Measurement errors in stock markets


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.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3


  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.

  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.


  1. Acharya, V. V., Pedersen, L. H., Philippon, T., Richardson, M. P. (2010). Measuring systemic risk. SSRN:

  2. Adrian, T., & Brunnermeier, M. (2011) . CoVaR, Working Paper, National Bureau of Statistics.

  3. Almeida, H., Campello, M., & Galvao, A. F. (2010). Measurement errors in investment equations. The Review of Financial Studies, 23(9), 3279–3328.

    Article  Google Scholar 

  4. Arztner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 3, 203–228.

    Google Scholar 

  5. Barnett, W. A. (2012). Getting it wrong: how faulty monetary statistics undermine the fed, the financial system, and the economy. Cambridge: MIT Press.

    Google Scholar 

  6. Barnett, W. A. (2015). Collaboration with or without coauthorship: Rocket science versus economic science. In M. Szenberg & L. Ramrattan (Eds.), Intellectual collaborative experiences. Cambridge: Cambridge University Press.

    Google Scholar 

  7. Barnett, W. A., & Chauvet, M. (2011). How better monetary statistics could have signaled the financial crisis. Journal of Econometrics, 161(1), 6–23.

    Article  Google Scholar 

  8. Barnett, W. A., Chauvet, M., & Tierney, H. L. R. (2009). Measurement error in monetary aggregates: a markov switching factor approach. Macroeconomic Dynamics, 13(S2), 381–412.

    Article  Google Scholar 

  9. Ben Ameur, H., Idi Cheffou, K., Jawadi, F., & Louhichi, W. (2015). Modeling beta changes with three regime threshold market model, Working Paper presented at the 9th CFE conference, London, December 12–14, 2015.

  10. Biglova, A., Ortobelli, S., Rachev, S. T., & Stoyanov, S. (2004). Different approaches to risk estimation in portfolio theory. Journal of Portfolio Management, 31, 103–112.

    Article  Google Scholar 

  11. Blackwell, M., Honaker, J., & King, G. (2015). A unified approach to measurement error and missing data: Overview. Sociological Methods & Research.

  12. Brownlees, C. T., & Engle, R. F. (2010). Volatility, correlation and tails for systemic risk measurement. SSRN:

  13. Carroll, R., Ruppert, J., & Stefanski, L. A. (1995). Measurement error in nonlinear models: A modern perspective. London: Chapman and Hall.

    Google Scholar 

  14. Chang, C. C., Chen, S. S., Chou, R. K., & Hsin, C. W. (2011). Intraday return spillovers and its variations across trading sessions. Review of Quantitative Finance and Accounting, 36, 355–390.

    Article  Google Scholar 

  15. Chen, X., Hong, H., & Nekipelov, D. (2011). Nonlinear models of measurement errors. Journal of Economic Literature, 49(4), 901–937.

    Article  Google Scholar 

  16. Darolles, S., Gouriéroux, C., & Jasiak, J. (2009). L-performance with an application to hedge funds. Journal of Empirical Finance, 16(4), 671–685.

    Article  Google Scholar 

  17. Dowd, K. (2000). Adjusting for risk: An improved sharpe ratio. International review of Economics and Finance, 9(3), 209–222.

    Article  Google Scholar 

  18. Drerup, T., Enke, B., & Von Gaudecker, H. M. (2014). Measurement error in subjective expectations and the empirical content of economic models. Netspar Discussion Paper No. 10/2014-043.

  19. Eling, M., & Schuhmacher, F. (2007). Does the choice of performance measure influence the evaluation of hedge fund? Journal of Banking and Finance, 31(9), 2632–2647.

    Article  Google Scholar 

  20. Fuller, W. (1987). Measurement Error Models. New York: Wiley.

    Google Scholar 

  21. Graham, J., & Harvey, C. (1994). Market timing ability and volatility implied in investment newsletters’ asset allocation recommendations. Unpublished working paper, National Bureau of Economic Research, Cambridge, MA.

  22. Graham, J. R., & Harvey, C. R. (1996). Market timing ability and volatility implied in investment newsletters’ asset allocation recommendations. Journal of Financial Economics, 42, 397–422.

    Article  Google Scholar 

  23. Hausman, J. (2001). Mismeasured variables in econometric analysis: problems from the right and problems from the left. The Journal of Economic Perspectives, 15, 57–67.

    Article  Google Scholar 

  24. Keating, C., & Shadwick, W. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.

    Google Scholar 

  25. Martin, D., Rachev, S., & Siboulet, F. (2003). Phi-alpha optimal portfolios and extreme risk management, Wilmott Magazine of Finance, November/2003, pp. 70–83.

  26. Modigliani, F., & Modigliani, L. (1997). Risk-adjusted performance. Journal of Portfolio Management, 23(2), 45–54.

    Article  Google Scholar 

  27. Pflug, G. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. In S. Uryasev (Ed.), Probabilistic constrained optimization: methodology and applications. Berlin: Kluwer Academic Publishers.

    Google Scholar 

  28. Scaillet, O. (2005). Nonparametric estimation of conditional expected shortfall. Insurance and Risk Management Journal, 74, 639–660.

    Google Scholar 

  29. Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119–138.

    Article  Google Scholar 

  30. Taylor, J. R. (1999). An introduction to error analysis: The study of uncertainties in physical measurements. Sausalito: University Science Books.

    Google Scholar 

  31. Treynor, J. (1965). How to rate management of investment funds. Harvard Business Review, 43(1), 63–75.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Hachmi Ben Ameur.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ben Ameur, H., Jawadi, F., Idi Cheffou, A. et al. Measurement errors in stock markets. Ann Oper Res 262, 287–306 (2018).

Download citation


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

JEL Classification

  • C2
  • C5
  • G10