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Uniform Pessimistic Risk and Optimal Portfolio

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  • Sungchul Hong
  • Jong-June Jeon

Abstract

The optimality of allocating assets has been widely discussed with the theoretical analysis of risk measures. Pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model, and the $\alpha$-risk plays a crucial role in deriving a broad class of pessimistic optimal portfolios. However, estimating an optimal portfolio assessed by a pessimistic risk is still challenging due to the absence of an available estimation model and a computational algorithm. In this study, we propose a version of integrated $\alpha$-risk called the uniform pessimistic risk and the computational algorithm to obtain an optimal portfolio based on the risk. Further, we investigate the theoretical properties of the proposed risk in view of three different approaches: multiple quantile regression, the proper scoring rule, and distributionally robust optimization. Also, the uniform pessimistic risk is applied to estimate the pessimistic optimal portfolio models for the Korean stock market and compare the result of the real data analysis. It is empirically confirmed that the proposed pessimistic portfolio presents a more robust performance than others when the stock market is unstable.

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  • Sungchul Hong & Jong-June Jeon, 2023. "Uniform Pessimistic Risk and Optimal Portfolio," Papers 2303.07158, arXiv.org.
    • Handle: RePEc:arx:papers:2303.07158
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    References listed on IDEAS

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    1. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 477-492.
    2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    3. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    4. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    5. Alexander Shapiro, 2013. "On Kusuoka Representation of Law Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 142-152, February.
    6. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    7. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    8. Shapiro, Alexander, 2012. "Minimax and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 219(3), pages 719-726.
    9. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    10. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    11. 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.
    12. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    13. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    14. Giovanni Bonaccolto, 2019. "Critical Decisions for Asset Allocation via Penalized Quantile Regression," Papers 1908.04697, arXiv.org.
    15. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    16. Gilbert W. Bassett Jr Bassett & Roger Koenker & Gregory Kordas, 2004. "Pessimistic portfolio allocation and Choquet expected utility," CeMMAP working papers 09/04, Institute for Fiscal Studies.
    17. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
    18. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    19. 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.
    20. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
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