Risk Measures: Robustness, Elicitability, and Backtesting

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Xue Dong He ◽  
Steven Kou ◽  
Xianhua Peng
Keyword(s):  
Risk Management ◽  
Financial Institutions ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Requirements ◽  
Annual Review ◽  
Publication Date ◽  
Regulatory Capital ◽  
Basel Accord ◽  
Economic Considerations

Risk measures are used not only for financial institutions’ internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk measure is a controversial issue. We review the literature on risk measures, particularly on issues such as subadditivity, robustness, elicitability, and backtesting. We also aim to clarify some misconceptions and confusions in the literature. In particular, we argue that, despite lacking some mathematical convenience, the median shortfall—that is, the median of the tail loss distribution—is a better option than the expected shortfall for setting the Basel Accords capital requirements due to statistical and economic considerations such as capturing tail risk, robustness, elicitability, backtesting, and surplus invariance. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

scholarly journals Risk Measures and Multivariate Extensions of Breiman's Theorem

2012 ◽  
Vol 49 (2) ◽  
pp. 364-384 ◽  
Author(s):  
Anne-Laure Fougeres ◽  
Cecile Mercadier
Keyword(s):  
Ruin Probability ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Requirements ◽  
Regulatory Capital ◽  
Tail Probabilities ◽  
Solvency Capital ◽  
Finite Time Horizon ◽  
Standard Risk

The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of Breiman's theorem. We thus present new situations where the ruin probability admits computable equivalents. We also derive asymptotics for the value at risk.

scholarly journals Risk Measures and Multivariate Extensions of Breiman's Theorem

2012 ◽  
Vol 49 (02) ◽  
pp. 364-384 ◽  
Author(s):  
Anne-Laure Fougeres ◽  
Cecile Mercadier
Keyword(s):  
Ruin Probability ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Requirements ◽  
Regulatory Capital ◽  
Tail Probabilities ◽  
Solvency Capital ◽  
Finite Time Horizon ◽  
Standard Risk

The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of Breiman's theorem. We thus present new situations where the ruin probability admits computable equivalents. We also derive asymptotics for the value at risk.

A LIQUIDATION RISK ADJUSTMENT FOR VALUE AT RISK AND EXPECTED SHORTFALL

2018 ◽  
Vol 21 (03) ◽  
pp. 1850010 ◽  
Author(s):  
LAKSHITHE WAGALATH ◽  
JORGE P. ZUBELLI
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Risk Adjustment ◽  
Value At Risk ◽  
Financial Institution ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Adjusted Risk ◽  
Risk Managers

This paper proposes an intuitive and flexible framework to quantify liquidation risk for financial institutions. We develop a model where the “fundamental” dynamics of assets is modified by price impacts from fund liquidations. We characterize mathematically the liquidation schedule of financial institutions and study in detail the fire sales resulting endogenously from margin constraints when a financial institution trades through an exchange. Our study enables to obtain tractable formulas for the value at risk and expected shortfall of a financial institution in the presence of fund liquidation. In particular, we find an additive decomposition for liquidation-adjusted risk measures. We show that such a measure can be expressed as a “fundamental” risk measure plus a liquidation risk adjustment that is proportional to the size of fund positions as a fraction of asset market depths. Our results can be used by risk managers in financial institutions to tackle liquidity events arising from fund liquidations better and adjust their portfolio allocations to liquidation risk more accurately.

RISK MEASURES DERIVED FROM A REGULATOR’S PERSPECTIVE ON THE REGULATORY CAPITAL REQUIREMENTS FOR INSURERS

2020 ◽  
Vol 50 (3) ◽  
pp. 1065-1092
Author(s):  
Jun Cai ◽  
Tiantian Mao
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Wasserstein Distance ◽  
Capital Requirements ◽  
Translation Invariance ◽  
Coherent Risk Measures ◽  
Regulatory Capital ◽  
Coherent Risk ◽  
Positive Homogeneity ◽  
Stop Loss

AbstractIn this study, we propose new risk measures from a regulator’s perspective on the regulatory capital requirements. The proposed risk measures possess many desired properties, including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and stop-loss order preserving. The new risk measures not only generalize the existing, well-known risk measures in the literature, including the Dutch, tail value-at-risk (TVaR), and expectile measures, but also provide new approaches to generate feasible and practical coherent risk measures. As examples of the new risk measures, TVaR-type generalized expectiles are investigated in detail. In particular, we present the dual and Kusuoka representations of the TVaR-type generalized expectiles and discuss their robustness with respect to the Wasserstein distance.

scholarly journals How Much Cash Is At Risk In U.S. Non-Financial Firms? A VaR-Type Measurement

2015 ◽  
Vol 31 (4) ◽  
pp. 1579
Author(s):  
Frantz Maurer
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Cash Flow ◽  
Management Practices ◽  
Risk Measures ◽  
Risk Measure ◽  
Empirical Studies ◽  
Firm Level ◽  
Level Data ◽  
Corporate Risk

