In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one,...

We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali, Demirtas, and Levy (2009) with a Markov switching mechanism. We show that the risk-return relationship identified by Bali, Demirtas, and...

The paper focuses on the interaction between the solvency probability of a banking firm and the diversification potential of its asset portfolio when determining optimal equity capital. The purpose of this paper is to incorporate value at risk (VaR) into the firm-theoretical model of a banking...

When measuring market risk, credit institutions and Alternative Investment Fund Managers may deviate from equally weighting historical data in their Value-at-Risk calculation and instead use an exponential time series weighting. The use of exponential weighting in the Value-at-Risk calculation...