The limits of diversification when losses may be large
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.
|Date of creation:||2007|
|Date of revision:|
|Publication status:||Published in Journal of Banking and Finance|
|Contact details of provider:|| Postal: Littauer Center, Cambridge, MA 02138|
Web page: http://www.economics.harvard.edu/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cotter, JOhn & Dowd, Kevin, 2006.
"Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements,"
3505, University Library of Munich, Germany.
- 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.
- John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Working Papers 200516, Geary Institute, University College Dublin.
- John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Papers 1103.5653, arXiv.org.
- Rustam Ibragimov, 2005. "On Efficiency of Linear Estimators Under Heavy-Tailedness," Harvard Institute of Economic Research Working Papers 2085, Harvard - Institute of Economic Research.
- 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 244-80, April.
- 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.
- Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- 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.
- 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.
- Kahneman, Daniel & Tversky, Amos, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Econometric Society, vol. 47(2), pages 263-91, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- 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.
- 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.
- 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.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Joseph E. Stiglitz, 1974.
"Incentives and Risk Sharing in Sharecropping,"
Review of Economic Studies,
Oxford University Press, vol. 41(2), pages 219-255.
- Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
- Loretan, M. & Phillips, P.C.B., 1992.
"Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets,"
9208, Wisconsin Madison - Social Systems.
- 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.
- Kenneth A. Froot, 2001.
"The Market for Catastrophe Risk: A Clinical Examination,"
NBER Working Papers
8110, National Bureau of Economic Research, Inc.
- 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.
- Kenneth A. Froot, 1999. "The Market for Catastrophe Risk: A Clinical Examination," NBER Working Papers 7286, National Bureau of Economic Research, Inc.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- 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.
- 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.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
- Donald W.K. Andrews, 2004.
"Cross-section Regression with Common Shocks,"
Yale School of Management Working Papers
ysm401, Yale School of Management.
- 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.
When requesting a correction, please mention this item's handle: RePEc:hrv:faseco:2624460. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Office for Scholarly Communication)
If references are entirely missing, you can add them using this form.