Systemic Risk and the Interconnectedness Between Banks and Insurers: An Econometric Analysis

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1 Systemic Risk and the Interconnectedness Between Banks and Insurers: An Econometric Analysis J. David Cummins Temple University SAFE-ICIR Workshop on Banking and Insurance Goethe University Frankfurt May 9, 14

2 Our Recent Systemic Risk Research Chen, Hua, J. David Cummins, Krupa Viswanathan, and Mary A. Weiss Systemic Risk and the Inter-Connectedness between Banks and Insurers: An Econometric Analysis, forthcoming, Journal of Risk and Insurance (September 14). Other relevant papers Cummins, J. David and Mary A. Weiss, Systemic Risk and the U.S. Insurance Sector, forthcoming in Journal of Risk and Insurance (September 14). Cummins, J. David and Mary A. Weiss, 14, Systemic Risk and the Regulation of the U.S. Insurance Industry, In Matther Richardson and John Biggs, eds., Modernizing Insurance Regulation (New York: John Wiley). Cummins, J. David and Mary A. Weiss, 13, Systemic Risk and the Insurance Industry, in Georges Dionne, ed., Handbook of Insurance, nd ed. (New York: Springer). Chen, Hua, J. David Cummins, Krupa Viswanathan, and Mary A. Weiss, 14, Systemic Risk Measures in the Insurance Industry: A Copula Approach, working paper, Temple University, Philadelphia To obtain the papers, please cummins@temple.edu.

3 What Is Systemic Risk? The risk that an event will trigger a loss of economic value or confidence in a substantial segment of the financial system serious enough to have significant adverse effects on the real economy. Group of 1 (1). Systemic financial risk involves A system-wide financial crisis... accompanied by a sharp decline in asset values and economic activity The spread of instability throughout the financial system (contagion) Sufficient to affect the real economy Financial distress at one or a few institutions (even large ones) is not necessarily systemic

4 Prior Literature: Prior Literature: Do Insurers Create Systemic Risk?

5 Before the AIG Crisis Swiss Re (3): investigated whether reinsurers pose systemic risk Group of 3 (6): investigated 3 potential channels through which the reinsurance sector could create systemic risk: its effects on primary insurers, banks, and capital markets No evidence that t the failure of an insurance or reinsurance company in the past has given rise to a significant episode of systemic risk.

6 After the AIG Crisis Bell and Keller (9) Classic insurers do not present a systemic risk and, as a consequence, ence are neither too big nor too interconnected to fail. Insurers engaging in non-traditional activities such as credit derivatives can pose systemic risk. Harrington (9) The AIG crisis was heavily influenced by the CDS written by AIG Financial Products, not by insurance products written by regulated insurance subsidiaries. The Geneva Association (1) Insurers did not play a major role in the financial crisis aside from monolines and dinsurers engaging in certain non-core activities. iti

7 After the AIG Crisis II Grace (1) Event study analysis on insurer stock prices AIG was systemically important but generally the insurance industry is not a significant source of systemic risk. Baluch, Mutenga, and Parsons (11) Investigate the role of the insurance industry in the financial crisis, with an emphasis on European markets. Systemic risk is lower in insurance than in banking but has grown in recent years due to increasing linkages and growing exposure to non-traditional insurance activities. Cummins and Weiss (14) Non-core activities such as financial guarantees and derivatives trading may cause systemic risk Insurer core activities iti not a significant ifi source of systemic risk

8 Measuring Systemic Risk Balance sheet information Financial soundness indicators used in the Finance Sector Assessment Program (FSAP) of IMF and WB Network-based measures (Cont 1) Market-value based indicators Distress insurance premium (DIP) (Huang et al. 9) CoVar & CoVar (Adrian and Brunnermeier 11) Modified CoVar & modified CoVar (Girardi et al. 11) SES and MES (Acharyaa et al. 1) Multi-variate extreme value theory (Zhou 1) Copula analysis (Chen et al. 14)

9 Measuring Systemic Risk II CoVaR and CoVaR (Adrian and Brunnermeier, 11) CoVaR is defined as the VaR of the whole portfolio m conditional on the VaR of an individual institution i mi i Pr mt CoVaR q it VaR q L L q CoVaR is defined as the difference in the VaR of the financial system when a particular financial institution i is in distress and when it is in the normal state. mi mr it VaRq mr it VaR q q q CoVaR CoVaR CoVaR i i.5 9

