0.034
	[0.147]	[0.130]	[0.099]	[0.137]	[0.147]	[0.121]	[0.179]	[0.133]	[0.170]
CCP market	−0.007	−0.016^*	−0.011^*	−0.002	0.003	0.000	0.005	−0.000	0.003
	[0.009]	[0.010]	[0.006]	[0.010]	[0.012]	[0.009]	[0.012]	[0.010]	[0.012]
CAPM Beta	−0.108	−0.213	−0.150	0.046	0.126	−0.093	0.025	−0.124	−0.042
	[0.207]	[0.197]	[0.135]	[0.212]	[0.231]	[0.174]	[0.206]	[0.191]	[0.216]
Solvency ratio	−0.033^*	−0.034^**	−0.020^*	−0.029^*	−0.020	−0.031	−0.022	−0.042^**	−0.038
	[0.018]	[0.014]	[0.010]	[0.015]	[0.015]	[0.021]	[0.024]	[0.021]	[0.024]
RoA	0.046^*	0.044^**	0.038^**	0.035	0.023	0.040	0.033	0.056^*	0.049
	[0.027]	[0.020]	[0.016]	[0.022]	[0.021]	[0.030]	[0.035]	[0.030]	[0.037]
Observations	124	124	124	124	124	112	112	112	112
log-likelihood	−52.066	−49.171	−44.875	−48.834	−45.469	−39.310	−34.257	−42.956	−41.207
Pseudo R^2	0.241	0.283	0.346	0.288	0.337	0.396	0.474	0.340	0.367
Area under ROC	0.822	0.854	0.879^*	0.842	0.864^**	0.895	0.927^**	0.872	0.886

NOTES: Table reports the marginal effect of variables derived from logit regressions on whether an institution received financial support or guarantees from central regulators during the Global Financial Crisis, see Table A3. Columns (2) through (9) differ in whether stock returns or CDS spreads are at the basis of the centrality measure, and between regional and industry link restrictions between institutions. The intensity of a link between two institutions is measured by CCP estimate’s value. The regressors are obtained in the precrisis period from January 2004 through August 2007. Bootstrap standard errors are reported in brackets, 1000 replications. “^***,” “^**,” and “^*” denote, respectively, significantly different from zero at the 1%, 5%, and 10% level. “Area under ROC curve” reports the coefficient of concordance and whether it differs significantly relative to the value obtained where Bonacich centrality measures are excluded, column (1).

Table 8. Rescue measures explained by tail-based Bonacich centrality

Received government support during the Global Financial Crisis
		Equity-based Bonacich centrality in nat. logs				CDS-based Bonacich centrality in nat. logs
					Country/				Country/
Precrisis		Overall	Industry	Country	industry	Overall	Industry	Country	industry
regressors	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Centrality		0.070	0.105^***	0.064^**	0.117^**	0.110^***	0.146^***	0.042	0.086^*
		[0.049]	[0.037]	[0.026]	[0.046]	[0.037]	[0.050]	[0.028]	[0.046]
Controls
ln(Total Assets)	0.100^***	0.091^***	0.067^***	0.100^***	0.083^***	0.103^***	0.087^***	0.112^***	0.102^***
	[0.022]	[0.023]	[0.026]	[0.021]	[0.021]	[0.026]	[0.026]	[0.027]	[0.027]
SRISK	0.014	0.009	0.029	0.018	−0.012	−0.034	−0.074	−0.012	−0.033
	[0.147]	[0.119]	[0.120]	[0.133]	[0.140]	[0.115]	[0.172]	[0.133]	[0.170]
CCP market	−0.007	−0.010	−0.010	−0.002	0.003	0.000	0.004	−0.000	0.004
	[0.009]	[0.008]	[0.007]	[0.010]	[0.011]	[0.009]	[0.012]	[0.010]	[0.012]
CAPM Beta	−0.108	−0.189	−0.223	−0.021	0.028	−0.091	0.012	−0.122	−0.029
	[0.207]	[0.210]	[0.195]	[0.213]	[0.227]	[0.166]	[0.196]	[0.191]	[0.216]
Solvency ratio	−0.033^*	−0.033^**	−0.026^**	−0.028^*	−0.021	−0.027	−0.019	−0.041^**	−0.036
	[0.018]	[0.014]	[0.011]	[0.015]	[0.014]	[0.022]	[0.023]	[0.021]	[0.024]
RoA	0.046^*	0.044^**	0.042^**	0.035^*	0.024	0.034	0.030	0.055^*	0.047
	[0.027]	[0.020]	[0.017]	[0.021]	[0.021]	[0.031]	[0.034]	[0.029]	[0.037]
Observations	124	124	124	124	124	112	112	112	112
log-likelihood	−52.066	−50.756	−46.787	−49.682	−46.726	−37.964	−32.655	−42.951	−41.036
Pseudo R^2	0.241	0.260	0.318	0.276	0.319	0.417	0.498	0.340	0.369
Area under ROC	0.822	0.837	0.869^*	0.837	0.857^*	0.907^*	0.934^**	0.874	0.886

NOTES: Table reports the marginal effect of variables derived from logit regressions on whether an institution received financial support or guarantees from central regulators during the Global Financial Crisis, see Table A3. Columns (2) through (9) differ in whether stock returns or CDS spreads are at the basis of the centrality measure, and between regional and industry link restrictions between institutions. A link between two institutions is found if we fail to reject the null of asymptotic dependence between two institutions’ stock or CDS spread return series and the test uses of the bootstrap standard error estimate of the tail index, see Section 3.4. The regressors are obtained in the precrisis period from January 2004 through August 2007. Bootstrap standard errors are reported in brackets, 1000 replications. “^***,” “^**,” and “^*” denote, respectively, significantly different from zero at the 1%, 5%, and 10% level. “Area under ROC curve” reports the coefficient of concordance and whether it differs significantly relative to the value obtained where Bonacich centrality measures are excluded, column (1).

Table 9. Centrality and the nature of ties

			Capital	Asset
			injections	guarantees
	Bailout	G-SIB	($B)	($B)
	(1)	(2)	(3)	(4)
Degree centrality in logs
Equity based	−0.172^*	0.063	−18.376^*	59.780
	[0.103]	[0.150]	[9.732]	[42.645]
CDS based	0.035	0.013	−6.533	−4.276
	[0.049]	[0.023]	[5.870]	[18.244]
Bonacich centrality in logs
Equity based	0.513^**	0.324^**	34.782^*	−43.955
	[0.223]	[0.154]	[19.823]	[68.964]
CDS based	0.005	−0.002	21.687^*	25.475
	[0.097]	[0.003]	[12.413]	[36.399]
Controls	YES	YES	YES	YES
Observations	105	105	105	105
log-likelihood	−30.031	−12.13	−135.738	−78.214
Pseudo R^2	0.522	0.706	0.200	0.161
Area under ROC	0.944^***	0.818^**

NOTES: Table reports the marginal effect of variables derived from logit regressions for whether an institution received financial support or guarantees from central regulators during the Global Financial Crisis, see Table A3. The variables are obtained in the precrisis period. Bootstrap standard errors are reported in brackets, 1000 replications. “^***,” “^**,” and “^*” denote, respectively, significantly different from zero at the 1%, 5%, and 10% level. “Area under ROC curve” reports the coefficient of concordance and whether it differs significantly relative to the value obtained where degree and Bonacich centrality measures are excluded.

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