Tid: 18 september 2006 kl 16.15-17.00
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Eric Karlsson
Titel: Non-Parametric Scenario Simulation and Portfolio Risk Management (Examensarbete)
Sammanfattning: The need for efficient simulation methods exists in many areas of the financial services industry, for example when training investors, testing investment strategies, and managing risk. This thesis presents a technique for non-parametric scenario generation that requires no subjective opinions on the properties of the assets in a portfolio. The technique used is based on Moving Block Bootstrap (MBB), using a block length optimized by applying Higher Order Crossings (HOC) characterization of financial time series. The technique creates realistic scenarios with preserved autocorrelation structures and the first four moments (mean, volatility, skewness and kurtosis) matched to a very satisfying degree. Furthermore, it goes beyond preceding works in the area by extending the method to full preservation of the cross-market correlation structures by introducing a global optimal block length for a specific set of financial assets. The technique can generate hundreds of thousands of scenarios with good output variation and desirable properties such as stretching of the loss tail, in just a few seconds.
The second part of this thesis brings the MBB method above into use in the field of portfolio risk management. Quantitative portfolio management is often based on mean-variance analysis, a method assuming Gaussian returns and failing due to non-linear, asymmetric return distributions. The most widely used risk measure Value-at-Risk (VaR) focuses on the frequency of large losses, but does not say anything about the size of these losses. This thesis uses a Conditional Value-at-Risk (CVaR) based approach to assess portfolio risk management. It shows how CVaR constraints can be used to optimize portfolios over a large number of scenarios, for example created using the MBB simulation technique presented in part one. It is shown how CVaR can be implemented as a set of linear constraints and used in conjunction with volatility constraints to optimize portfolios for different risk and confidence levels. Furthermore, the model allows for easy addition of preferred demands on portfolio composition and trading restrictions, as well as allowing the user to run the model with proprietary models for return forecasting.