Path-dependent Risk Measures - Theory and Applications

von Philipp Maximilian Möller
Dissertation
Datum der mündl. Prüfung:2021-01-12
Erschienen:2021-01-22
Betreuer:Prof. Dr. Olaf Korn
Gutachter:Prof. Dr. Olaf Korn
Gutachter:Prof. Dr. Stefan Dierkes
Gutachter:Prof. Dr. Holger A. Rau
Zum Verlinken/Zitieren: http://dx.doi.org/10.53846/goediss-8406

 

 

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Zusammenfassung

Englisch

This dissertation addresses various key aspects in risk measurement with path-dependent risk measures. In contrast to most classical risk measures like value-at-risk, (semi-)variance, expected shortfall, or lower partial moments, path-dependent measures like drawdown incorporate the risky object’s path, instead of being functions of the distribution of the risky object at the end of the investment horizon alone. While including this information about the path is beneficial for many reasons – including liquidity, behavioral, and information efficiency reasons –, it adds substantially to the complexity of these measures, which is why little is known about their properties so far. The dissertation addresses this question by analyzing fundamental properties of drawdown measures. Its main findings can be summarized as follows: While changes in lower return moments affect a wide range of drawdown measures similarly, the effect of higher moments varies by drawdown measure. Autocorrelation in the returns does not increase the drawdown as long as the return variance is controlled adequately. A unified framework is devised that comprises almost all current drawdown measures, facilitates the construction of new drawdown measures, simplifies their implementation, and highlights their conceptual differences. All drawdown measures exhibit the capacity to identify stock picking skill in portfolio managers to some degree, and rank their portfolios differently. Moreover, fund drawdown is discovered to exhibit robust relative persistence, which underscores its potential to inform investment decisions. Methodologically, these insights are derived from either simulation studies, portfolio simulations, or the empirical analysis of stock or fund data. They substantially expand the current level of understanding of path-dependent risk measurement, provide a firm basis for further research in this area, and substantiate the application of drawdown measures in practice.
Keywords: Risk Measures; Risk Measurement; Drawdown; Drawdown Risk Measures; Asset Management; Performance Measurement; Regret; Exponential Lévy Processes; Risk Persistence
 
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