Vergleichsanalyse von verschiedenen Ansätzen zur Risikoschätzung in der Portfoliotheorie

• Applicant: Professor Dr. Svetlozar T. Rachev
• Subject Area: Statistics and Econometrics
• Term: from 2004 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5436949

• Final Report Year: 2008

Final Report Abstract

The results of the evaluation of the reward-risk criteria based on the cumulative realized profit, Sharpe measure (i.e., we use this term in the context of strategy evaluation), and independent performance measure. For portfolios formed with the 6 month/6 month strategy, the best performance value of 0.0218 on the independent performance measure is obtained for the R-ratio(99%,99%). The next two best values of 0.0187 and 0.0155 are obtained by the R-ratio( 91%,91%) and R-ratio(95%,95%), respectively. The cumulative return criterion obtains the fourth highest value of 0.01398 and the Sharpe ratio obtains the fourth lowest value of 0.0139. These results imply that the Sharpe ratio as the risk-adjusted criterion for a given set of data is not providing an optimal risk-adjusted performance. The risk adjusted performance of the best R-ratio is approximately 150% times better than that of the cumulative return criterion and almost three times better than that of the Sharpe ratio. To summarize, although the cumulative return criterion obtains the largest cumulative profits, the alternative R-ratios obtain the best risk-adjusted performance based on the applied independent performance measure. If we use the independent riskadjusted performance measure in the form of the STARR ratio with different significance levels of the parameter, the results on the ranking of the criteria may change, reflecting different risk-return objectives and levels of risk-aversion of the investor. With the financial support of the DFG project RA 861/2, we proposed a risk measure based on the alpha-stable distribution. With the help of this risk measure, we proposed a method for portfolio selection. Empirical result shows that our methods have superior performance. We also proposed the Bayesian methods in the process of investment management. We published our results in twelve referred journals and two handbooks. Based on our results, we organized them with a systematic way in four monographs.

Publications

• Chernobai, A., C. Menn, S. Rachev, S. Trück, M. Moscadelli (2006). Treatment of Incomplete Data in the Field of Operational Risk: The Effects on Parameter Estimates, EL and UL Figures, in: E. Davis (ed), The Advanced Measurement Approach to Operational Risk, Risk Books, London, 145-168.
  
  
• Bertocchi, M., R. Giacometti, S. Ortobelli, S. Rachev (2005). The impact of different distributional hypothesis on returns in asset allocation, Finance Letters, 3(1), 17-27.
  
  
• Biglova A., S. Rachev (2007). Portfolio Performance Attribution, Investment Management and Financial Innovations, 4/3, 7-22.
  
  
• Biglova, A., S. Ortobelli, S. Rachev, S. Stoyanov (2004). Comparison among different approaches for risk estimation in portfolio theory, Journal of Portfolio Management 13(1):103-112.
  
  
• Bol, G., S. Rachev, R. Wuerth (2007). Risk Assessment: Decisions in Banking and Finance(eds.), Physika Verlag, Springer.
  
  
• Chernobai, A., K. Burnecki, S. Rachev, S. Tr¨uck, R. Weron (2006). Modeling Catstrophe Claims with Left-Truncated Severity Distribution, omputational Statistics, 21 , 537-555.
  
  
• Chernobai, A., S. Rachev (2006). Applying robust methods to operational risk modeling, Journal of Operational Risk, 1(1), 27-42.
  
  
• Hoechstoetter, M., S. Rachev, F. Fabozzi (2005). Distributional Analysis of the Stocks Comprising the DAX 30, Probability and Mathematical Statistics, 25(2), 363-383.
  
  
• Klebanov, L., T. Kozubowski, S. Rachev (2006). Ill-Posed Problems in Probability and Stability of Random Sums, Nova Science Publishers, New York.
  
  
• Lamantia F., S. Ortobelli, S. Rachev (2006). An Empirical Comparison among VaR Models and Time Rules with Elliptical and Stable Distributed Returns, Investment Management and Financial Innovations 3, 8-29.
  
  
• Lamantia F., S. Ortobelli, S. Rachev (2006). VaR, CVaR and Time Rules with Elliptical and Asymmetric Stable Distributed Returns, Investment Management and Financial Innovations 4, 19-39.
  
  
• Menn, C., S. Rachev (2005). A GARCH Option Pricing Model with a-Stable Innovations, European Journal of Operations Research, 163(1), 201-209.
  
  
• Ortobelli, S., S. Rachev, S. Stoyanov, F. Fabozzi, A. Biglova (2005) The proper use of risk measures in portfolio theory, International Journal of Theoretical and Applied Finance, 8( 8 ), 1107-1133.
  
  
• Rachev, S., J. Hsu, B. Bagasheva, F. Fabozzi (2007). Bayesian Methods in Finance, John Wiley.
  
  
• Rachev, S., S. Stoyanov, C. Wu, F. Fabozzi (2007). Empirical Analyses of Industry Stock Index Return Distributions for the Taiwan Stock Exchange, Annals of Economics and Finance, 1, 21-31.
  
  
• Rachev, S., S. Stoyanov, F. Fabozzi (2007) Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures, John Wiley.
  
  
• Stoyanov, S., G. Samorodnitsky, S. Rachev, S. Ortobelli (2006). Computing the portfolio Conditional Value-at-Risk in the a-stable case. Probability and Mathematical Statistics 26, 1-22.