Value at risk using independent component analysis.

Abstract

Value at risk (VaR) is a metric that gives the risk of making a loss for investments. In current scenario, the investors try to minimise the risk by investing in a portfolio containing several stocks rather than a single stock. This means that there is a need to evaluate the combined Value at Risk for a given portfolio. The conventional method of doing this is by using the Variance Covariance process where the joint probability is arrived using the correlations between various stocks. However, the actual returns of the stocks tend to have fat tailed distributions, do not meet the normality assumptions and hence results in an under estimation of Var. The aim of this report is to understand the best possible approaches to build a mathematical model that can predict the Value at Risk close to the actual VaR. The study looks at time-series modelling using ARMA-GARCH on stock returns to take care of the variations in mean and volatility of returns over a long period of time. The model is built on the assumption the errors follow a Pearson Type IV distribution. Principal Component Analysis and Independent Component Analysis carried out on these distributions would then provide a lesser number of parameters than controls the VaR. A joint probability function built from these variables would then yield a value of VaR that is nearly accurate.