Tail Dependence and Systemic Risk in Operational Losses of the US Banking Industry

• Author: Azamat Abdymomunov,Ibrahim Ergen
• DOI: http://doi.org/10.1111/irfi.12117
• Published date: 01 June 2017
• Date: 01 June 2017

Tail Dependence and Systemic Risk

in Operational Losses of the US

Banking Industry*

AZAMAT ABDYMOMUNOV AND IBRAHIM ERGEN

Federal Reserve Bank of Richmond, Richmond, VA, USA

ABSTRACT

Using supervisory operational loss data of the US banking industry,we analyze

dependence among operational losses within banks and across banks. We find

evidence of relatively strong dependence among tail losses of different opera-

tional loss types within banks. Applying a copula framework, we estimate that

the median correlation parameter for the key operational loss types is around

30% and exceeds 50% for some banks in our sample. Our results contrast with

the previous literature that documents that correlation parameter estimates

are in the range of 5–10% and typically do not exceed 20%. Further, we dem-

onstrate significant model risk from not accounting for dependence among

tail losses, resulting in material underestimation of operational risk. In addi-

tion, we investigate dependence of operational losses across banks. Using a

copula framework, we estimate correlation parameters between losses of large

banks in our sample to be 42% on average. This result suggests the presence of

systemic risk from the simultaneous occurrence of operational tail losses in

different large banks.

JEL Codes: C22; C23; G21

I. INTRODUCTION

The Basel Committee on Banking Supervision (2006) defines operational risk as

the risk of loss resulting from inadequate or failed internal processes, people,

and systems or from external events. In recent years, the banking industry expe-

rienced numerous large operational losses. For example, Bank of America Corpo-

ration, JPMorgan Chase & Co., Wells Fargo & Company, Citigroup Inc., and Ally

Financial Inc. collectively agreed to a $25 billion settlement with the US federal

government to address past improper mortgage loan servicing and foreclosure

* The views expressed in this paper are those of the authors and do not necessarily reflect the posi-

tion of the Federal Reserve Bank of Richmond or the Federal Reserve System. We would like to thank

Ross Podbielski and Jeffrey Cheng for providing excellent research assistance. We have benefited from

discussions with Gara Afonso, Brian Clark, Filippo Curti, Alireza Ebrahim, Ping McLemore, Marco

Migueis, Atanas Mihov, and Robert Stewart. We would like to thank the anonymous referee for con-

structive recommendations. All remaining errors are our own.

© 2017 International Review of Finance Ltd. 2017

International Review of Finance, 17:2, 2017: pp. 177–204

DOI: 10.1111/irfi.12117

fraud.

1

Historical operational loss data suggest that many banks experience large

losses in various areas, reflecting the weaknesses of their overall risk management

and internal control practices. The risk from simultaneously occurring large oper-

ational losses within a bank may have a significant impact on the quantification

of operational risk. Thus, quantification methods that do not account for possi-

ble dependence among tail losses may lead to significant model risk. In addition,

recent banking history provides evidence of common drivers of large operational

losses across banks. For example, many banks experienced large losses related to

the same causes such as deficient practices in mortgage servicing and foreclosure

processing, London Interbank Offered Rate (LIBOR) and currency manipulations,

and massive cyber-security attacks. The simultaneous occurrence of large opera-

tional losses across banks may raise concerns of systemic risk.

In this paper, using supervisoryoperational loss data from largeUS bank holding

companies (BHCs),we analyze dependence amongoperational losses withinbanks

and across banks.First, applying a copula-based method, we analyzedependence of

tail losses and the impacts of modeling assumptions on operational risk estimates.

Given the wide variationof operational loss types,relatively large banks commonly

model operational risk by separate risk cells and then aggregate risks by modeling

dependenceamong losses in these risk cells. Thus, ouranalysis should demonstrate

the strength of loss dependence within banks and the relative impact of modeling

assumptions on aggregated operational risk capital. Our analysis of modeling as-

sumptions is in line with the supervisory guidance on model risk management,

outlined by the Board of Governors of the Federal Reserve System (2011). Specifi-

cally, the impactsof accounting for the tail dependence on model outcomesfitinto

supervisory requirements on sensitivity analyses and benchmarking to alternative

models. Second, we investigate the dependence of operational losses across banks.

Evidence of strongly dependent tail losses across banks may indicate the presence

of systemic risk arising from operational tail losses.

We summarize our findings with the following three main results. First, we find

evidence of relatively strong dependence among operational losses of different

risk cells within banks. Following the industry practice and previous literature

[e.g., (Cope and Antonini 2008)], we estimate dependence using a time series of

losses aggregated at a quarterly frequency. Using copula models, we estimate that

the median correlation parameter among key loss types within banks is around

30% and exceeds 50% for some banks. Second, we show that both correlation

parameter estimates and the choice of copula significantly impact the aggregated

operational risk estimate. Specifically, our analysis demonstrates that

underestimating the correlation parameters among losses by 10 percentage points

may cause an underestimation of aggregated operational risk by up to 4%. We also

demonstrate that selecting a copula that does not account for stronger depen-

dence among tail losses, such as a Gaussian or t-copula with high degrees of

freedom, substantially underestimates aggregated operational risk. While many

1 http://www.justice.gov/opa/pr/federal-government-and-state-attorneys-general-reach-25-billion-

agreement-five-largest

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© 2017 International Review of Finance Ltd. 2017178