Consistency of Risk Measure Estimates

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not quantify the risk beyond VaR, while CVaR shows some computational instabilities and is not 'elicitable' (Gneiting 2010, Ziegel 2013). It is argued in this paper that such questions are best addressed from the point of view of probability forecasting or Dawid's 'prequential statistics.' We introduce a concept of 'consistency' of a risk measure, which is close to Dawid's 'strong prequential principle,' and show that VaR indeed has special properties not shared by any other risk measure.

[1]  T. Gneiting.  Making and Evaluating Point Forecasts , 2009, 0912.0902.

[2]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[3]  Xianhua Peng,et al.  The Fundamental Review of the Trading Book , 2013 .

[4]  A. P. Dawid,et al.  Present position and potential developments: some personal views , 1984 .

[5]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[6]  A. Dawid,et al.  Prequential probability: principles and properties , 1999 .

[7]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[8]  B. Mandelbrot.  Fractals and Scaling In Finance: Discontinuity, Concentration, Risk , 2010 .

[9]  Romain Deguest,et al.  Robustness and sensitivity analysis of risk measurement procedures , 2008 .

[10]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[11]  Dudley,et al.  Real Analysis and Probability: Integration , 2002 .

[12]  G. Gripenberg,et al.  On the prediction of fractional Brownian motion , 1996, Journal of Applied Probability.

[13]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[14]  Howard M. Taylor,et al.  On the Distribution of Stock Price Differences , 1967, Oper. Res..

[15]  James S. Kennedy,et al.  EVALUATING PROBABILITY FORECASTS. , 1969 .

[16]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[17]  Gary James Jason,et al.  The Logic of Scientific Discovery , 1988 .

[18]  P. Embrechts,et al.  Statistics and Quantitative Risk Management for Banking and Insurance , 2014 .

[19]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[20]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[21]  Johanna F. Ziegel,et al.  COHERENCE AND ELICITABILITY , 2013, 1303.1690.

[22]  Marc S. Paolella,et al.  Value-at-Risk Prediction: A Comparison of Alternative Strategies , 2005 .

[23]  M A H Dempster,et al.  An automated FX trading system using adaptive reinforcement learning , 2006, Expert Syst. Appl..

[24]  L. J. Savage.  Elicitation of Personal Probabilities and Expectations , 1971 .

[25]  Rama Cont,et al.  Robustness and sensitivity analysis of risk measurement procedures , 2010 .

[26]  Stefan Reichelstein,et al.  Information-eliciting compensation schemes , 1985 .

[27]  R. Cont.  Empirical properties of asset returns: stylized facts and statistical issues , 2001 .