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Type	Master's Thesis
Scope	Discipline-based scholarship
Title	Diversification Effect in case of Heavy-Tailed Distributions
Organization Unit	Quantitative Finance (Erich Walter Farkas)
Authors	Matthias Erdin
Supervisors	Erich Walter Farkas Michel Dacorogna
Language	English
Institution	University of Zurich
Faculty	Faculty of Business, Economics and Informatics
Number of Pages	136
Date	2022
Abstract Text	The diversification gain (DG) measures the reduction in risk-based capital by bundling risks in a portfolio rather than holding them individually. We use the Value-at-Risk (VaR), Expected-Shortfall (ES), and Expectile to estimate the DG for Frechet distributed risks with different tail indices based on Monte Carlo simulations. This leads to the following results: The DG is lower for heavier tails. However, the DG is not significantly affected by the tail for dependent risks with finite second moment. The DG is higher for a higher number of risks, but with marginally decreasing effects. For dependent risks, the DG does not increase from a certain number of risks. Exposure limits significantly increase the DG for heavy-tailed risks. Lower limits lead to a higher DG. Higher dependencies decrease the DG. The behaviour of the DG for the ES and Expectile are similar. We observe several risk conditions where the VaR is increased by diversification. But the coherent risk measure ES and the Expectile always show positive diversification gains for risks with finite expectation. The VaR increase due to diversification is a measurement error rather than a risk increase. We also address the advantages of using the diversification gain by Burgi, Dacorogna, and Iles (2008) as a diversification measure. It allows for comparison across different distributions and is economically intuitive. The results of the DG approach are also compared to the expected utility framework. We also explore the conditions for negative diversification effects in the expected utility approach of Ibragimov, Jaffee, and Walden (2009).
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