<p>Risk management techniques first developed by, and for, banks are now being adopted by non-financial corporations. However, while firms are already engaged in activities intended to develop their risk management practices, they often do not possess risk measures focused on key corporate financial results such as earnings or cash flow. The main contribution of this paper is to develop a cash flow-based risk measure conditional on specific company-level factors. With U.S. firm-level data, we present evidence that Cash Flow-at-Risk and Expected shortfall differ across main non-financial industries. Our results call for renewed attention to the role that VaR-type measures for cash flow can play in empirical studies dedicated to corporate risk analysis, and with respect to corporate-level risk management purposes.</p>

Computing Sensitivities for Distortion Risk Measures

2021 ◽  
Author(s):  
Peter W. Glynn ◽  
Yijie Peng ◽  
Michael C. Fu ◽  
Jian-Qiang Hu
Keyword(s):  
Risk Management ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Risk Measures ◽  
Risk Measure ◽  
Tail Probability ◽  
Sample Paths ◽  
Distortion Risk Measure ◽  
Distortion Functions ◽  
Ratio Estimators

Distortion risk measure, defined by an integral of a distorted tail probability, has been widely used in behavioral economics and risk management as an alternative to expected utility. The sensitivity of the distortion risk measure is a functional of certain distribution sensitivities. We propose a new sensitivity estimator for the distortion risk measure that uses generalized likelihood ratio estimators for distribution sensitivities as input and establish a central limit theorem for the new estimator. The proposed estimator can handle discontinuous sample paths and distortion functions.

Do Financial Regulations Shape the Functioning of Financial Institutions’ Risk Management in Asset-Backed Securities Investment?

2019 ◽  
Vol 33 (6) ◽  
pp. 2506-2553 ◽  
Author(s):  
Xuanjuan Chen ◽  
Eric Higgins ◽  
Han Xia ◽  
Hong Zou
Keyword(s):  
Risk Management ◽  
Financial Institutions ◽  
Capital Requirements ◽  
Historical Cost ◽  
Oxford University ◽  
Financial Regulations ◽  
The 2008 Financial Crisis ◽  
Asset Backed Securities ◽  
Management Functions ◽  
Risk Managers

Abstract We show that installing stronger risk management into financial institutions—a proposal widely discussed following the 2008 financial crisis—is insufficient to constrain institutions’ exposure to investment with lurking risk, such as asset-backed securities (ABS). Regulations affect the functioning of risk management: risk management constrains institutions’ exposure to risky ABS when they face mark-to-market reporting combined with capital requirements; however, this role is considerably weaker when capital requirements are combined with historical cost accounting. We find suggestive evidence that financial regulations affect risk management functions through promoting risk managers’ efforts in uncovering ABS risk and curbing executives’ incentives to take excessive risk. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

scholarly journals Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

2020 ◽  
Author(s):  
Denisa Banulescu-Radu ◽  
Christophe Hurlin ◽  
Jérémy Leymarie ◽  
Olivier Scaillet
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Marginal Expected Shortfall

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as the systemic expected shortfall (SES), the systemic risk measure (SRISK), or the delta conditional value-at-risk ([Formula: see text]CoVaR). We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application to a panel of U.S. financial institutions is conducted to assess the validity of MES, SRISK, and [Formula: see text]CoVaR forecasts issued from a bivariate GARCH model with a dynamic conditional correlation structure. Our results show that this model provides valid forecasts for MES and SRISK when considering a medium-term horizon. Finally, we propose an early warning system indicator for future systemic crises deduced from these backtests. Our indicator quantifies how much is the measurement error issued by a systemic risk forecast at a given point in time which can serve for the early detection of global market reversals. This paper was accepted by Kay Giesecke, finance.

scholarly journals The regulatory treatment of liquidity risk in South Africa

2012 ◽  
Vol 15 (3) ◽  
pp. 294-308 ◽  
Author(s):  
Johann Jacobs
Keyword(s):  
South Africa ◽  
Liquidity Risk ◽  
Credit Market ◽  
Capital Requirements ◽  
Regulatory Capital ◽  
Risk Regulation ◽  
Basel Accord ◽  
Playing Field ◽  
Liquidity Crises ◽  
Bank Solvency

The Basel accord describes the regulatory capital requirements for credit, market and operational risk. The accord aims to provide guidelines to level the playing field for all internationally active banks and to protect consumers against these risks. Despite the growing significance to bank solvency of liquidity risk, it is omitted from the new accord2. Banks are not required to measure and manage this risk yet they are often considerably exposed to the threat of severely diminished liquidity. This omission from the accord could have dire consequences for banks and the economy in which they operate: liquidity crises can occur without warning and spread quickly to other parts of the financial system. This article critically explores current practices in South Africa and proposes guidelines for effective liquidity risk regulation.

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