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

Related South Africa’s Cities and Growth Spatial Challenges and Policy Interventions Content

Request for Proposals: The role of cities as drivers of growth and employment
Background Urbanization in South Africa is expected to reach 80% by...
Call for Work
South Africa’s future will be decided in our cities
Discussion Document 14 South Africa’s cities face multiple, overlap...
Dieter von Fintel, Justin Visagie, Ivan Turok, Takwanisa Machemedze, Claus Rabe, Sebastian Galiani, Edward Glaeser
Discussion Document
Monitoring South Africa’s metropolitan economies: A survey of the data landscape
Discussion Document 13 Disparities in data across different metropo...
Dieter von Fintel
Discussion Document
Cities, productivity and Jobs in SA: Problems and potential
Discussion Document 12 Cities contribute to national prosperity bec...
Ivan Turok, Justin Visagie
Discussion Document
Place-based economic policies: international lessons for South Africa
Discussion Document 11 Place-based policies are designed to support...
Harris Selod, Claus Rabe
Discussion Document
What luminosity data can and cannot reveal about South Africa’s urban economies
Discussion Document 10 As novel types of data are becoming availabl...
Takwanisa Machemedze
Discussion Document
Crime: A policy-oriented survey
Discussion Document 9 South Africa has a reputation for having high...
Sebastian Galiani
Discussion Document
Virtual CDE Workshop on SA Cities and Growth
Urban economics has provided powerful insights into how the charact...

Search Resources

Ground Floor Brookside Building
11 Imam Haron Road
Claremont, 7700
Cape Town

PostNet Suite # 109
Private Bag X1005
Claremont 7735
Cape Town

Get Social