Scenario-Based Asset Allocation With Fat Tails And Non-Linear Correlation

Abstract

This paper highlights the shortfalls of Modern Portfolio Theory (MPT). Amongst other flaws, MPT assumes that returns are normally distributed, that correlations are linear and risks are symmetrical. We propose a dynamic and flexible scenario-based approach to portfolio selection that incorporates an investor's economic forecast. Extreme Value Theory (EVT) is used to capture the skewness and kurtosis inherent in asset class returns and account for the volatility clustering and extreme co-movements across asset classes. The estimation consists of using an asymmetric GJR-GARCH model to extract filtered residuals for each asset class return. Subsequently, a marginal cumulative distribution function (CDF) of each asset class is constructed by using a Gaussian-kernel estimation for the interior, together with a generalised Pareto distribution (GPD) for the upper and lower tails. The distribution of exceedance method is applied to find residuals in the tails. A Student's t copula is then fitted to the data to induce correlation between the simulated residuals of each asset class. A Monte Carlo technique is applied to simulate standardised residuals, which represent a univariate stochastic process when viewed in isolation but maintain the correlation induced by the copula. The results are mean-CVaR optimised portfolios, which are derived based on an investor's forward-looking expectation.