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Capturing the Black Swan: Scenario-Based Asset Allocation with Fat Tails and Non-Linear Correlations

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 that 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 it also accounts for the volatility clustering and the extreme co-movements across asset classes. The estimation consists of using an asymmetric GJR-GARCH model to extract the 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; and then used 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 it maintains the correlation induced by the copula. The results are mean-CVaR optimised portfolios, which are derived based on an investor’s forward-looking expectation.

Working paper 695
1 August 2017
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