In this paper, we analyze the consequences of bank regulation on the size of the real sector. In particular, we address the question whether exogenous shocks on the return-risk characteristics of the technology and on the equity of the real sector are intensified or damped by a value-at-risk constraint on the credit portfolio of a bank. We consider a one-period model with three risk-averse agen...

Value at risk (VaR) and conditional value at risk (CVaR) are the most frequently used risk measures in current risk management practice. As an alternative to VaR, CVaR is attractive since it is a coherent risk measure. We analyze the problem of computing the optimal VaR and CVaR portfolios. In particular, we illustrate that VaR and CVaR minimization problems for derivatives portfolios are typic...

In this paper we solve the problem of static portfolio allocation based on historical Value at Risk (VaR) by using genetic algorithm (GA). VaR is a predominantly used measure of risk of extreme quantiles in modern finance. For estimation of historical static portfolio VaR, calculation of time series of portfolio returns is required. To avoid daily recalculations of proportion of capital investe...

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we are able to test if the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more sui...

Value-at-Risk (VaR) is one of the most widely accepted risk measures in the financial and insurance industries, yet efficient optimization of VaR remains a very difficult problem. We propose a computationally tractable approximation method for minimizing the VaR of a portfolio based on robust optimization techniques. The method results in the optimization of a modified VaR measure, Asymmetry-Ro...

Traditional risk-adjusted performance measures, such as the Sharpe ratio, the Treynor index or Jensen’s alpha, based on the mean-variance framework, are widely used to rank mutual funds. However, performance measures that consider risk by taking into account only losses, such as Value-at-Risk (VaR), would be more appropriate. Standard VaR assumes that returns are normally distributed, though th...

Recently, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several applications. For continuous distributions, CVaR is defined as the expected loss exceeding Value-at Risk (VaR). However, generally, CVaR is the weighted average of VaR and losses exceeding VaR. Central to the approach is an optimization technique for calculating VaR and optimizing...

A new robust version of Support Vector Machine (SVM) based on value-at-risk (VaR) measure referred to as VaR-SVM is proposed in three closely related formulations, and relationships between those VaRSVM formulations is established. In contrast to classical SVMs (hard-margin SVM, soft-margin SVM, and ν-SVM), VaR-SVM is stable to data outliers. Computational experiments confirm that compared to ν...

A two-sided Weibull is developed to model the conditional financial return distribution, for the purpose of forecasting Value at Risk (VaR) and conditional VaR. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that ...