1、 BIS Working PapersNo 856Volatility spillovers and capital buffers among the G-SIBsby Paul D McNelis and James YetmanMonetary and Economic DepartmentApril 2020JEL classification: C58, F65, G21, G28.Keywords: G-SIBs; contagion; connectedness; bank capital; cross validation.BIS Working Papers are writ

2、ten by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their au

3、thors and not necessarily the views of the BIS.This publication is available on the BIS website ().Bank for International Settlements 2020. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated.ISSN 1020-0959 (print)ISSN 1682-7678 (online)Volatility spillo

4、vers and capital buffers among the G-SIBsPaul D McNelis and James Yetman1April 2020AbstractWe assess the dynamics of volatility spillovers among global systemically important banks (G-SIBs). We measure spillovers using vector-autoregressive models of range volatility of the equity prices of G-SIBs,

5、together with machine learning methods. We then compare the size of these spillovers with the degree of systemic importance measured by the Basel Committee on Banking Supervisions G-SIB bucket designations. We find a high positive correlation between the two. We also find that higher bank capital re

6、duces volatility spillovers, especially for banks in higher G-SIB buckets. Our results suggest that requiring banks that are designated as being more systemically important globally to hold additional capital is likely to reduce volatility spillovers from them to other large banks.Keywords: G-SIBs;

7、contagion; connectedness; bank capital; cross validation. JEL classifications: C58, F65, G21, G28.1 Robert Bendheim Professor of Economic & Financial Policy, Gabelli School of Business, Fordham University, 45 Columbus Avenue, Room 602A, New York, NY 10023, USA, mcnelis; and Principal Economist, Bank

8、 for International Settlements. Representative Office for Asia and the Pacific, 78th Floor, Two IFC, 8 Finance Street, Central, Hong Kong SAR, HYPERLINK mailto:james.yetman james.yetman. We thank Stijn Claessens, Page Conkling, Simonetta Iannotti, Eli Remolona, Ilhyock Shim, Costas Stephanou, Vlad S

9、ushko, Nikola Tarashev, Goetz von Peter and Raihan Zamil, as well as seminar participants at the Bank for International Settlements and the Asia School of Business for comments and Chenlu Sun, Yaxian Li, Pamela Pogliani, Giulio Cornelli, Zuzana Filkova, Jimmy Shek and Amanda Liu for excellent resear

10、ch assistance. Any remaining errors are our own. The views expressed in this paper are those of the authors and are not necessarily shared by the Bank for International Settlements.IntroductionThis paper examines volatility spillovers among global systemically important banks (G-SIBs), based on co-m

11、ovements in equity price volatility at daily frequency.2 A list of G-SIBs have been identified by the Financial Stability Board (FSB) in consultation with Basel Committee on Banking Supervision (BCBS) and national authorities each year since 2011.Volatility spillovers are one way to assess the degre

12、e of connectedness among banks and is related to notions of contagion, although the latter typically refers to connectedness in extremis. When we think about banking-sector contagion effects, the focus was historically on runs on bank deposits (see eg Saunders and Wilson (1996), and Aharony and Swar

13、y (1983). When one bank experiences problems, this can result in system-wide effects as depositors, with imperfect information, withdraw deposits from all banks, including those that are otherwise healthy.More recently, volatility spillovers has been seen to depend more on interbank linkages on asse

14、ts or on liabilities than the risk of depositor runs. Several measures have been proposed for assessing the systemic importance of banks in such an environment. To give a few examples, Zhou and Tarashev (2013) apply extreme value theory to credit default swaps and expected default probabilities to c

15、onstruct a price-based measure of systemic importance for 50 global banks for 20072011. Drehmann and Tarashev (2013) instead use simulations based on balance sheet data for 20 large banks to measure systemic importance as either i) the expected losses that a bank imposes on non-bank investors or ii)

16、 how much a bank contributes to the risk of other banks in systemic events.3 Acharya et al (2009, 2017) instead use the average return on bank equities during the 5% worst days for market performance as a basis for measuring systemic risk. Finally, Adrian and Brunnermeier (2016) measure systemic ris

