A Bayesian approach to measuring risk on portfolios with many assets

Abstract

Modern financial markets continue to undergo significant developments to keep up with the rapid growth of technology. These advancements have led to the worldwide integration of financial markets and consequential global market crashes. In turn, this has driven firms and authorities operating within the industry to appreciate the need for an effective model to measure the risk of potential losses. In this study we suggest a method for measuring risk on portfolios with many assets via three main steps; performing dimension reduction using dynamic principal component analysis, followed by volatility modelling and forecasting using a Bayesian generalized autoregressive conditional heteroscedastic (GARCH) model and finally, estimating the risk of the portfolio using value at risk (VaR) and expected shortfall (ES). To determine the optimal balance between dimension reduction and accurate forecasts, we applied this method on 4, 11, and 36 dynamic principal components based on the total variation of the data that they account for. Furthermore, to evaluate and compare the difference in performances, we applied cross-validation using pseudo-maximum likelihood. We conclude that our method was not accurate when taking 4 dynamic principal components, and while both remaining models performed relatively well, the model using 11 dynamic principal components performed marginally better.