Quantitative measures of operational risk: an application to funds management

Basel II defines operational risk as the risk of direct or indirect loss resulting from inadequate or failed internal processes, people or systems or from external events. In the past decade, there have appeared a number of quantitative approaches to measuring this risk, approaches that abstract from market risk and reputational risk. The challenge is to develop operational risk measures in an asset management context where there is only limited information available about the incidence and severity of operational loss events. We survey different approaches to this problem and argue that managing this risk through operational due diligence is a source of alpha in this funds management context.     

Practical methods for measuring and managing operational risk in the financial sector: A clinical study

This paper analyzes the implications of the advanced measurement approach (AMA) for the assessment of operational risk. Through a clinical case study on a matrix of two selected business lines and two event types of a large financial institution, we develop a procedure that addresses the major issues faced by banks in the implementation of the AMA. For each cell, we calibrate two truncated distributions functions, one for “normal” losses and the other for the “extreme” losses. In addition, we propose a method to include external data in the framework. We then estimate the impact of operational risk management on bank profitability, through an adapted measure of RAROC. The results suggest that substantial savings can be achieved through active management techniques.     

Operational risk

This paper provides an economic and mathematical characterization of operational risk useful for clarifying the issues related to estimation and the determination of economic capital. The insights for this characterization originate in the corporate finance literature. Operational risk is subdivided into two types, either: (i) the risk of a loss due to the firm’s operating technology, or (ii) the risk of a loss due to agency costs. These two types of operational risks generate loss processes with different economic characteristics. We argue that the current methodology for the determination of economic capital for operational risk is overstated. It is biased high because the computation omits the bank’s net present value (NPV) generating process. We also show that although it is conceptually possible to estimate the operational risk processes’ parameters using only market prices, the non-observability of the firm’s value makes this an unlikely possibility, except in rare cases. Instead, we argue that data internal to the firm, in conjunction with standard hazard rate estimation procedures, provides a more fruitful alternative.     

Who moves first? An intensity-based measure for information flows across stock exchanges

In this paper we propose an innovative measure for information flows between stock exchanges. We develop an intensity-based information share using Russell’s (1999) autoregressive conditional intensity model. Thereby we maintain the irregular nature of financial high frequency data and use durations and timing of price changes to determine the informationally dominant market. From our empirical application to US-listed Canadian stocks we conclude that the home market mostly reflects information first. On the basis of a cross-sectional analysis we find a positive correlation between the intensity-based information share and liquidity.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Internal loss data collection implementation: evidence from a large UK financial institution

The paper conducts a critical analysis of internal loss data collection implementation in a UK financial institution. We use elite semi-structured interviews, with a sample of 15 operational risk consultants from a leading international financial institution. Using content analysis, the data covers a wide range of business areas, with particular attention drawn towards the development of internal loss collection and operational risk management. The results suggest that the development of operational risk management as a function stems from external compliance (Basel II) and the internal pressure to add value to the business portfolio. This need for compliance was augmented as a driver of internal loss data collection; however, participants also recognised that the function of loss data collection is a tool of solid internal risk management and enhances managerial decision-making. The research also highlights the problems in cleansing data in order to ensure that all information implemented in the capital allocation model is valid and reliable.     

Malmquist-type indices in the presence of negative data: An application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.     

INDIVIDUAL EQUITY RETURN DATA FROM THOMSON DATASTREAM: HANDLE WITH CARE!

We compare individual U.S. equity return data from Thomson Datastream (TDS) with similar data from the Center for Research in Security Prices (CRSP) to evaluate TDS for use in studies involving large numbers of individual equities in markets outside the United States. We document important issues of coverage, classification, and data integrity and find that naive use of TDS data can have a large impact on economic inferences. We show that after careful screening of the TDS data, inferences drawn from TDS data are similar to those drawn from CRSP. We illustrate the importance of the screens we develop using U.S. TDS data by applying the screens to TDS data from four European equity markets.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

U.S. Banking Sector Operational Losses and the Macroeconomic Environment

Using supervisory data from large U.S. bank holding companies (BHCs), we find that BHCs incur more operational losses in adverse macroeconomic conditions driven significantly by the higher frequency and severity of tail events. Among different operational risk types, we find that losses from BHCs' failure to meet obligations to clients or from the design of their products are particularly countercyclical. We also show that larger and more leveraged BHCs have a higher macroeconomic sensitivity of operational risk. Overall, our findings provide new evidence regarding U.S. banking organizations' exposure to macroeconomic shocks with implications for risk management practices and supervisory policy.     

Best-performing US mutual fund families from 1993 to 2008: Evidence from a novel two-stage DEA model for efficiency decomposition

When analyzing relative performance, especially at the institutional level, the traditional data envelopment analysis (DEA) models do not recognize vastly different and important activities as separate functions and therefore cannot identify which function may be the main source of inefficiency. We propose a novel two-stage DEA model that decomposes the overall efficiency of a decision-making unit into two components and demonstrate its applicability by assessing the relative performance of 66 large mutual fund families in the US over the period 1993–2008. By decomposing the overall efficiency into operational management efficiency and portfolio management efficiency components, we reveal the best performers, the families that deteriorated in performance, and those that improved in their performance over the sample period. We also make frontier projections for poorly performing mutual fund families and highlight how the portfolio managers have managed their funds relative to the others during financial crisis periods.     

