VALUE-AT-RISK Value-at-Risk (VaR) measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. As one of our references states: “VaR answers the question: how much can I lose with x% probability over a pre-set horizon” (J.P. Morgan, RiskMetrics–Technical Document). Another way of expressing this is that VaR is the lowest quantile of ...

The technique (VaR) is a statistical measure of the risk. It associated with financial risks related to high volatility in prices, interest rates, or exchange rates. used massively by entities because necessity risk constantly traded portfolios.

in this paper, linear data envelopment analysis models are used to estimate markowitz efficient frontier. conventional dea models assume non-negative values for inputs and outputs. however, variance is the only variable in these models that takes non-negative values. therefore, negative data models which the risk of the assets had been used as an input and expected return was the output are uti...

Abstract The main objective of this study was to examine the relationship between Value at Risk (VaR) and expected returns from 2002 to 2013 in Tehran’s Stock Exchange. In this study parametric value at risk, which considers the distribution of returns as normal and the historical value at risk as abnormal, was used to test the presence of the volatility anomaly in the companies listed i...

The concept of Value-at-Risk is described. We discuss how this risk characteristic can be used for supervision and for internal control. Several parametric and non-parametric methods to measure Value-at-Risk are discussed. The non-parametric approach is represented by historical simulations and Monte-Carlo methods. Variance covariance and some analytical models are used to demonstrate the param...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures. Mathematical solution methods for solving these optimization problems are inadequate and very complex for a portfolio with high number of assets. For t...