Measurement errors in stock markets

Abstract

This paper points to further measurement errors in stock markets. In particular, we show that the application of usual performance ratios to evaluate financial assets can lead to inappropriate findings and consequently wrong conclusions. To this end, we analyze standard performance ratios as well as extreme loss-based financial ratios and compare the conclusions with those provided by systemic risk measures. The application of these different measures to both conventional and Islamic stock indexes for developed and emerging countries in the context of the financial crisis yields two interesting results. First, the analysis of financial performance exhibits further measurement errors. Second, the consideration of extreme loss and systemic risk in computing performance measures increases the reliability of performance analysis.

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Notes

  1. 1.

    For more details, see Fuller (1987), Caroll, Ruppert and Stefanski (1995), Hausman (2001), etc.

  2. 2.

    See Barnett (2015) for an excellent comparative analysis between Rocket Science and Economics Science.

  3. 3.

    See Cheng et al. (2011) for a survey of the treatment of classical and non-classical measurement errors. Blackwell et al. (2015) also focused on the treatment of measurement errors and developed a unified approach to deal with missing data problems and to limit measurement errors.

  4. 4.

    See Chen et al. (2011) for a recent survey on Nonlinear Models of Measurement Errors.

  5. 5.

    http://sem.society.cmu.edu/home.html.

  6. 6.

    Performance is often defined and measured through a risk-adjusted return. The most widely known performance measure is given by the ratio of Sharpe (1966).

  7. 7.

    To our knowledge, this is the first paper on the topic.

  8. 8.

    Sharpe ratio, Treynor ratio, Jensen alpha, Omega ratio, Sortino ratio, Kappa 3, the upside potential ratio, Calmar ratio, Sterling ratio, Burke ratio, the excess return on Value at Risk, the conditional Sharpe ratio and the modified Sharpe ratio.

  9. 9.

    Treynor ratio requires also implicitly normality distribution for stock returns as it is also based on first two moments. The main difference with Sharpe ratio is that it involves the systematic risk instead of the intrinsic risk.

  10. 10.

    In the literature, the parametric and non-parametric approaches can be used to estimate the Value-at-Risk model. We identified three main methods: variance–covariance approach, historical simulation and Monte Carlo simulation. The first is a parametric method based on the normality assumption of the distribution of the market parameters and index. The second, non-parametric method is the easiest approach as only historical data are used to determine the VaR for the market and the index. The third is also a non-parametric method that requires two steps. In the first step, the volatilities and correlation parameters are calibrated using the historical data. In the second step, simulation of the stochastic processes is used to establish the return distribution, and the VaR can then be determined from this distribution.

  11. 11.

    The results of the unit root tests are not reported but are available upon request.

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Correspondence to Hachmi Ben Ameur.

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Ben Ameur, H., Jawadi, F., Idi Cheffou, A. et al. Measurement errors in stock markets. Ann Oper Res 262, 287–306 (2018). https://doi.org/10.1007/s10479-016-2138-z

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Keywords

  • Measurement error
  • Financial performance
  • Systemic risk
  • Var
  • CoVaR and MES

JEL Classification

  • C2
  • C5
  • G10