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The limits of diversification when losses may be large

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  • Ibragimov, Rustam
  • Walden, Johan

Abstract

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that generally it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar non-diversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in markets for risky assets where the number of assets is limited compared with the (bounded) distribution support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

Suggested Citation

  • Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:2624460
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    1. Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
    2. Joseph E. Stiglitz, 1974. "Incentives and Risk Sharing in Sharecropping," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(2), pages 219-255.
    3. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, vol. 139(2), pages 318-339, August.
    4. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    7. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    8. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    10. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    11. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    12. Rustam Ibragimov, 2005. "On Efficiency of Linear Estimators Under Heavy-Tailedness," Harvard Institute of Economic Research Working Papers 2085, Harvard - Institute of Economic Research.
    13. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
    14. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
    15. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    16. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    17. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
    18. Stiglitz, Joseph E & Weiss, Andrew, 1981. "Credit Rationing in Markets with Imperfect Information," American Economic Review, American Economic Association, vol. 71(3), pages 393-410, June.
    19. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    20. Rustam Ibragimov & Johan Walden, 2006. "The Limits of Diversification When Losses May Be Large," Harvard Institute of Economic Research Working Papers 2104, Harvard - Institute of Economic Research.
    21. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    22. F. M. Scherer & Dietmar Harhoff & J, rg Kukies, 2000. "Uncertainty and the size distribution of rewards from innovation," Journal of Evolutionary Economics, Springer, vol. 10(1), pages 175-200.
    23. Brad M. Barber & Terrance Odean, 2000. "Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors," Journal of Finance, American Finance Association, vol. 55(2), pages 773-806, April.
    24. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    25. Blume, Marshall E & Friend, Irwin, 1975. "The Asset Structure of Individual Portfolios and Some Implications for Utility Functions," Journal of Finance, American Finance Association, vol. 30(2), pages 585-603, May.
    26. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    27. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    28. Rustam Ibragimov, 2005. "Portfolio Diversification and Value at Risk Under Thick-Tailedness," Harvard Institute of Economic Research Working Papers 2086, Harvard - Institute of Economic Research.
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