Diversification and Value-at-Risk
Diversification and Value-at-Risk
By Christophe Perignon, and Daniel Smith
Journal of Banking and Finance (2010)
Abstract Paper

Christophe Perignon

HEC Paris

France

Coder Page  

Daniel Smith

Queensland University of Technology

Australia

Coder Page  

This file contains the data used in Figures 1 and 2. Specifically, it contains the individual Value-at-Risk (credit spread, commodity, foreign exchange, equity, and interest rate) and diversified (i.e., firm level) Value-at-Risk for Bank of America, Citigroup, HSBC, and JPMorgan Chase between 2004Q1 and 2007Q1.
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November 21, 2012
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45
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November 23, 2012
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9999
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21
Abstract
A pervasive and puzzling feature of banks’ Value-at-Risk (VaR) is its abnormally high level, which leads to excessive regulatory capital. A possible explanation for the tendency of commercial banks to overstate their VaR is that they incompletely account for the diversification effect among broad risk categories (e.g., equity, interest rate, commodity, credit spread, and foreign exchange). By underestimating the diversification effect, bank’s proprietary VaR models produce overly prudent market risk assessments. In this paper, we examine empirically the validity of this hypothesis using actual VaR data from major US commercial banks. In contrast to the VaR diversification hypothesis, we find that US banks show no sign of systematic underestimation of the diversification effect. In particular, diversification effects used by banks is very close to (and quite often larger than) our empirical diversification estimates. A direct implication of this finding is that individual VaRs for each broad risk category, just like aggregate VaRs, are biased risk assessments.
Perignon, C., and D. Smith, "Diversification and Value-at-Risk", Journal of Banking and Finance , 34.
Coders:

