Regulators often set value-at-risk (VaR) constraints to limit the portfolio risk of institutional investors. For some investors, notably pension funds, the VaR constraint is enforced over a horizon which is significantly shorter than the investment horizon of the investor. Our paper aims to...

This paper studies a basket of risk statistics that are widely used to measure investment performance. Those risk statistics were used to rank the performance of the assets. The dependent information was removed from the set of risk measures that were used in the test. The risk statistics were...

Value-at-Risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a new simple approach to estimation of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting...

The difference between market risk and potential market risk is emphasized and a measure of the latter risk is proposed. Specifically, it is argued that the spectrum of smooth Lyapunov exponents can be utilized in what we call (λ, σ2)-analysis, which is a method to monitor the aforementioned...

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management...

Historical VaR, CVaR and ES (Expected Shortfall) to LIQUIDATION Software is a model characterized by its straightforwardness, allowing regulators measure risk using a standard database of primitive factors and portfolio positions only, leaving little error margin in comparing market risk for...

The optimization of a large random portfolio under the Expected Shortfall risk measure with an ℓ₂ regularizer is carried out by analytical calculation. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition...

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in and are present also in at least thirty other papers referencing it, including the recent survey on...

We study alternative specifications of conditional quantile models that are used to estimate Value at Risk (VaR). Our proposed specifications include the incorporation of a slow moving component in the quantile process, along with recent aggregate returns as regressors. We consider a range of...