Extreme Risk Measures for International REIT Markets


Extreme risks associated with extraordinary market conditions are catastrophic for all investors. The ongoing financial crisis has perfectly exemplified this point. Surprisingly, there are few studies exploring this issue for REITs. This study aims to close the knowledge gap. We conduct a comprehensive study by utilizing all three methodological categories to examine their forecasting performances of VaR and ES for nine major global REIT markets. Our findings indicate that there is no universally adequate method to model extreme risks across global markets. Also, estimating risks for the stock and REIT markets may require different methods. In addition, we compare the risk profiles between the stock and REIT markets, and find that the extreme risks for REITs are generally higher than those of stock markets. The fluctuations of risk levels are well synchronized between the two types of markets. The current crisis has significantly increased the extreme risk exposure for both REIT and stock investors. In all, our results have significant implications for REIT risk management, portfolio selection, and evaluation.

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  1. 1.

    We are grateful for an anonymous referee for suggesting to include more countries.

  2. 2.

    Our focus on day-ahead forecast is consistent with the holding period considered for internal risk control by most financial firms. To generate multiple-day risk forecasts, some complicated simulation techniques are needed. This issue is better suited for a follow-up study which is currently being conducted by the authors. However, there do exist some simple ways to make multiple-day forecasts. For instance, the simple scaling method assumes that \( VaR_p^t(h) = VaR_p^t{h^\lambda } \), where \( VaR_p^t(h) \)is the h-day forecast of VaR, \( VaR_p^t \) is the 1-day forecast, and λ is a scaling exponent. However, the validity of this method has been hotly debated in the literature. See Danielsson and de Vries (1997), Diebold et al. (1998) and McNeil and Frey (2000).

  3. 3.

    We thank an anonymous referee for the suggestion of considering the GED distribution.

  4. 4.

    This is defined for the quantiles on the left tail (1% & 5%). For those (95% & 99%) on the right tail, the hit sequence is defined as \( {I_{t + 1}} = \left\{ \begin{gathered} 1,\mathop {}\nolimits if\mathop {}\nolimits {x_{t + 1}} > VaR_p^t \hfill \\0,\mathop {}\nolimits if\mathop {}\nolimits {x_{t + 1}} < VaR_p^t \hfill \\\end{gathered} \right. \).

  5. 5.

    To preserve space, the plots of 1% and 99% VaR forecasts are not presented here but are available upon request.

  6. 6.

    In this table, we choose 07/01/2009 as the cut-off date between the pre-crisis and during-crisis periods. Even though the choice of this date seems arbitrary, it has some merits because moving the cut-off date backwards and forwards several months does not significantly change our results.


  1. Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1997). Thinking coherently. Risk, 10, 68–71.

    Google Scholar 

  2. Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1999). Coherent measures of risks. Mathematical Finance, 9, 203–28.

    Article  Google Scholar 

  3. Bao, Y., Lee, T.-H., & Saltoglu, B. (2006). Evaluating predictive performance of Value-at-Risk models in emerging markets: a reality check. Journal of Forecasting, 25, 101–28.

    Article  Google Scholar 

  4. Balkema, A. A., & de Haan, L. (1974). Residual lifetime at great age. Annals of Probability, 2, 792–804.

    Article  Google Scholar 

  5. Barone-Adesi, G., Giannopoulos, K., & Vosper, L. (1999). VaR without correlations for portfolios of derivative securities. Journal of Futures Markets, 19, 583–602.

    Article  Google Scholar 

  6. Barone-Adesi, G., Giannopoulos, K., & Vosper, L. (2002). Backtesting derivative portfolios with filtered historical simulation(FHS). European Financial Management, 8, 31–58.

    Article  Google Scholar 

  7. Basle Committee on Banking Supervision. (1996) Overview of the Amendment to the Capital Accord to Incorporate Market Risks, available at http://www.bis.org.

  8. Christofferson, P. (1998). Evaluating Internal Forecasts. International Economic Review, 39, 841–62.

    Article  Google Scholar 

  9. Christofferson, P. (2003). Elements of Financial Risk Management. San Diego: Academic Press.

    Google Scholar 

  10. Danielsson, J., & de Vries, C. (1997). Tail index and quantile estimation with very high frequency data. Journal of Empirical Finance, 4, 241–57.

    Article  Google Scholar 

  11. Diebold, F., Schuermann, T., Hickmann, A., & Inoue, A. (1998). Scale models. Risk, 11, 104–07.

    Google Scholar 

  12. Efron, B., & Tibshirani, J. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.

    Google Scholar 

  13. Gilli, M., & Kellezi, E. (2006). An application of extreme value theory for measuring financial risk. Computational Economics, 27, 207–28.

    Article  Google Scholar 

  14. Hendricks, D. (1996) Evaluation of value-at-risk models using historical data, Economic Policy Review, Federal Reserve Bank of New York, April, 39–69

  15. Hull, J., & White, A. (1998). Incorporating volatility updating into the historical simulation method for VaR. Journal of Risk, 1, 5–19.

    Google Scholar 

  16. Kuester, K., Mittnik, S., & Paolella, M. (2006). Value-at-Risk prediction: a comparison of alternative strategies. Journal of Financial Econometrics, 4, 53–89.

    Article  Google Scholar 

  17. Kupiec, P. (1995). Techniques for verifying the accuracy of risk management models. Journal of Derivatives, 3, 73–84.

    Article  Google Scholar 

  18. Liow, K. H. (2008). Extreme returns and value-at-risk in international securitized real estate markets. Journal of Property Investment & Finance, 26, 418–46.

    Article  Google Scholar 

  19. Longin, F. (2000). From value-at-risk to stress testing: the extreme value approach. Journal of Banking and Finance, 24, 1097–1130.

    Article  Google Scholar 

  20. Lu, C., Wu, S. C., & Ho, L. C. (2009). Applying VaR to REITs: a comparison of alternative methods. Review of Financial Economics, 18, 97–102.

    Article  Google Scholar 

  21. Manganelli, S., and R.F. Engle. (2004) A comparison of Value-at-Risk models in finance, in Risk Measures for the 21 st Century (Ed.) G. Szegö, Chichester, UK: Wiley, pp. 123–44.

  22. McNeil, A. J., & Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, 7, 271–300.

    Article  Google Scholar 

  23. Neftci, S. N. (2000). Value at Risk Calculations. Extreme Events, and Tail Estimation, Journal of Derivatives, 7, 23–38.

    Google Scholar 

  24. Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–31.

    Article  Google Scholar 

  25. Poon, S., & Granger, C. W. (2003). Forecasting volatility in rinancial markets: a review. Journal of Economic Literature, 41, 478–539.

    Article  Google Scholar 

  26. Pritsker, M. (2001). The hidden dangers of historical simulation, Finance and Economics Discussion Series 27. Washington, D.C: Board of Governors of the Federal Reserve System.

    Google Scholar 

  27. Taylor, J. W. (2008). Estimating Value at Risk and Expected Shortfall using expectiles. Journal of Financial Econometrics, 6, 232–52.

    Article  Google Scholar 

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We thank the Editor and anonymous referee for their valuable comments and suggestions. We also thank Joshua Harris and Matthew Hurst for their research assistance. All errors remain our own.

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Correspondence to Jian Zhou.

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Zhou, J., Anderson, R.I. Extreme Risk Measures for International REIT Markets. J Real Estate Finan Econ 45, 152–170 (2012). https://doi.org/10.1007/s11146-010-9252-5

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  • Value-at-Risk
  • Expected shortfall
  • Extreme risks
  • Financial crisis
  • REITs