The Limitations of the Value at Risk (VaR) Model in Portfolio Volatility Evaluation; Pitfalls and Mitigations

Abstract

Determining multiple assets’ portfolio volatility using the VaR model has proven to have so many pitfalls; once the portfolio assets are more than two, the value at risk tends to become erratic while repeated computations generate different values therefore making the VaR model ineffective.

This project focused on using historical methods, analytical methods and Monte-Carlo simulations to showcase the limitations of VaR estimation when there are multiple portfolio data. From the limitations, an adjusted approach is developed that utilizes probability distribution within a relative confidence interval and expected volatility to compute the amended VaR. While executing the adjusted VaR using this introduced optimization method, it was highlighted that the adjusted VaR can accommodate any probability distribution; depending on which applies best to the portfolio. The test is carried out using eight-assets portfolio with daily closing price for a one-year period to ensure the generated adjusted VaR estimate can optimize complex portfolios.

The developed adjusted model is both tested using Microsoft Excel and R-Studio; both options showed better VaR values than the other three comparative methods. This implies that when portfolios are complex with multiple assets and with differing probability distribution, the developed model may be more adaptable than existing VaR models.

Keywords: Value at Risk, portfolio volatility, Monte-Carlo simulation

JEL Classification: C52, C53, C58