A Bayesian approach for more reliable tail risk forecasts

This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.     

Conditional higher order moments in metal asset returns

This study examines the role of higher order moments in the returns of four important metals, aluminium, copper, gold and silver, using the asymmetric GARCH (AGARCH) model with a conditional skewed generalized-t (SGT) distribution. Implications of higher order moments in metal returns are evaluated by comparing the performances of conditional value-at-risk measures obtained from the AGARCH models with SGT distributions to those obtained from the AGARCH models with normal and student-t distributions. With the exception of gold, the AGARCH model with the SGT distribution appears to have the best fit for all metals examined.     

A robust VaR model under different time periods and weighting schemes

This paper analyses several volatility models by examining their ability to forecast Value-at-Risk (VaR) for two different time periods and two capitalization weighting schemes. Specifically, VaR is calculated for large and small capitalization stocks, based on Dow Jones (DJ) Euro Stoxx indices and is modeled for long and short trading positions by using non parametric, semi parametric and parametric methods. In order to choose one model among the various forecasting methods, a two-stage backtesting procedure is implemented. In the first stage the unconditional coverage test is used to examine the statistical accuracy of the models. In the second stage a loss function is applied to investigate whether the differences between the models, that calculated accurately the VaR, are statistically significant. Under this framework, the combination of a parametric model with the historical simulation produced robust results across the sample periods, market capitalization schemes, trading positions and confidence levels and therefore there is a risk measure that is reliable.

THE TEN COMMANDMENTS FOR OPTIMIZING VALUE-AT-RISK AND DAILY CAPITAL CHARGES

Abstract.  Credit risk is the most important type of risk in terms of monetary value. Another key risk measure is market risk, which is concerned with stocks and bonds, and related financial derivatives, as well as exchange rates and interest rates. This paper is concerned with market risk management and monitoring under the Basel II Accord, and presents Ten Commandments for optimizing value-at-risk (VaR) and daily capital charges, based on choosing wisely from (1) conditional, stochastic and realized volatility; (2) symmetry, asymmetry and leverage; (3) dynamic correlations and dynamic covariances; (4) single index and portfolio models; (5) parametric, semi-parametric and non-parametric models; (6) estimation, simulation and calibration of parameters; (7) assumptions, regularity conditions and statistical properties; (8) accuracy in calculating moments and forecasts; (9) optimizing threshold violations and economic benefits; and (10) optimizing private and public benefits of risk management. For practical purposes, it is found that the Basel II Accord would seem to encourage excessive risk taking at the expense of providing accurate measures and forecasts of risk and VaR.     

Bankruptcy risk induced by career concerns of regulators

We introduce a model in which a regulator employs mechanism design to embed her human capital beta signal(s) in a firm’s capital structure. This can enhance her compensation at the firm, and the value of her contract with the firm in the form of an executive stock option. We prove that the agency cost of this revolving door behavior increases the firm’s financial leverage, bankruptcy risk, and affects estimation of firm value at risk (VaR).     

Risk models-at-risk

The experience from the global financial crisis has raised serious concerns about the accuracy of standard risk measures as tools for the quantification of extreme downward risks. A key reason for this is that risk measures are subject to a model risk due, e.g. to specification and estimation uncertainty. While regulators have proposed that financial institutions assess the model risk, there is no accepted approach for computing such a risk. We propose a remedy for this by a general framework for the computation of risk measures robust to model risk by empirically adjusting the imperfect risk forecasts by outcomes from backtesting frameworks, considering the desirable quality of VaR models such as the frequency, independence and magnitude of violations. We also provide a fair comparison between the main risk models using the same metric that corresponds to model risk required corrections.     

Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima increases exponentially with the number of states, implying computational complexity. The optimal constrained portfolio allocation may therefore not be monotonic in the state–price density. We propose a type of financial innovation, which splits states of nature, that is shown to weakly enhance welfare, restore monotonicity of the optimal portfolio allocation in the state-price density, and reduce computational complexity. We are grateful to Ken Kavajecz and seminar participants at Harvard Business School, London School of Economics, Maastrict University, ZEI Bonn, and Danske Bank Symposium on Asset allocation and Value-at-Risk: Where Theory Meets Practice for comments on an earlier version of this paper. We also benefitted from the suggestions of two anonymous referees. Our papers can be downloaded from www.RiskResearch.org.     

Risk forecasting in (T)GARCH models with uncorrelated dependent innovations

(G)ARCH-type models are frequently used for the dynamic modelling and forecasting of risk attached to speculative asset returns. While the symmetric and conditionally Gaussian GARCH model has been generalized in a manifold of directions, model innovations are mostly presumed to stem from an underlying IID distribution. For a cross section of 18 stock market indices, we notice that (threshold) (T)GARCH-implied model innovations are likely at odds with the commonly held IID assumption. Two complementary strategies are pursued to evaluate the conditional distributions of consecutive TGARCH innovations, a non-parametric approach and a class of standardized copula distributions. Modelling higher order dependence patterns is found to improve standard TGARCH-implied conditional value-at-risk and expected shortfall out-of-sample forecasts that rely on the notion of IID innovations.     

Expected shortfall estimation for apparently infinite-mean models of operational risk

Statistical analyses on actual data depict operational risk as an extremely heavy-tailed phenomenon, able to generate losses so extreme as to suggest the use of infinite-mean models. But no loss can actually destroy more than the entire value of a bank or of a company, and this upper bound should be considered when dealing with tail-risk assessment. Introducing what we call the dual distribution, we show how to deal with heavy-tailed phenomena with a remote yet finite upper bound. We provide methods to compute relevant tail quantities such as the Expected Shortfall, which is not available under infinite-mean models, allowing adequate provisioning and capital allocation. This also permits a measurement of fragility. The main difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution. Our methodology is useful with apparently infinite-mean phenomena, as in the case of operational risk, but it can be applied in all those situations involving extreme fat tails and bounded support.     

The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis

This paper proposes an approach to constructing the insured portfolios under the VaR-based portfolio insurance strategy (VBPI) and provides a comprehensive analysis of its hedging effectiveness in comparison with the buy-and-hold (B&H) as well as the constant proportion portfolio insurance (CPPI) strategies in the context of the Chinese market. The results show that both of the insurance strategies are able to limit the downward returns while retaining certain upside returns, and their capabilities of reshaping the return distributions increase as the guarantee or the confidence level rises. In general, the VBPI strategy tends to outperform the CPPI strategy in terms of both the degree of downside protection and the return performance.