17、k of each institution as the change in the value at risk of the financial system as a whole conditional on the individual institution being in distress relative to its median state.4Here, we take a complementary approach to assess the strength of inter-relationships between banks, focusing on the de

18、gree of volatility spillovers. We follow Demirer et al (2018) in using a market- based measure of the riskiness of banks, as reflected by equity price volatility, and look for commonality in that measure to examine connectedness.5 A perception that a banks riskiness is likely to spill over to other

19、banks should be reflected in high levels of co-movement in their equity price volatility at high frequency, due to the implications of connectedness for bank profitability.We first focus on the 20 G-SIBs that are listed on the New York Stock Exchange, including those listed via American Depository R

20、eceipts. We then extend the sample to 31 G-SIBs based on listings in their domestic markets.62A full list of the G-SIB banks for each year is given in Appendix Table A1. The process for designating benchmarks has evolved over time, and is summarised in BCBS (2011, 2013 and 2018).3See also Tarashev e

21、t al (2016) for related work.4For a survey of different measures of contagion, see Benoit et al (2017).5Our departures from Demirer et al (2018) include linking connectedness to bank capital and G-SIB designation by the BCBS.6In the case of the four Chinese banks in the larger sample, we use equity

22、price data from their Hong Kong listing since capital controls may influence the equity price volatility of their Shanghai listings, especially at high frequency,We measure risk using range volatility, based on an approximation for intra-day volatility. This is constructed using the logarithmic valu

23、es of the opening, closing, high and low values of the daily bank share prices, following Garman and Klass (1980). We then apply the methods of Diebold and Yilmaz (2012) to assess how important each G-SIB is in influencing the equity price volatility of the other G- SIBs, measured by its outward con

24、nectedness.Our sample runs from October 2007 to September 2018. Not surprisingly, the periods surrounding the Great Financial Crisis (GFC) saw volatility spillovers spike. But, even as these have moderated in subsequent periods, they have by no means disappeared.The FSB first published a list of 29

25、banks designated as G-SIBs in November 2011. Starting with a wider list of large banks, they use twelve different proxies to measure five different aspects of systemic importance: the size of the bank, its interconnectedness, the availability of substitutes for the banks services, the size of its cr

26、oss-border lending and funding, and the complexity of its portfolio. These indicators are then normalised and combined to produce a single measure of systemic importance.7 The number of designated banks has varied over time along with these indicators.Since November 2012, G-SIBs have been further de

27、marcated by the BCBS into buckets based on their relative systemic importance, with the list of banks and bucket allocations updated annually.8 Then, beginning with the 2014 assessment, G-SIBs have been required to incrementally hold higher capital buffers in the form of Common Equity Tier 1 (CET1),

28、 with banks in higher buckets required to hold more, in reflection of their greater systemic importance. These requirements are phased in over time. Taking the 2014 cohort of G-SIBs as an example, provided they remained G-SIBs in subsequent years, their prescribed capital was increased in steps from

29、 1 January 2016, with the full additional amount to be held by 1 January 2019.Focusing on the period beginning November 2012, we find that outward connectedness our measure of volatility spillovers is strongly positively correlated with the G-SIB bucket categorisation of the BCBS, where higher bucke

30、t designations indicate greater outward volatility spillovers. We also find that a higher CET1 capital ratio reduces volatility spillovers, especially for banks in higher G-SIB buckets. Our results provide empirical support for current policy approaches: 1. banks that are designated more systemicall

31、y important globally do exert greater influence on other banks stock prices; and 2. the efficacy of higher capital in mitigating this influence supports these banks being required to meet higher capital requirements.In related work, Goel et al (2019) assess the effectiveness of post-crisis regulator

32、y reforms aimed at mitigating systemic risks from G-SIBs. They find that overall financial system risks have declined since the GFC, and that G-SIBs have tended to reduce their systemic importance. In part, this is because G- SIBs expanded their balance sheets less quickly than other large banks, an

