ANALYSIS. Stanislav Bozhkov 1. Supervisor: Antoaneta Serguieva, PhD 1,2. Brunel Business School, Brunel University West London, UK

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1 MEASURING THE OPERATIONAL COMPONENT OF CATASTROPHIC RISK: MODELLING AND CONTEXT ANALYSIS Stanislav Bozhkov 1 Supervisor: Antoaneta Serguieva, PhD 1,2 1 Brunel Business School, Brunel University West London, UK 2 Centre for the Analysis of Risk and Optimisation Modelling Applications, Brunel University West London, UK February 27, 2009 Abstract Recent debacles in the financial industry are a reminder that although risk management tools have greatly developed over the past 15 years, industry vulnerability has not declined proportionately. In our study, we build on Allen and Bali (2007), and infer extreme risk in financial institutions and its operational component. Our contribution is twofold: first, extending the specification and estimation procedure for the model, and then estimating on a dataset of European institutions, spanning major turmoil episodes in the past two decades. Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 1

2 1 Introduction In order to survive extreme losses banks are required to maintain enough capital that should allow them to survive adverse years with probability of at least 99.9%. Capital requirement is set based on institution s exposure to credit, market and operational risk. In this research we focus on methods to estimate economic and regulatory capital for operational risk. Achieving the high level of precision required by Basel II necessitates the efficient combination of various data sources for risk analysis internally collected loss data, expert evaluations (scenario analysis), loss experience of peer bank (external loss data). Directive 2006/48/EC 1 explicitly mandates the use of external data to estimate the probability and impact of rare, yet severe, loss events: The credit institution's operational risk measurement system shall use relevant external data, especially when there is reason to believe that the credit institution is exposed to infrequent, yet potentially severe, losses. A credit institution must have a systematic process for determining the situations for which external data must be used and the methodologies used to incorporate the data in its measurement system. (Directive 2006/48/EC, Annex X, Part 3, Sec ) There are two inter-related types of information an analyst aims to extract from external data: the frequency of large losses, and the severity of large losses. The purpose of this research is to critically assess how different sources of external loss experience can be used to in the estimation of frequency and severity of large losses to the satisfaction of the requirements of directive 2006/48/EC. 1 The implementation of Basel II in European Communities (EC) member countries is laid down in community directives 2006/48/EC relating to the taking up and pursuit of the business of credit institutions, and 2006/49/EC on the capital adequacy of investment firms and credit institutions. Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 2

3 Available external losses generally fall into two categories: data pools created by banks in order to build a shared operational loss database (e.g. ORX consortium), or publicly available loss reports gathered by external parties (e.g. Moody s OpVantage). An interesting variant of the latter approach has recently been pursued by Allen & Bali (2007) that employs extremes of stock returns to estimate loss exposure. We demonstrate that while that approach has certain limitations, judicious use of stock market data could provide valuable insights into the likelihood of extreme losses. 2 Context Basel II provided a positive list of what is considered operational risk: the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk (Para.644). This definition is now the de facto standard definition of operational risk. Compared to comprehensive definitions, the Basel II definition excludes strategic and reputational risks. This omission was arguably due not to some fundamental reason but to the lack of a concept how to assess those risks and how to translate that assessment into a capital requirement. However, the still ongoing financial turmoil clearly supports the use of a more comprehensive definition for internal economic and regulatory capital measurement. The loss distribution approach (LDA) to operational risk capital measurement is an excellent example of both the strengths and weaknesses of bottom-up approaches currently dominating operational risk modelling. It accounts for the loss experience of the particular modelled institution, the structure of its business, and the efficiency of its internal control framework. The downside is the use of a fairly small database one that spans usually six to seven years to model the maximum annual loss that is expected to be exceeded with Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 3

4 probability 0.1%. Insufficiency of loss data can be tackled by combining losses of different institutions in a common, shared database, but modelling challenges do remain, e.g. as to how the different reporting thresholds and data accuracy should be accounted for, or whether loss data from different institutions should be scaled or not. An interesting direction of research is risk inference based stock market data. Such research has often focused on stock market responses to various events. Such research on responses to operational events, in particular, tends to discover overreaction of stock prices to announcements of certain types of losses usually ones that might imply failed processes or deliberate misrepresentation of financial performance. A plausible explanation of is that the overreaction is due to asymmetric information between issuers and investors; the latter could not know if a loss announcement is due to an one-off event or due to flawed processes that could result in uncovering further losses. Hence the stock s risk premium increases, which in turn results in overreaction. Therefore, the overreaction could be interpreted as a reputational loss. Cummins et al. (2006) study the market reaction for 403 bank events and 89 insurer events due to operational losses, and find that stock prices overreact to announcements for operational losses, with a stronger overreaction for insurers and growth companies. Perry and de Fontnouvelle (2005) evaluate the reputational effect of loss announcements, financial shenanigans and earning restatements between 1974 and 2004, and find that operational losses due to external events, on average, do not cause reputational damage. Internal fraud announcement, on the other hand, result in reputational loss roughly equal to the loss amount. Institutions with weak corporate governance experienced similar response for internal and external losses, while for companies with strong shareholders rights the response to internal frauds was six times the loss amount. Palmrose et al. (2004) examine the stock market Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 4