Christophe Perignon also created these companion sites

The Risk Map: A New Tool for Validating Risk Models
Abstract
This paper presents a new tool for validating risk models. This tool, called the Risk Map, 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 Value-at-Risk (VaR) super exception, which is defined as a situation in which the loss exceeds both the standard VaR and a VaR defined at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions is rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic (e.g. CoVaR) risk estimates or to assess the performance of the margin system of a clearing house.
Colletaz, G., C. Hurlin, and C. Perignon, "The Risk Map: A New Tool for Validating Risk Models", SSRN.
Authors: Colletaz
Hurlin
Perignon
Coders: Colletaz
Hurlin
Perignon
Last update
07/25/2013
Ranking
51
Runs
146
Visits
431
A New Approach to Comparing VaR Estimation Methods
Abstract
We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
Perignon, C., and D. Smith, C. Hurlin, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives , 15, 54-66.
Authors: Perignon
Smith
Coders: Perignon
Smith
Hurlin
Last update
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Ranking
54
Runs
11
Visits
270
Backtesting Value-at-Risk: A Duration-Based Approach
Abstract
Financial risk model evaluation or backtesting is a key part of the internal model’s approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests.
Hurlin, C., and C. Perignon, "Backtesting Value-at-Risk: A Duration-Based Approach", Journal of Financial Econometrics, 2, 84-108.
Authors: Pelletier
Christoffersen
Coders: Hurlin
Perignon
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Evaluating Interval Forecasts
Abstract
A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage. Consequently, the author sets out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.
Hurlin, C., C. Perignon, "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
Authors: Christoffersen
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The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk
Abstract
The hybrid approach combines the two most popular approaches to VaR estimation: RiskMetrics and Historical Simulation. It estimates the VaR of a portfolio by applying exponentially declining weights to past returns and then finding the appropriate percentile of this time-weighted empirical distribution. This new approach is very simple to implement. Empirical tests show a significant improvement in the precision of VaR forecasts using the hybrid approach relative to these popular approaches.
Hurlin, C., C. Perignon, "The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk", Risk, 1, 64-67.
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A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR
Abstract
In this paper, we propose a theoretical and empirical comparison of two popular systemic risk measures - Marginal Expected Shortfall (MES) and Delta Conditional Value at Risk (ΔCoVaR) - that can be estimated using publicly available data. First, we assume that the time-varying correlation completely captures the dependence between firm and market returns. Under this assumption, we derive three analytical results: (i) we show that the MES corresponds to the product of the conditional ES of market returns and the time-varying beta of this institution, (ii) we give an analytical expression of the ΔCoVaR and show that the CoVaR corresponds to the product of the VaR of the firm's returns and the time-varying linear projection coefficient of the market returns on the firm's returns and (iii) we derive the ratio of the MES to the ΔCoVaR. Second, we relax this assumption and propose an empirical comparison for a panel of 61 US financial institutions over the period from January 2000 to December 2010. For each measure, we propose a cross-sectional analysis, a time-series comparison and rankings analysis of these institutions based on the two measures.
Benoit, S., G. Colletaz, C. Hurlin, and C. Perignon, "A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR", SSRN.
Authors: Benoit
Colletaz
Hurlin
Perignon
Coders: Benoit
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Hurlin
Perignon
Last update
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Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)
Abstract
Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk, Second Edition, will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)", McGraw-Hill, Second edition.
Authors: Jorion
Coders: Hurlin
Perignon
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Techniques for Verifying the Accuracy of Risk Management Models
Abstract
Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.
Hurlin, C., C. Perignon, "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives, 3, 73-84.
Authors: Kupiec
Coders: Hurlin
Perignon
Last update
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Ranking
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Visits
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The pernicious effects of contaminated data in risk management
Abstract
Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.
Fresard, L., C. Perignon, and A. Wilhelmsson, "The pernicious effects of contaminated data in risk management", Journal of Banking and Finance, 35.
Authors: Fresard
Perignon
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Coders: Fresard
Perignon
Wilhelmsson
Last update
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Ranking
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Runs
N.A.
Visits
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The level and quality of Value-at-Risk disclosure by commercial banks
Abstract
In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.
Perignon, C., and D. Smith, "The level and quality of Value-at-Risk disclosure by commercial banks", Journal of Banking and Finance, 34.
Authors: Perignon
Smith
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
25
A New Approach to Comparing VaR Estimation Methods
Abstract
We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
Authors: Smith
Perignon
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
43
Margin Backtesting
Abstract
This paper presents a validation framework for collateral requirements or margins on a derivatives exchange. It can be used by investors, risk managers, and regulators to check the accuracy of a margining system. The statistical tests presented in this study are based either on the number, frequency, magnitude, or timing of margin exceedances, which are de…ned as situations in which the trading loss of a market participant exceeds his or her margin. We also propose an original way to validate globally the margining system by aggregating individual backtesting statistics ob- tained for each market participant.
Hurlin, C., and C. Perignon, "Margin Backtesting", University of Orleans, HEC Paris.
Authors: Hurlin
Perignon
Coders: Hurlin
Perignon
Last update
07/23/2014
Ranking
36
Runs
377
Visits
433
Value-at-Risk (Chapter 5: Computing VaR)
Abstract
Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 5: Computing VaR)", MacGraw-Hill, Third Edition.
Authors: Jorion
Coders: Hurlin
Perignon
Last update
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Ranking
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Runs
63
Visits
328

Daniel Smith also created these companion sites

A New Approach to Comparing VaR Estimation Methods
Abstract
We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
Perignon, C., and D. Smith, C. Hurlin, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives , 15, 54-66.
Authors: Perignon
Smith
Coders: Perignon
Smith
Hurlin
Last update
07/16/2012
Ranking
54
Runs
11
Visits
270
The level and quality of Value-at-Risk disclosure by commercial banks
Abstract
In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.
Perignon, C., and D. Smith, "The level and quality of Value-at-Risk disclosure by commercial banks", Journal of Banking and Finance, 34.
Authors: Perignon
Smith
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
25
A New Approach to Comparing VaR Estimation Methods
Abstract
We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
Authors: Smith
Perignon
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
43

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Diversification and Value-at-Risk