33、d also shifted to less complex assets. In addition, as Neanidis (2019) has recently shown, the importance of effective banking regulation is crucial for mitigating the negative effects of volatile capital flows on economic growth for many countries and for various categories of capital flows.7For mo

34、re details, see BCBS (2013).8See HYPERLINK /work-of-the-fsb/policy-development/systematically-important-financial-institutions-sifis/global- /work-of-the-fsb/policy-development/systematically-important-financial-institutions-sifis/global- systemically-important-financial-institutions-g-sifis/.In the

35、 next section we describe the data set we use as well as the methodology for obtaining the realised daily range volatility measures for the banks. Section 2 describes our empirical methodology and reports the level of connectedness among G-SIBs listed in the US market. Section 3 analyses the relatio

36、nships over time between connectedness, G-SIB designation, CET1 capital ratios and the home domicile of banks. Section 4 extends the results to a wider sample of G-SIBs based on their domestic listings. We then conclude in Section 5.Data and measurement of risk and contagionDataWe first consider twe

37、nty US listed G-SIBs. These banks represent around two-thirds of the G-SIB universe, but offer the advantage of sharing the same trading hours and trading days, so provide a clean environment to assess the drivers of spillovers.9Table 1 gives the names of the banks. Four are foreign banks whose shar

38、es are traded in the US markets either through the American Depository Shares or American Depository Receipts. The data span the period from 18 October 2007 to 28 September 2018.Globally systemically important banks: US listings1Table 1Code2NameType3MeanMedianStd DevMinMaxBACBank of America-1.111-1.

39、1310.473-2.7110.004BKBank of New York Mellon-0.845-0.8880.340-1.5030.049BCSBarclays-1.172-1.1230.376-2.9040.018BBVABBVA-0.263-0.2720.289-0.9350.280CCitigroup-2.101-2.2050.553-3.7660.000CSCredit SuisseADS-0.892-0.8830.436-1.8650.005DBDeutsche Bank-1.224-1.1640.588-2.4620.046GSGoldman Sachs-0.327-0.30

40、90.281-1.4270.199HSBCHSBC-0.681-0.6750.226-1.4380.025INGING Bank-1.254-1.2600.425-2.6800.000JPMJP Morgan Chase0.1320.0640.369-1.0980.949MSMorgan Stanley-0.996-1.0670.302-1.4730.049MFGMizuho Financial GroupADR-0.776-0.7690.367-1.9530.021RBCRoyal Bank of Canada0.0170.0380.226-0.9940.431RBSRoyal Bank o

41、f ScotlandADS-2.876-3.0040.803-4.1530.013SANSantander-0.873-0.9500.416-1.7030.088STTState Street-0.630-0.6440.253-1.0580.203SMFGSumitomo Mitsui FGADS-0.234-0.1330.331-1.5480.413UBSUBS-1.191-1.2010.273-2.0570.000WFCWells Fargo0.1230.1030.332-1.3610.670Notes: 1 Changes in log bank share prices, in USD

42、. 2 On the NYSE. 3 ADR: American Depository Receipt; ADS: American Depository Share. Otherwise conventional listing.9We will later extend the sample to include all G-SIB banks.To illustrate changes in bank share prices over the sample period, we first normalise each series by dividing by the first o

43、bservation, and then take natural logarithms. The resulting series are summarised in Table 1. With the exception of JP Morgan, Royal Bank of Canada and Wells Fargo, we see that the mean and median values over this period are negative, ie the end of period share price is below the starting observatio

44、n, in October 2007. In terms of volatility, the standard deviation is largest for the Royal Bank of Scotland and lowest for the Royal Bank of Canada.tThe realised daily range volatility measure, denoted by R, comes from an approximation based on difference between the daily opening (o) and closing (

45、c), as well as maximum (h) and minimum (l) of the natural logarithmic values of the share prices observed each day, based on Garman and Klass (1980):tR = .511( )2 .019( )( + 2) 2( )( ) .383( )2.(1)These authors found that range volatility closely approximated daily within sample realised volatility