5 response to 403 restatements of financial reports between 1995 and 1999, and report strong negative abnormal return for filings pertaining to intentional non-gaap financial reporting. The response is stronger for restatements that involve more accounts, or where core income is affected. Loughran and Marietta-Westberg (2005) study the performance of stocks that have experienced significant daily return shock (±15%), and find that companies that have undergone a significant negative shock are expected to underperform their peers by some 5% per annum in the three years following the shock event. We contribute to these studies by refining existing procedures for evaluation of catastrophic and operational value at risk, and estimating the modified specification using information on European financial institutions spanning major turmoil episodes (Asian and Russian financial crises, dot com bubble, 9/11, sub-prime lending losses). 3 Methodology Extreme value theory (EVT) as a branch of statistics studies the probability distribution of rare, extreme events. There are two approaches for modelling the distribution of extreme events one is the block maxima approach, the other the peaks over threshold (POT) approach (refer to Embrechts et al., 2003 for details). In this study, we employ the latter in order to estimate the high quantiles of monthly catastrophic and operational losses. Suppose that F(X) is the distribution of a random variable X, and let us denote the conditional distribution of the excesses (X - u) over a threshold u as F u (y) = P(X - u y X > u). The major proposition in the POT approach is that when u then F u (y) G(y), where G(y) is a member of the (two-parameter) Generalised Pareto Distribution (GPD) family: Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 5

6 Here y = X - u is the excess over the threshold u, σ > 0, y > 0 when ξ > 0, 0 y < -σ ξ when ξ < 0, and (1 + ξy σ) > 0. Among the parameters of the GPD, ξ is of particular interest since it controls the thickness of the tail. Distributions with ξ>0 correspond to medium- (ξ 0.5) and heavy tailed (ξ>0.5) distributions. k-th moments of GPD do not exist for k>1/ξ; in particular, when ξ>0.5 GPD has no variance, and when ξ>, it has no mean. The result holds asymptotically, i.e. the larger the threshold (u), the better approximation is achieved. Therefore, the choice of threshold is a fine balance between bias and standard error. Once the parameters of the distribution have been estimated, the unconditional distribution of losses is constructed by multiplying the probability of observing losses beyond the threshold u times the distribution of excess losses as approximated by the GPD. The natural estimate of exceedances of the threshold is given by k n, where n is the total number of observations in the dataset, and k = card{i : i = 1, 2,,n,X i > u} is the number of exceedances of the threshold in the dataset. Finally, the unconditional distribution of losses is used to derive the quantile function and thus the value at risk (VaR) is obtained for a given confidence level. We use a two step procedure in order to analyse risk exposure of financial companies. As a first step, an overall loss measure is obtained based on extremes of monthly stock returns. Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 6

7 Two alternative estimation approaches are considered one based on fitting threshold excesses to GPD (Allen and Bali, 2007), the other based on fitting a linear mixture of Pareto distributions. Idiosyncratic risk is then estimated based on the co-variation of stock returns and market factors. Three approaches are compared one using rolling linear regressions of risk factors on stock returns the approach advocated by (Allen and Bali, 2007). The second approach uses Akaike Information Criterion (AIC) in order to identify the relevant set of risk factors, as advocated by Serguieva et al. (2008a), Serguieva et al. (2008b), Scurr et al. (2008). Finally, a new estimate based on factors extracted from data using Principal Component Analysis (PCA) is used (Jones, 2001). We argue that it is a more appropriate procedure to investigate this particular research given the ratio of explanatory variables to rolling window length, the correlations between explanatory variables, and correlations between market returns. 4 Data Our dataset comprises all shares or depository receipts of financial companies traded on the stock exchanges in the UK, Germany and France. In order to ensure homogeneity of the sample in terms of risk profile, we focus on issuers classified as Banks, Life insurance, or Nonlife insurance in our sample. Share prices and sectoral classification are collected from the Thompson s Datastream database. Explanatory variables values are obtained from Eurostat, Thompson s Datastream, Markit.com and CBOE. Both active and dead (delisted or suspended) instruments are included. References Allen, L. and Bali, T. G. (2007), Cyclicality in catastrophic and operational risk measurements, Journal of Banking & Finance 31, Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 7

8 Cummins, J. D., Lewis, C. M. and Wei, R. (2006), The market value impact of operational loss events for us banks and insurers, Journal of Banking & Finance 30(10), Embrechts, P., Kluppelberg, C. and Mikosch, T. (2003), Modelling Extremal Events for Insurance and Finance, Springer Varlag Berlin. corrected fourth printing. Jones, C. (2001), Extracting Factors from Heteroskedastic Asset Returns, Journal of Financial Economics 62, Loughran, T. and Marietta-Westberg, J. (2005), Determinants of market reaction to restatement announcements, European Financial Management 11(5), Palmrose, Z.-V., Richardson, V. J. and Scholz, S. (2004), Determinants of market reaction to restatement announcements, Journal of Accounting and Economics 37(1), Perry, J. and de Fontnouvelle, P. (2005), Measuring reputational risk: The market reaction to operational loss announcements, unpublished manuscript. Scurr, A., Bozhkov, S., Serguieva, A., Yu, K. and Dolutas, O. (2008), Quantifying operational risk of financial institutions, International Federation of Operational Research Societies Conference. South Africa. Serguieva, A., Bozhkov, S., Scurr, A. and Yu, K. (2008a), Computational approaches to estimating catastrophic and operational risk, Fifth International Conference on Computational Management Science Conference. Abstracts, pp 43-45, London. Serguieva, A., Bozhkov, and Yu, K. (2008b), Catastrophic and Operational Risk Measurement for Financial Institutions, Centre for the Analysis of Risk and Optimisation Modelling Applications, Technical Report Center 79-08, September. Stanislav Bozhkov Measuring the Operational Component of Catastrophic Risk 8