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A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR
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In this paper, we propose a theoretical and empirical comparison of two popular systemic risk measures - Marginal Expected Shortfall (MES) and Delta Conditional Value at Risk (ΔCoVaR) - that can be estimated using publicly available data. First, we assume that the time-varying correlation completely captures the dependence between firm and market returns. Under this assumption, we derive three analytical results: (i) we show that the MES corresponds to the product of the conditional ES of market returns and the time-varying beta of this institution, (ii) we give an analytical expression of the ΔCoVaR and show that the CoVaR corresponds to the product of the VaR of the firm's returns and the time-varying linear projection coefficient of the market returns on the firm's returns and (iii) we derive the ratio of the MES to the ΔCoVaR. Second, we relax this assumption and propose an empirical comparison for a panel of 61 US financial institutions over the period from January 2000 to December 2010. For each measure, we propose a cross-sectional analysis, a time-series comparison and rankings analysis of these institutions based on the two measures.
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181
Visits
398
Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts
Abstract
Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model(CAPM)implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.
Patton, J. A., and A. Timmermann, "Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts", Journal of Financial Economics, 98, 605-625.
Authors: Patton
Timmermann
Coders: Patton
Timmermann
Last update
11/17/2012
Ranking
63
Runs
19
Visits
116
Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach
Abstract
When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observation is not explicitely computable. Using Hermite polynomials, I construct an explicit sequences of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.
Aït-Sahalia, Y., "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach", Econometrica, 70, 223-262.
Authors: Aït-Sahalia
Coders: Aït-Sahalia
Last update
10/29/2014
Ranking
2
Runs
119
Visits
621
Copula-Based Models for Financial Time Series
Abstract
This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) cross-sectional dependence between individual time series, and in univariate time series analysis, where they are used to characterise the dependence between a sequence of observations of a scalar time series process. The paper includes a broad, brief, review of the many applications of copulas in finance and economics.
Patton, J. A., "Copula-Based Models for Financial Time Series", Handbook of Financial Time Series, Springer Verlag, -.
Authors: Patton
Coders: Patton
Last update
10/08/2012
Ranking
3
Runs
38
Visits
572
Evaluating Interval Forecasts
Abstract
A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage. Consequently, the author sets out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.
Hurlin, C., C. Perignon, "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
Authors: Christoffersen
Coders: Hurlin
Perignon
Last update
03/09/2012
Ranking
32
Runs
57
Visits
167
Backtesting Value-at-Risk: A Duration-Based Approach
Abstract
Financial risk model evaluation or backtesting is a key part of the internal model’s approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests.
Hurlin, C., and C. Perignon, "Backtesting Value-at-Risk: A Duration-Based Approach", Journal of Financial Econometrics, 2, 84-108.
Authors: Pelletier
Christoffersen
Coders: Hurlin
Perignon
Last update
07/23/2012
Ranking
26
Runs
17
Visits
207
Backtesting Value-at-Risk Accuracy: A Simple New Test
Abstract
This paper proposes a new test of value-at-risk (VAR) validation. Our test exploits the idea that the sequence of VAR violations (hit function) – taking value 1 - α if there is a violation, and -α otherwise – for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the multivariate portmanteau statistic of Li and McLeod (1981), an extension to the multivariate framework of the test of Box and Pierce (1970), to jointly test the absence of autocorrelation in the vector of hit sequences for various coverage rates considered relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VAR validation test for reasonable sample sizes.
Hurlin, C., and S. Tokpavi, "Backtesting Value-at-Risk Accuracy: A Simple New Test", Journal of Risk, 9, 19-37.
Authors: Hurlin
Tokpavi
Coders: Hurlin
Tokpavi
Last update
03/13/2012
Ranking
49
Runs
2
Visits
240
Forecasting Realized Volatility Using a Nonnegative Semiparametric Model
Abstract
This paper introduces a parsimonious and yet exible nonnegative semi-parametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndor-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional form of its error component is left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Asymptotic properties are established for the new estimation method. Simulation studies validate the new estimation method. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.
Preve, D., J. Yu, "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model", Uppsala University.
Authors: Eriksson
Preve
Yu
Coders: Preve
Yu
Last update
06/06/2012
Ranking
64
Runs
19
Visits
114
Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)
Abstract
Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk, Second Edition, will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 7: Portfolio Risk - Analytical Methods)", McGraw-Hill, Second edition.
Authors: Jorion
Coders: Hurlin
Perignon
Last update
03/16/2012
Ranking
33
Runs
9
Visits
303
Value-at-Risk (Chapter 5: Computing VaR)
Abstract
Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 5: Computing VaR)", MacGraw-Hill, Third Edition.
Authors: Jorion
Coders: Hurlin
Perignon
Last update
03/19/2012
Ranking
44
Runs
63
Visits
328
The pernicious effects of contaminated data in risk management
Abstract
Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.
Fresard, L., C. Perignon, and A. Wilhelmsson, "The pernicious effects of contaminated data in risk management", Journal of Banking and Finance, 35.
Authors: Fresard
Perignon
Wilhelmsson
Coders: Fresard
Perignon
Wilhelmsson
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
42
Techniques for Verifying the Accuracy of Risk Management Models
Abstract
Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.
Hurlin, C., C. Perignon, "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives, 3, 73-84.
Authors: Kupiec
Coders: Hurlin
Perignon
Last update
04/17/2012
Ranking
57
Runs
26
Visits
339
Outliers and GARCH Models in Financial Data
Abstract
We propose to extend the additive outlier (AO) identification procedure developed by Franses and Ghijsels(Franses, P.H., Ghijsels, H., 1999. Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15, 1–9) to take into account the innovative outliers (IOs) in a GARCH model. We apply it to three daily stock market indexes and examine the effects of outliers on the diagnostics of normality.
Charles, A., and O. Darné, D. Banulescu, E. Dumitrescu, "Outliers and GARCH Models in Financial Data", Economics Letters, 86, 347-352.
Authors: Charles
Darné
Coders: Charles
Darné
Banulescu
Dumitrescu
Last update
06/22/2012
Ranking
15
Runs
61
Visits
238
The level and quality of Value-at-Risk disclosure by commercial banks
Abstract
In this paper we study both the level of Value-at-Risk (VaR) disclosure and the accuracy of the disclosed VaR figures for a sample of US and international commercial banks. To measure the level of VaR disclosures, we develop a VaR Disclosure Index that captures many different facets of market risk disclosure. Using panel data over the period 1996–2005, we find an overall upward trend in the quantity of information released to the public. We also find that Historical Simulation is by far the most popular VaR method. We assess the accuracy of VaR figures by studying the number of VaR exceedances and whether actual daily VaRs contain information about the volatility of subsequent trading revenues. Unlike the level of VaR disclosure, the quality of VaR disclosure shows no sign of improvement over time. We find that VaR computed using Historical Simulation contains very little information about future volatility.
Perignon, C., and D. Smith, "The level and quality of Value-at-Risk disclosure by commercial banks", Journal of Banking and Finance, 34.
Authors: Perignon
Smith
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
25
Extracting Factors from Heteroskedastic Asset Returns
Abstract
This paper proposes an alternative to the asymptotic principal components procedure of Connor and Korajczyk (Journal of Financial Economics, 1986) that is robust to time series heteroskedasticity in the factor model residuals. The new method is simple to use and requires no assumptions stronger than those made by Connor and Korajczyk. It is demonstrated through simulations and analysis of actual stock market data that allowing heteroskedasticity sometimes improves the quality of the extracted factors quite dramatically. Over the period from 1989 to 1993, for example, a single factor extracted using the Connor and Korajczyk method explains only 8.2% of the variation of the CRSP value-weighted index, while the factor extracted allowing heteroskedasticity explains 57.3%. Accounting for heteroskedasticity is also important for tests of the APT, with p-values sometimes depending strongly on the factor extraction method used.
Jones, S. C., "Extracting Factors from Heteroskedastic Asset Returns", Journal of Financial Economics, 62, 293-325.
Authors: Jones
Coders: Jones
Last update
11/17/2012
Ranking
30
Runs
17
Visits
81
A New Approach to Comparing VaR Estimation Methods
Abstract
We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
Authors: Smith
Perignon
Coders: Perignon
Smith
Last update
11/23/2012
Ranking
9999
Runs
N.A.
Visits
43
Pitfalls in backtesting Historical Simulation VaR models
Abstract
Abstract Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most popular Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the unconditional backtest is always inconsistent for backtesting HS and FHS models, with a power function that can be even smaller than the nominal level in large samples. Our findings have fundamental implications in the determination of market risk capital requirements, and also explain Monte Carlo and empirical findings in previous studies. We also propose a data-driven weighted backtest with good power properties to evaluate HS and FHS forecasts. A Monte Carlo study and an empirical application with three US stocks confirm our theoretical findings. The empirical application shows that multiplication factors computed under the current regulatory framework are downward biased, as they inherit the inconsistency of the unconditional backtest.
Escanciano, J., and P. Pei, "Pitfalls in backtesting Historical Simulation VaR models", Journal of Banking and Finance, 36, 2233-2244.
Authors: Escanciano
Pei
Coders: Escanciano
Pei
Last update
02/22/2013
Ranking
9999
Runs
N.A.
Visits
32
A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics
Abstract
This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the Expected Shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.
Colletaz, G., "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics", Journal of Econometrics, 157, 297-305.
Authors: Zhu
Galbraith
Coders: Colletaz
Last update
05/05/2012
Ranking
38
Runs
6
Visits
95
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