10 Measuring Systemic Risk III Modified CoVaR and modified CoVaR (Girardi et al.) Conditioning on the event that institution i is at most at its VaR, as opposed to being exactly at its VaR mi i Pr mt MCoVaR q it VaR q L L q mi mr it VaRq mr it VaR q q q MCoVaR MCoVaR MCoVaR i Mainik and Schaanning (1): CoVaR is not dependence consistent, whereas the modified CoVaR is a continuous and increasing function of the dependence parameter. Modified CoVaR is consistent with the traditional view that high dependence leads to higher systemic risk. i.5 1

11 Measuring Systemic Risk IV Systemic expected shortfall (SES) and marginal expected shortfall (MES) (Acharya et al. 1) SES: the expected loss conditional on the loss being greater than some threshold N SES E L L VaR we L L VaR mt, 1 t1 mt mt q i t1 it mt q i 1 MES measures sensitivity of the system s aggregate risk with respect to the exposure of firm i in the market portfolio SES mt, 1 MES it Et 1 Lit Lmt VaRq w i 11

12 Prior Literature: Insurers & Banks Two prior papers measure systemic risk in banking and insurance using market data Billio et al. (1) monthly stock returns Hedge funds, brokers, banks, and insurance companies Principal components and linear Granger causality tests Conclusion: All four sectors have become highly interrelated in the past decade, increasing the level of systemic risk in the banking and insurance industries Acharya et al. (1) daily stock data Systemic expected shortfall (SES) propensity to be undercapitalized when the system as a whole is undercapitalized Conclusion: 9 insurers among the top 5 systemic financial institutions

13 Chen et al. (14): Econometric Analysis of Interconnectedness Between Banks and Insurers

14 Purpose of Our Paper Develop and implement a robust systemic risk measure for insurance Investigate interconnectedness between banking and insurance during financial crisis We use credit default swap (CDS) quotes and intra-day equity returns to estimate systemic risk in the insurance and banking industries Are insurers instigators or victims of systemic risk?

15 Purpose II Our systemic risk measure relies on Daily-frequency market price data for CDS (Markit) Intra-day trading data on stock prices (TA) Systemic risk measure is risk-neutral neutral, forward- looking and economically intuitive Direction of interconnectedness investigated Linear and non-linear Granger causality Correcting for heteroskedasticity

16 Contribution to Literature First paper to use data on CDS spreads and intra- day stock prices to study systemic risk for the insurance industry Different econometric methodology than Billio et al. (1) and Acharya et al. (1) New evidence on whether insurers are victims or sources of systemic risk

17 Preview of Results After adjustment for heteroscedasticity, impact of banks on insurers found to be stronger and of longer duration than impact of insurers on banks Stress tests indicate that banks create economically significant systemic risk for insurers & not vice versa Insurers are primarily victims rather than instigators of systemic risk

18 Measuring Systemic Risk Two major components that determine risk profile of sample firms: Probability of default of each insurer (based on CDS premiums Markit.com) Default correlation (estimated indirectly from underlying equity return correlation TA intraday data) Measure of systemic risk uses portfolio credit risk methodology (developed by Huang et al., 9)

19 A Measure of Systemic Risk Estimate forward-looking, risk-neutral indicator of systemic risk of insurance industry: price of insurance against financial distress the default insurance premium (DIP) Define financial distress by choosing a threshold (e.g., 15%) such that the ratio of portfolio credit losses to total liabilities of the insurance sector is equal to or above threshold

20 Distress Insurance Premium (DIP)

21 A Measure of Systemic Risk II Construct a hypothetical portfolio Consists of debt instruments issued by the sample banks/insurers, weighted by the liability size of each firm. Conduct Monte Carlo simulation (Tarashev and Zhu 8) Probability of joint default (PD) Loss given default (LGD) Systemic risk measure: the price of insurance against financial distress or DIP

22 A Measure of Systemic Risk III Systemic risk measure is calculated as risk-neutral expectation of portfolio credit losses that reach at least a minimum share (15%) of sector s total liability INS SR t = systemic risk measure for insurance industry L t = portfolio credit losses TL t = total liability of insurance sector at time t

23 A Measure of Systemic Risk IV Similar estimation procedure is performed for firms in BANK banking sector to obtain SR t SR INS and SR BANK t t used to analyze degree of interconnectedness between insurance and banking industries.