46、measures coming from very high-frequency data.tGraph 1 displays the median values across the 20 banks, through time, of the range volatility R. The volatility around the time of the GFC dominates. However, while volatility diminished after 2010, it has by no means disappeared.Median values of intra-

47、day range volatilityGraph 110-3151052008Source: authors calculations201020122014201602018Graph 2 illustrates the median range volatility (in levels, at daily frequency) in two charts, with different scales, showing the range volatility before 2010 and after 2010. The period after 2010 displays disti

48、nct periods of high volatility across the banking sector: in late 2010, in 2011 and in 20152016. These are periods of high bank stock price volatility due to fears of contagion from the European sovereign debt crisis as well as the downgrading of the US credit rating from AAA to AA+ on 6 August 2011

49、. In the 20152016 period, factors such as the Brexit vote, the fall in oil prices, the slowing of the Chinese economy and the election in the United States are plausible explanations for the spikes in the volatility measure.We next model the connections between these volatility measures, focusing on

50、 how much of the volatility of each G-SIB can be explained by the volatility of each of the others. We work with the levels of the range volatility measures for our primary results, but have confirmed that they are robust tousing logarithmic transformations instead. We then check to see if more syst

51、emic banks have larger volatility spillovers on other banks, and whether higher capital adequacy will work to reduce this.Range volatility: GFC and post-GFCGraph 210-3151050Jan 2008Apr 2008Jul 2008Oct 2008Jan 2009Apr 2009Jul 2009Oct 2009543210201020112012201320142015201620172018Source: Authors calcu

52、lationsRegularisation of a big VARFollowing a series of papers by Diebold and Yilmaz (2012), Diebold and Yilmaz (2013) and Yilmaz (2018), we examine the volatility measures, and also their evolving connectedness, through time. We estimate a vector autoregressive (VAR) model on the daily range volati

53、lity measures, first for the full sample and then based on a rolling window of 150 days, in order to estimate time-varying measures of volatility spillovers. We use a lag length of five trading days for our VAR.i=1iGiven that the VAR model is a relatively large one, with 100 parameters plus a consta

54、nt term for each bank, our model requires regularisation. We use the elastic net estimator due to Zou and Hastie (2005) for parameter reduction:t=1Enet = argminT(t i iit)2 + k|i| + (1 )2.(2)As with other, familiar, criteria for reducing parameters, such as the Akaike (AIC), Schwartz (BIC) and Hannan

55、-Quinn (HQIC) information criteria, the elastic net penalises models for having more parameters. With this net, the choices of and are key. These control the degree of shrinkage and,by extension, the variables that remain in the estimated model. In moderation, shrinkage can improve both prediction a

56、nd interpretability of estimated models. However, excessive regularisation would result in important variables being left out of the model and can harm both predictive capacity and the inferences drawn about the system being studied.The elastic net generalises many different estimators. The LASSO (L

57、east Absolute Shrinkage Selection Operator) and Ridge penalty are both special cases, based on , values of 1, + and 0, + respectively (Yilmaz 2018). With = 0, there is no penalty for the number of non-zero parameters, and the estimates are simply least-squares.We set the parameter = 0.5, and estimat

58、e the coefficients of the model for alternative values of. As increases, more and more parameters go to zero. We choose based on the widely used machine learning algorithm called cross validation (CV).Using this method, we select a grid of values for , ranging from the lowest, = 0, to the minimal va

59、lue of for which i = 0 , . We then partition into a grid of 100 values over 0, and choose the that minimises the out-of-sample mean squared error based on a test set of withheld data. Once we have identified in this fashion, we then estimate over the full sample. We thus effectively use the in-sampl

60、e training-set data to select , but the full sample to estimate . For the split between in- sample and out-of-sample, we divide the data into five equally sized time periods and withhold each of these in turn, with the chosen based on out-of-sample mean squared forecast errors across the five sample