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Asset allocation by penalized least squares

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  • Manganelli, Simone

Abstract

This paper shows how the problem of mean-downside risk portfolio allocation can be cast in terms of penalized least squares (PLS). The penalty is given by a power function of the returns below a certain threshold. We derive the asymptotic properties of the PLS estimator, allowing for possible nonlinearities and misspecification of the model. We illustrate the usefulness of this new class of estimators with two empirical applications. First, we estimate an autoregressive model, in the spirit of the GARCH literature. Second, we suggest a simple strategy to derive the optimal portfolio weights associated to a mean-downside risk model. JEL Classification: C14, C22, G11

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Bibliographic Info

Paper provided by European Central Bank in its series Working Paper Series with number 0723.

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Date of creation: Feb 2007
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Handle: RePEc:ecb:ecbwps:20070723

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Keywords: mean-risk utility model; Portfolio otpimization; stochastic;

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References

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  1. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
  2. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
  3. Gilbert W. Bassett Jr & Roger Koenker & Gregory Kordas, 2004. "Pessimistic portfolio allocation and Choquet expected utility," CeMMAP working papers CWP09/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, April.
  5. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
  6. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  7. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  10. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  11. Simone Manganelli, 2004. "Asset Allocation by Variance Sensitivity Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 370-389.
  12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  13. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, 07.
  14. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
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Cited by:
  1. Gonzalo, J. & Olmo, J., 2008. "Testing Downside Risk Efficiency Under Market Distress," Working Papers 08/11, Department of Economics, City University London.

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