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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

Suggested Citation

  • Manganelli, Simone, 2007. "Asset allocation by penalized least squares," Working Paper Series 723, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2007723
    Note: 196912
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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp723.pdf
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    References listed on IDEAS

    as
    1. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    2. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 477-492.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    5. 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.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. 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.
    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, July.
    9. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    10. Simone Manganelli, 2004. "Asset Allocation by Variance Sensitivity Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 370-389.
    11. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    12. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, July.
    13. 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.
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    Cited by:

    1. Olmo, José & Gonzalo, Jesús, 2008. "Testing downside risk efficiency under market distress," UC3M Working papers. Economics we084321, Universidad Carlos III de Madrid. Departamento de Economía.

    More about this item

    Keywords

    mean-risk utility model; Portfolio otpimization; stochastic;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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