24 A Measure of Systemic Risk V Advantage of method is that does not require large sample of firms Huang et al. (9) 1 banks Conclusions apply to relatively large firms since they have traded CDS Large insurers have lower default probabilities than smaller insurers so results likely to apply more strongly to small insurers

25 Granger Causality Tests Testing Granger causality involves using F-tests to determine whether lagged information on a variable X provides any significant information about a variable Y in the presence of lagged Y. If not, then X does not Granger-cause Y If so, then X Granger-causes Y Linear Granger causality tests t conducted d first Then do nonlinear Granger causality tests Nonlinear Granger causality test t uses the residuals from the linear causality test Then do Hiemstra-Jones (HJ) Test on residuals

26 Data and Systemic Risk Measures Sample Selection Sample of banks and insurers (Markit, SIC code) Check whether the firm is publicly traded on a US exchange (TA) Focus on 5-year, Senior, No Restructuring CDS uotes on Friday Fill in missing values Use other quotes on the same day for conversion Trace back one (two,, five) day(s) before Interpolation Determine a common time period Our sample: 11 insurers and banks with CDS quotes over the period Feb to May 8

27 Sample Firms

28 Sample Firms II Of 11 insurers, 8 are classified as property-liability insurers Of remaining three, Lincoln National had only life-health operations MetLife group has property-liability operations Prudential divested property-liability p y operations, but owned these operations at the beginning of sample. Because of AIG role in the crisis, the analysis was conducted both including and excluding AIG The results were not sensitive to excluding AIG

29 Risk Neutral Probability of Default PV of CDS premium pmt = PV of protection pmt tt tt r ( T ) r ( T ) it, it, i, t t s e d LGD e q d where r τ is the risk-free rate and s it i,t is CDS spread, q i,t is annualized unconditional risk-neutral default intensity of borrower i, 1q dv, i, v i is the associated risk-neutral survival probability over the following τ years and LGD i,t = [,1] is date-t expectation of loss given default

30 Risk Neutral Probability of Default (PD) II Using this relationship, we solve for the probability of default (PD): PD q it, it, as t algd i, t bs t i, t t i, t where tt tt r r at e d and bt e d t t

31 Risk Neutral Probability of Default (PD) III PD it is risk neutral measure since reflects actual i,t default probability and a risk premium It is forward looking as well i.e., reflects average risk-neutral probability of default of underlying entity during contract period

32 Average Probability of Default Default probability begins to spike in 3 rd quarter of 7. D Weighted Average PD Date group Bank Group Insurance Group

33 Measuring Asset Return Correlation Default correlation estimated indirectly from underlying asset return correlation Since equity is a call option on underlying firm assets, the co-movement in equity prices tends to reflect the co-movement among underlying assets Equity values observed frequently so changes in default risk will be immediately reflected in stock price Rationale for using intra-day data is so that correlations can be measured frequently

34 Measuring Asset Return Correlation II Use intra-day stock prices (tick-by-tick data) to compute correlations (data from TA) Use equally spaced 3 minute returns to construct realized correlation measure Compute 3 minute geometric returns by taking difference between two adjacent logarithmic prices

35 Measuring Asset Return Correlation III Suppose M observations in each time period, the realized correlation between stock k and l for i-th period calculated as: kl i M k l ri, jri, j j1 M M k l ( r, ) i j ( ri, j) j1 j1 where r k i,j and r l i,j are the j-th returns for i-th period for stocks k and l

36 Measuring Asset Return Correlation IV To be consistent with forward-looking probability of default use forecasted asset return correlations to measure portfolio credit risk tt, 1 ck1t 1, t k i tit, i1 Xt t l i1 where ρ t,t+1 is average asset return correlation one quarter ahead ρ t-1,t is one quarter lagged average correlation. X t consists of financial market variables

37 Average Equity Return Correlations 7.8 turn Correlation verage Equity Ret.3.4 Av.1. Date group Bank Group Insurance Group 37

38 Asset Return Correlations During -3 and 7-8 average correlations trended upwards (just as in Huang et al. 9) Severe stock market downturns in both periods O ll i h t fl t ti i Overall, insurers have greater fluctuation in average correlations than banking returns

39 Forecasting Asset Return Correlations Several regressions were run to find best fit for correlation forecasts Independent variables are average weekly equity return correlations lagged one-week and one- quarter Explanatory power boosted when macro variables and cycle variable are added d Regressions run for sample banks, too

40 Asset Return Correlations (Insurers) Systemic Risk in the Insurance Industry 4

41 Measuring Systemic Risk (continued) After measuring probabilities of default and asset return correlations, the systemic risk measure can be computed for each week Systemic risk measure represents a weekly price of insurance against distressed losses over the following three months. To make comparisons, unit price of insurance = ratio of nominal price to total liabilities of sample firms in each sector

