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Portfolio Risk Measures: The Time’s Arrow Matters

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The traditional ex post risk measure associated to a portfolio, a fund or a market performance, is the standard deviation of a series of past returns, called volatility. We propose an alternative risk measure, that turns out to better quantify the risk actually supported by an investor or asset manager with respect to a portfolio or a fund. This alternative measure is computed from the actual dispersion of successive cumulated returns relative to the corresponding successive cumulated returns produced by an accrued performance of null volatility, which better reflects the dynamics of the risk-return relationship over time. Hence, the proposed name of “accrued returns variability”, for such a risk measure that incorporates the passage of time. Applications are presented, to enlighten the advantage of this risk measure.

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  • Acar, E., & James, S. (1997). Maximum loss and maximum drawdown in financial markets. In Proceedings of International Conference on Forecasting Financial Markets. London: ICFFM.

  • Artzner P., Delbaen F., Eber J. -M., Heath D. (1999) Coherent measure of risk. Mathematical Finance 9: 203–228

    Article  Google Scholar 

  • Bacon C. R. (2008) Practical portfolio performance measurement and attribution, 2nd ed. Wiley, New York

    Google Scholar 

  • Lo A. (2002) The statistics of sharpe ratios. Financial Analysts Journal 58(4): 36–45

    Article  Google Scholar 

  • Ortobelli, S., Rachev, S., Shalit, H., Fabozzi, F. J. (2008). Practical portfolio selection problems consistent with a given preference ordering. Management Sciences, 52(9), 1409–1423.

    Google Scholar 

  • Ortobelli S., Rachev S., Shalit H., Fabozzi J. F. (2009) Orderings and probability functional consistent with preferences. Applied Mathematical Finance 16(1): 81–106

    Article  Google Scholar 

  • Rachev, S., Ortobelli, S., Stoyanov, S., Fabozzi, F. J., Biglova, A. (2008). Desirable properties of an ideal risk measure in portfolio theory. International Journal of Theoretical and Applied Finance, 11, 447–469.

    Article  Google Scholar 

  • Rachev S., Stoyanov S., Fabozzi F. J. (2011) A probability metrics aproach to financial risk measures. Wiley, London

    Book  Google Scholar 

  • Ruttiens, A. (2011). New performance measurement methods and how the time’s arrow matters. Working paper presented at the J.P. Morgan Cazenove Equity Quantitative Conference, London.

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Correspondence to Alain Ruttiens.

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Ruttiens, A. Portfolio Risk Measures: The Time’s Arrow Matters. Comput Econ 41, 407–424 (2013).

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  • Market risk measure
  • Variability
  • Volatility