Juan-Ángel Jiménez-Martín

The Ten Commandments for Managing Value-at-Risk under the Basel II Accord

Under the Basel II Accord, banks and other Authorized Deposit-taking Institutions (ADIs) are required to communicate their daily market risk estimates to the relevant national monetary authority at the beginning of each trading day, using one of a variety of Value-at-Risk (VaR) models to measure risk. The purpose of this paper is to provide a simple explanation and a set of prescriptions for managing VaR under the Basel II Accord. The commandments deal with understanding the Basel II colours, understanding the risk model before choosing, varying the choice of risk model, avoiding the green zone and being willing to violate, incurring large violations, stopping before the red zone, avoiding frequent violations, avoiding the estimation of large portfolios, aggregating portfolios into a single index, and interpreting commandments sensibly as guidelines.

International Evidence on GFC-Robust Forecasts for Risk Management under the Basel Accord

A risk management strategy that is designed to be robust to the Global Financial Crisis (GFC), in the sense of selecting a Value-at-Risk (VaR) forecast that combines the forecasts of different VaR models, was proposed in McAleer et al. (2010c). The robust forecast is based on the median of the point VaR forecasts of a set of conditional volatility models. Such a risk management strategy is robust to the GFC in the sense that, while maintaining the same risk management strategy before, during and after a financial crisis, it will lead to comparatively low daily capital charges and violation penalties for the entire period. This paper presents evidence to support the claim that the median point forecast of VaR is generally GFC-robust. We investigate the performance of a variety of single and combined VaR forecasts in terms of daily capital requirements and violation penalties under the Basel II Accord, as well as other criteria. In the empirical analysis, we choose several major indexes, namely French CAC, German DAX, US Dow Jones, UK FTSE100, Hong Kong Hang Seng, Spanish Ibex35, Japanese Nikkei, Swiss SMI and US S&P500. The GARCH, EGARCH, GJR and Riskmetrics models, as well as several other strategies, are used in the comparison. Backtesting is performed on each of these indexes using the Basel II Accord regulations for 2008-10 to examine the performance of the Median strategy in terms of the number of violations and daily capital charges, among other criteria. The Median is shown to be a profitable and safe strategy for risk management, both in calm and turbulent periods, as it provides a reasonable number of violations and daily capital charges. The Median also performs well when both total losses and the asymmetric linear tick loss function are considered.

Risk Management of Risk Under the Basel Accord: Forecasting Value-at-Risk of VIX Futures

The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. McAleer, Jimenez-Martin and Perez- Amaral (2009) proposed a new approach to model selection for predicting VaR, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. This paper addresses the question of risk management of risk, namely VaR of VIX futures prices. We examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). We find that an aggressive strategy of choosing the Supremum of the single model forecasts is preferred to the other alternatives, and is robust during the GFC. However, this strategy implies relatively high numbers of violations and accumulated losses, though these are admissible under the Basel II Accord.

The rise and fall of S&P500 variance futures

Modelling, monitoring and forecasting volatility are indispensible to sensible portfolio risk management. The volatility of an asset of composite index can be traded by using volatility derivatives, such as volatility and variance swaps, options and futures. The most popular volatility index is VIX, which is a key measure of market expectations of volatility, and hence also an important barometer of investor sentiment and market volatility. Investors interpret the VIX cash index as a “fear” index, and of VIX options and VIX futures as derivatives of the “fear” index. VIX is based on S&P500 call and put options over a wide range of strike prices, and hence is not model based. Speculators can trade on volatility risk with VIX derivatives, with views on whether volatility will increase or decrease in the future, while hedgers can use volatility derivatives to avoid exposure to volatility risk. VIX and its options and futures derivatives has been widely analysed in recent years. An alternative volatility derivative to VIX is the S&P500 variance futures, which is an expectation of the variance of the S&P500 cash index. Variance futures are futures contracts written on realized variance, or standardized variance swaps. The S&P500 variance futures are not model based, so the assumptions underlying the index do not seem to have been clearly understood. As variance futures are typically thinly traded, their returns and volatility are not easy to model accurately using a variety of volatility model specifications. This paper analyses the volatility in S&P500 3-month and 12-month variance futures Before, During and After the GFC, as well as for the full data period, for each of three alternative conditional volatility models and three densities, in order to determine whether exposure to risk can be incorporated into a financial portfolio without taking positions on the S&P500 index itself.

THE TEN COMMANDMENTS FOR MANAGING VALUE AT RISK UNDER THE BASEL II ACCORD: THE TEN COMMANDMENTS FOR MANAGING VALUE AT RISK

Under the Basel II Accord, banks and other authorized deposit-taking institutions are required to communicate their daily market risk estimates to the relevant national monetary authority at the beginning of each trading day, using one of a variety of value-at-risk (VaR) models to measure risk. The purpose of this paper is to provide a simple explanation and a set of prescriptions for managing VaR under the Basel II Accord. The commandments deal with understanding the Basel II colours, understanding the risk model before choosing, varying the choice of risk model, avoiding the green zone and being willing to violate, incurring large violations, stopping before the red zone, avoiding frequent violations, avoiding the estimation of large portfolios, aggregating portfolios into a single index and interpreting commandments sensibly as guidelines.