42 Granger Causality Tests: Linear Tests Suppose X t and Y t are stationary time series. Construct a univariate autoregression of Y t with a proper number of lags p: p t i t i t i1 Y a ay Next, the autoregression is augmented by including lagged values of X t with a proper number of lags q: p Y a ay X t i ti tj t i 1 j 1 q

43 Granger Causality Tests: Linear Tests II Null hypothesis that X t does not Granger-cause Y t is accepted if and only if the coefficients of the lagged values of X t are not jointly significantly different from zero Reverse erse model can be run to determine if feedback effect from Y t to X t : r X c c X dy t i ti i tj t i1 j1 s

44 Linear Granger Causality Tests Distress Insurance Premiums are not stationary ti SR INS t and SR BANK t Differenced time series are stationary Linear causality tests are performed on the differenced series

45 Linear Granger Causality Tests The results imply that systemic risk of insurers Granger-causes systemic risk of banks Also, systemic risk of banks Granger-causes systemic risk of insurers However, results of BDS tests indicate that nonlinearities are present in the univariate systemic risk measures for both banks and insurers Therefore, we must conduct nonlinear Granger causality tests BDS = Brock-Dechert-Scheinkman.

46 Nonlinear Granger Causality Tests Linear Granger causality test cannot capture nonlinear and higher-order causal effects Then do nonlinear Granger causality test To do nonlinear Granger causality test, linear test is conducted first. The residuals are saved Then do Hiemstra-Jones (HJ) Test on residuals

47 Nonlinear Granger Causality Tests II Diks and Panchenko (5, 6) HJ test could produce spurious results in the presence of conditional heteroskedasticity Ross (1989), Andersen (1996) Volatility of a time series can measure the rate of information flow. Use the GARCH model to assess whether the bidirectional causality changes.

48 Conditional Heteroscedasticity If conditional heteroskedasticity exists, causality test results can be biased Residuals from Granger-causality tests reveal Little autocorrelation Conditional heteroskedasticity exists Therefore, use GARCH (1,1) model to assess whether the bi-directional causality changes Re-do linear and nonlinear Granger tests using GARCH

49 Non-Linear GARCH Models: Main Results Nonlinear effect of insurers on banks is highly significant at one lag Significance fades after 3 lags Banks in contrast have persistent predictive power on insurers up to five lags Systemic risk of banks has longer duration of impact on insurers Impact is also stronger than insurer effect on banks

50 Interconnectedness: Stress Testing Stress testing conducted to study the impact of systemic risk movements in the banking sector on the insurance sector and then vice versa A hypothetical shock in systemic risk of banking sector is fed into GARCH regression to generate future dynamic movements of systemic risk in the banking and insurance sectors Shocks of 5%, 1%, 15%, and % are applied Systemic risk of insurance sector fed into GARCH model as well to generate future dynamic movements of systemic risk

51 Inter-Sector Impact of % Systemic Shock 14% 1% 1% 8% 6% 4% % Banks to Insurers Insurers to Banks % -% T=1 T= T=3 T=4 T=5 T=6 T=7 T=8 T=9 T=1T=11T=1 Weeks After Shock

52 Non-Linear Tests: Conclusions Banks create economically significant systemic risk for insurers but not vice versa Based on linear and non-linear Granger causality tests correcting for heteroskedasticity Therefore, insurers seem to be victims of systemic risk rather than instigators Insurer shocks have statistically but not economically significant effect on banks Banks are instigators of systemic risk

53 Measuring Systemic Risk: Conclusions Important to correct for various econometric problems when analyzing systemic risk Significant non-linearities are present in the data such that results of linear causality tests are misleading Non-linear causality tests also can be misleading if heteroskedasticity is not recognized and corrected

54 Systemic Risk: Policy Implications Regulators should focus on banks to prevent/ameliorate systemic shocks from banks Regulators should focus on non-core rather than insurance activities of large insurers Insurance regulators should focus on mitigating effect of shocks from banks (e.g., investment restrictions and tighter capital requirements for life insurers)

55 Systemic Risk: Further Research Conduct our econometric analysis on a broader sample of insurers Smaller insurers as well as large ones Insurers traded on European exchanges Conduct systemic risk analysis using other methodologies Copulas Network connectivity analysis the network analysis can use accounting data and therefore measure both traded and non-traded insurers

56 Thank you!