Risk and performance measures are objective methods to quantify the risk or performance of a financial portfolio or entire company. Ongoing from the quantile-based Value-at-Risk (VaR) the theory has developed fast over the last decade. Comprehensive methods like coherent measures (Expected Shortfall) have been invented. The main goal of risk capital allocation is the fair determination of risk contributions of single positions in a portfolio.

Members of the Approximity team contributed to the following publications:

  • Risk and performance optimization for portfolios of bonds and stocks Download
    Fischer, T., Roehrl, A.
    working paper
    We explain how to optimize portfolios of bonds and stocks with respect to the Expected Shortfall (ES), respectively RORC or RORAC based on ES. In a pragmatic approach we combine and correlate a stock market model with geometric brownian motions with a two-factor Cox-Ingersoll-Ross (CIR-2) model for the interest rates/bonds. We use recent results from the theory of risk capital allocation, performance measurement and Swarm Intelligence for optimization. Examples for German market data as well as an analysis of the scalability of the solution to assure fast run-times on clusters of computers for large real-life portfolios are given.
    Approximity sells the accompanying software.
    Online html-version
  • A statistical analysis of the shareprice of the SAIR group (1996-2001) from a risk manager's point of view. Download
    Chavez-Demoulin, V., Embrechts, P., Roehrl, A.
    Derivatives Use, Trading & Regulation, Volume 8, 2/2002
    Over the recent years, Extreme Value Theory (EVT) has been used in order to statistically analyse financial data showing clear non-normal behaviour. Several examples coming from market, credit and operational risk have been discussed. In the present paper we look at the particular case of Swissair and quantify, using EVT, the extremal behaviour of the returns. For this, we go beyond the traditional EVT and introduce new methodology such as smoothing and more advanced maximum likelihood techniques.
  • Risk Capital Allocation by Coherent Risk Measures Based on One-Sided Moments. Download
    Tom Fischer
    Insurance: Mathematics and Economics 32 (1), 135-146
  • Kohärente Risikomaße und ihre Anwendung in Versicherungsunternehmen Download
    Tom Fischer
    47. Tagung der ASTIN-Gruppe der Deutschen Aktuarvereinigung e.V. (DAV), Freitag, 15. November 2002, Hamburg
    (talk)
  • Risk Capital Allocation by Coherent Risk Measures Based on One-Sided MomentsDownload
    Tom Fischer
    6th Conference of the Swiss Society for Financial Market Research, Zürich/Rüschlikon, SwissRe Centre for Global Dialogue, April 4, 2003
    (talk)
  • Examples of Coherent Risk Measures Depending on One-Sided Moments Download
    Tom Fischer
    working paper
    We give examples of coherent risk measures that depend on the mean and the one-sided moments of a risky position. Upper boundaries of default probabilities can be obtained by the one-sided Chebyshev inequality. By recurrence, we define a special class of coherent risk measures that features discrete degrees of attitude towards risk, converging to the maximum loss. An example shows, how these risk measures can be used for insurance purposes.

risk/performance specialists

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