GFC-Robust Risk Management Strategies under the Basel Accord

A risk management strategy is proposed as being robust to the Global Financial Crisis (GFC) by selecting a Value-at-Risk (VaR) forecast that combines the forecasts of different VaR models. The robust forecast is based on the median of the point VaR forecasts of a set of conditional volatility models. This risk management strategy is GFC-robust in the sense that maintaining the same risk management strategies before, during and after a financial crisis would lead to comparatively low daily capital charges and violation penalties. The new method is illustrated by using the S&P500 index before, during and after the 2008-09 global financial crisis. We investigate the performance of a variety of single and combined VaR forecasts in terms of daily capital requirements and violation penalties under the Basel II Accord, as well as other criteria. The median VaR risk management strategy is GFC-robust as it provides stable results across different periods relative to other VaR forecasting models. The new strategy based on combined forecasts of single models is straightforward to incorporate into existing computer software packages that are used by banks and other financial institutions.

A stochastic dominance approach to financial risk management strategies

The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realized losses exceed the estimated VaR. In this paper we define risk management in terms of choosing sensibly from a variety of risk models and discuss the optimal selection of the risk models. Previous approaches to model selection for predicting VaR proposed combining alternative risk models and ranking such models on the basis of average DCC, or other quantiles of its distribution. These methods are based on the first moment, or specific quantiles of the DCC distribution, and supported by restrictive evaluation functions. In this paper, we consider robust uniform rankings of models over large classes of loss functions that may reflect different weights and concerns over different intervals of the distribution of losses and DCC. The uniform rankings are based on recently developed statistical tests of stochastic dominance (SD). The SD tests are illustrated using the prices and returns of VIX futures. The empirical findings show that the tests of SD can rank different pairs of models to a statistical degree of confidence, and that the alternative (recentered) SD tests are in general agreement.

Currency Hedging Strategies, Strategic Benchmarks and the Global and Euro Sovereign Financial Crises

This paper investigates dynamic currency hedging benefits, with a further focus on the impact of currency hedging before and during the recent financial crises originated from the subprime and the Euro sovereign bonds. We take the point of view of a Euro-based institutional investor who considers passive investment strategies in portfolios holding European, British and US assets. We analyze the impact of the model specification to improve the risk-return tradeoff when currency risk is hedged. Hedging strategies of currency risk, using exchange rates futures and driven by several multivariate GARCH models, depend on the portfolio composition and period analyzed. Dynamic covariance models provide limited evidences of a decrease in hedging rations compared to naive hedging strategies based on linear regressions or variance smoothing. Nevertheless, those results are coupled with better performances of dynamic covariance models in terms of hedging effectiveness an improved Sharpe ratios. The empirical evidences are observed both in-sample as well as in an out-of-sample exercise.

Seasonal fluctuations and equilibrium models of exchange rate

Most of the evidence on dynamic equilibrium exchange rate models is based on seasonally adjusted consumption data. Equilibrium models have not worked well in explaining the actual exchange rate. However, the use of seasonally adjusted data might be responsible for the spurious rejection of the model. This article presents a new equilibrium model for the exchange rates that incorporates seasonal preferences. The fit of the model to the data is evaluated for five industrialized countries using seasonally unadjusted data. Our findings indicate that a model with seasonal preferences can generate monthly time series of the exchange rate without seasonality even when the variables that theoretically determine the exchange rate show clear seasonal behaviours. Further, the model can generate theoretical exchange rates with the same order of integration than actual exchange rates, and in some cases, with the same stochastic trend.

Original article: GFC-robust risk management under the Basel Accord using extreme value methodologies

In this paper we provide further evidence on the suitability of the median of the point VaR forecasts of a set of models as a GFC-robust strategy by using an additional set of new extreme value forecasting models and by extending the sample period for comparison. The median is not affected by extremes, unlike the mean. In periods of contagion, wherein the number and values of extremes are substantially greater, the use of the median would be expected to be even more robust than the mean. These extreme value models include DPOT and Conditional EVT. Such models might be expected to be useful in explaining financial data, especially in the presence of extreme shocks that arise during a GFC. Our empirical results confirm that the median remains GFC-robust even in the presence of these new extreme value models. This is illustrated by using the S&P500 index before, during and after the 2008-2009 GFC. We investigate the performance of a variety of single and combined VaR forecasts in terms of daily capital requirements and violation penalties under the Basel II Accord, as well as other criteria, including several tests for independence of the violations. The strategy based on the median, or more generally, on combined forecasts of single models, is straightforward to incorporate into existing computer software packages that are used by banks and other financial institutions.