Comparative Analysis of Value at Risk (VAR) Methods for Portfolio with Non-Linear Return

Abstract

In this study various value at risk methods such as Historical Simulation, Variance-Covariance Approach and Monte Carlo Simulation are calculated, compared and tested for accuracy. Backtesting for the VaR methods is applied to check the accuracy of the VaR methods. The portfolio includes equally weighted three banking stock and one at-the-money (ATM) call option for one of the banking stock in the portfolio. The log return for the portfolio and individual investments are calculated. Different VaR calculation methods are used to calculate the downside risk of the portfolio and individual investments. VaR is calculated at 95% and 99% confidence level for the portfolio and individual securities. The value at risk for the portfolio at 95% confidence level from all the three methods are within the defined level of downside risk, while at 99% confidence level only Mote Carlo Simulation method provides good approximation of downside risk for a portfolio with options. Thus from this study it is inferred that for instrument or portfolio with non-linear return structure Monte Carlo simulation method provide good approximation of the downside risk.

Keywords: Value at Risk, VaR, Historical Simulation, Variance-Covariance method, Monte Carlo Simulation method, Backtesting