Large deviations theorems for optimal investment problems with large portfolios
The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two-assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.
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- Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006.
"Risk Management with Benchmarking,"
INFORMS, vol. 52(4), pages 542-557, April.
- Basak, Suleyman & Shapiro, Alex & Teplá, Lucie, 2005. "Risk Management with Benchmarking," CEPR Discussion Papers 5187, C.E.P.R. Discussion Papers.
- Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
- Kandel, Shmuel & Stambaugh, Robert F, 1996. " On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
- Shmuel Kandel & Robert F. Stambaugh, 1995. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," NBER Working Papers 4997, National Bureau of Economic Research, Inc.
- G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
- Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
- Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(02), pages 255-271, June.
- J. L. Knight & S. E. Satchell & K. C. Tran, 1995. "Statistical modelling of asymmetric risk in asset returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 155-172.
- Knight, J.L. & Stachell, S.E. & Tran, K.C., 1995. "Statistical Modeling of Asymetric Risk in Asset Returns," Papers 95-3, Saskatchewan - Department of Economics.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April. Full references (including those not matched with items on IDEAS)
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