Portfolio diversification under local and moderate deviations from power laws

Insurance: Mathematics and Economics

Volumn 42, Issue 2, 2008, Pages 594-599

  Ibragimov, Rustam ^a   Walden, Johan ^b  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Diversification; Domain of attraction of stable distributions; Heavy tailed risks; Local and moderate deviations; Nonlinear transformations; Pareto type distributions; Portfolios; Power laws; Risk bounds; Riskiness; Value at risk

Indexed keywords

EID: 41049109342     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2007.06.006     Document Type: Article

References (31)

1. An M.Y. Logconcavity versus logconvexity: A complete characterization. Journal of Economic Theory 80 (1998) 350-369
2. Birnbaum Z.W. On random variables with comparable peakedness. Annals of Mathematical Statistics 19 (1948) 76-81
3. Dharmadhikari S.W., and Joag-Dev K. Unimodality, Convexity and Applications (1988), Academic Press, Boston
4. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events for Insurance and Finance (1997), Springer, New York
5. Fama E.F. Portfolio analysis in a stable Paretian market. Management Science 11 (1965) 404-419
6. Fama E.F. The behavior of stock market prices. Journal of Business 38 (1965) 34-105
7. Gabaix X., Gopikrishnan P., Plerou V., and Stanley H.E. A theory of power-law distributions in financial market fluctuations. Nature 423 (2003) 267-270
8. Ibragimov, R., 2004a. On the robustness of economic models to heavy-tailedness assumptions. Mimeo, Yale University. Available at: http://post.economics.harvard.edu/faculty/ibragimov/Papers/HeavyTails.pd f
9. Ibragimov, R., 2004b. Portfolio diversification and value at risk under thick-tailedness. Harvard University Research Discussion Paper 2086. Available at: http://post.economics.harvard.edu/hier/2005papers/HIER2086.pdf
10. Ibragimov, R., 2005. New majorization theory in economics and martingale convergence results in econometrics. Ph.D. Dissertation. Yale University
11. Ibragimov R., and Walden J. The limits of diversification when losses may be large. Journal of Banking and Finance 31 (2007) 2551-2569 10.1016/j.jbankfin.2006.11.014. Also available as Harvard Institute of Economic Research Discussion Paper No. 2104. http://www.economics.harvard.edu/hier/2006papers/HIER2104.pdf.
12. Jansen D.W., de Vries, and C.G. On the frequency of large stock returns: Putting booms and busts into perspective. Review of Economics and Statistics 73 (1991) 18-32
13. Kaas R., Goovaerts M., and Tang Q. Some useful counterexamples regarding comonotonicity. Belgian Actuarial Bulletin 4 (2004) 1-4
14. Loretan M., and Phillips P.C.B. Testing the covariance stationarity of heavy-tailed time series. Journal of Empirical Finance 1 (1994) 211-248
15. Malevergne Y., and Sornette D. VaR-efficient portfolios for a class of super- and sub-exponentially decaying assets return distributions. Quantitative Finance 4 (2003) 17-36
16. Malevergne Y., and Sornette D. High-order moments and cumulants of multivariate Weibull asset returns distributions: Analytical theory and empirical tests: II. Finance Letters 3 (2004) 54-63
17. Malevergne Y., and Sornette D. Multivariate Weibull distributions for asset returns: I. Finance Letters 2 (2004) 16-32
18. Mandelbrot B. The variation of certain speculative prices. Journal of Business 36 (1963) 394-419
19. McCulloch J.H. Measuring tail thickness to estimate the stable index alpha: A critique. Journal of Business and Economic Statistics 15 (1997) 74-81
20. Nešlehova J., Embrechts P., and Chavez-Demoulin V. Infinite mean models and the LDA for operational risk. Journal of Operational Risk 1 (2006) 3-25
21. Phillips P.C.B. Regression theory for near-integrated time series. Econometrica 56 (1988) 1021-1043
22. Phillips, P.C.B., Magdalinos, T., 2004. Limit theory for moderate deviations from a unit root. Cowles Foundation Discussion Paper 1471. Available at: http://cowles.econ.yale.edu/P/cd/d14b/d1471.pdf
23. Proschan F. Peakedness of distributions of convex combinations. Annals of Mathematical Statistics 36 (1965) 1703-1706
24. Rachev S.T., Menn C., and Fabozzi F.J. Fat-tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection, and Option Pricing (2005), Wiley, Hoboken, NJ
25. Rachev S.T., and Mittnik S. Stable Paretian Models in Finance (2000), Wiley, New York
26. Ross, S.A., 1976. A note on a paradox in portfolio theory. Working paper, University of Pennsylvania
27. Samuelson P.A. Efficient portfolio selection for Pareto-Lévy investments. Journal of Financial and Quantitative Analysis 2 (1967) 107-122
28. Scherer F.M., Harhoff D., and Kukies J. Uncertainty and the size distribution of rewards from innovation. Journal of Evolutionary Economics 10 (2000) 175-200
29. Shaked M., and Shanthikumar J.G. Stochastic Orders and their Applications (1994), Academic Press, Boston
30. Silverberg G., and Verspagen B. The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance. Journal of Econometrics 139 (2007) 318-339
31. Zolotarev V.M. One-dimensional Stable Distributions (1986), American Mathematical Society, Providence