Bayesian estimation of truncated data with applications to operational risk measurement

Data insufficiency and reporting threshold are two main issues in operational risk modelling. When these conditions are present, maximum likelihood estimation (MLE) may produce very poor parameter estimates. In this study, we first investigate four methods to estimate the parameters of truncated distributions for small samples—MLE, expectation-maximization algorithm, penalized likelihood estimators, and Bayesian methods. Without any proper prior information, Jeffreys’ prior for truncated distributions is used. Based on a simulation study for the log-normal distribution, we find that the Bayesian method gives much more credible and reliable estimates than the MLE method. Finally, an application to the operational loss severity estimation using real data is conducted using the truncated log-normal and log-gamma distributions. With the Bayesian method, the loss distribution parameters and value-at-risk measure for every cell with loss data can be estimated separately for internal and external data. Moreover, confidence intervals for the Bayesian estimates are obtained via a bootstrap method.     

A systematic approach to multi-period stress testing of portfolio credit risk

We propose a new method for analysing multi-period stress scenarios for portfolio credit risk more systematically than in current macro stress tests. The plausibility of a scenario is quantified by its distance from an average scenario. For a given level of plausibility, we search systematically for the most adverse scenario. This ensures that no plausible scenario will be missed. We show how this method can be applied to some models already in use by practitioners. While worst case search requires numerical optimisation we show that we can work with reasonably good linear approximations to the portfolio loss function. This makes systematic multi-period stress testing computationally efficient and easy to implement. Applying our approach to data from the Spanish loan register we show that, compared to standard stress test procedures, our method identifies more harmful scenarios that are equally plausible.     

Pricing catastrophe options with stochastic claim arrival intensity in claim time

We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of a one-claim bond and the premium of a reinsurance contract. We implement a stochastic time change from calendar time to claim time to more efficiently price the CAT option as a random sum – a binomial sum of claim time binomial Asian option prices. This choice of the operational time dimension allows us to incorporate different patterns of catastrophe arrivals by adjusting the claim arrival probability. We demonstrate this versatility by incorporating a mean-reverting Ornstein-Uhlenbeck intensity arrival process. Simulation results verify our model predictions and demonstrate how the claim arrival probability varies with the expected claim arrival intensity.     

Comparative advantage,demand for external finance,and financial development

This paper analyzes the effect of comparative advantage in international trade on a country's level of financial development. Countries with comparative advantage in financially intensive goods experience a higher demand for external finance, and therefore financial development. By contrast, financial development is lower in countries that primarily export goods which do not rely on external finance. We use disaggregated trade data to develop a measure of a country's external finance need of exports, and demonstrate this effect empirically. In order to overcome the simultaneity problem, we develop a novel instrumentation strategy based on the exogenous geographic determinants of trade patterns.     

The Risk Map: A new tool for validating risk models

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.     

An improved estimation method and empirical properties of the probability of informed trading

We report evidence that boundary solutions can cause a bias in the estimate of the probability of informed trading (PIN). We develop an algorithm to overcome this bias and use it to estimate PIN for nearly 80,000 stock-quarters between 1993 and 2004. We obtain two sets of PIN estimates by using the factorized likelihood functions in both [Easley et al., 2010] and [Lin and Ke, 2011], respectively. We find that the estimate based on the EHO factorization is systematically smaller than the estimate based on the LK factorization, meaning that there is a downward bias associated with the EHO factorization. In addition, we find that boundary solutions appear with a very high frequency when the LK factorization is used. Thus it is necessary to use the LK factorization together with the algorithm in this paper. At last, we document several interesting empirical properties of PIN.     

Cyclicality in catastrophic and operational risk measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973–2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the generalized Pareto distribution and the skewed generalized error distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.     

Hedge fund pricing and model uncertainty

This article uses Bayesian model averaging to study model uncertainty in hedge fund pricing. We show how to incorporate heteroscedasticity, thus, we develop a framework that jointly accounts for model uncertainty and heteroscedasticity. Relevant risk factors are identified and compared with those selected through standard model selection techniques. The analysis reveals that a model selection strategy that accounts for model uncertainty in hedge fund pricing regressions can be superior in estimation/inference. We explore potential impacts of our approach by analysing individual funds and show that they can be economically important.     

Modeling and measuring intraday overreaction of stock prices

We introduce a model for stock prices consisting of a fundamental price process and a news impact curve, which allows for either overreaction, underreaction, or correct response to changes of the fundamental value. We further develop statistics based on OHLC data, which separately measure upside and downside overreaction. The distribution of these statistics under the hypothesis of correct response and fundamental prices following Brownian motions is used to derive tests for upside and downside overreaction. We show that more realistic and frequently used fundamental price processes with correct response leave the distribution of the test statistics widely unaffected or lead to conservative tests. Empirical application to different stock markets provides strong evidence for intraday overreaction, particularly to bad news. The economic significance of the discrimination induced by the proposed statistics is further illustrated by analyzing the performance of a simple buy on bad news strategy.