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Portfolio choice algorithms, including exact stochastic dominance

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  • Vinod, H.D.

Abstract

Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions f(xj) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved f(xj) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe f(xj). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.

Suggested Citation

  • Vinod, H.D., 2024. "Portfolio choice algorithms, including exact stochastic dominance," Journal of Financial Stability, Elsevier, vol. 70(C).
    • Handle: RePEc:eee:finsta:v:70:y:2024:i:c:s1572308923000967
    DOI: 10.1016/j.jfs.2023.101196
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    References listed on IDEAS

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    1. Hrishikesh Vinod, 2023. "Pandemic-proofing Out-of-sample Portfolio Evaluations," Fordham Economics Discussion Paper Series dp2023-04er:dp2023-04, Fordham University, Department of Economics.
    2. Bawa, Vijay S, et al, 1985. "On Determination of Stochastic Dominance Optimal Sets," Journal of Finance, American Finance Association, vol. 40(2), pages 417-431, June.
    3. 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.
    4. Vinod, H D, 1985. "Measurement of Economic Distance between Blacks and Whites: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 408-409, October.
    5. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    6. Clark, Ephraim & Kassimatis, Konstantinos, 2014. "Exploiting stochastic dominance to generate abnormal stock returns," Journal of Financial Markets, Elsevier, vol. 20(C), pages 20-38.
    7. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    8. Grant L. Harley & R. Stockton Maxwell & Bryan A. Black & Matthew F. Bekker, 2020. "A multi-century, tree-ring-derived perspective of the North Cascades (USA) 2014–2016 snow drought," Climatic Change, Springer, vol. 162(1), pages 127-143, September.
    9. Vinod, Hrishikesh D. & Lopez-de-Lacalle, Javier, 2009. "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i05).
    10. Vinod, H. D., 2004. "Ranking mutual funds using unconventional utility theory and stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 353-377, June.
    11. Philippa A. Higgins & Jonathan G. Palmer & Martin S. Andersen & Christian S. M. Turney & Fiona Johnson, 2023. "Extreme events in the multi-proxy South Pacific drought atlas," Climatic Change, Springer, vol. 176(8), pages 1-20, August.
    12. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    13. Olga Kolokolova & Olivier Le Courtois & Xia Xu, 2022. "Is the index efficient? : A worldwide tour with stochastic dominance," Post-Print hal-04325540, HAL.
    14. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    15. Hrishikesh D Vinod, 2022. "Hands-on Intermediate Econometrics Using R:Templates for Learning Quantitative Methods and R Software," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 12831, August.
    16. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    17. Josef Hadar & Tae Kun Seo, 1988. "Asset Proportions in Optimal Portfolios," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(3), pages 459-468.
    18. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    19. A. Talha Yalta, 2016. "Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 339-366, August.
    20. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    21. James E. Hodder & Jens Carsten Jackwerth & Olga Kolokolova, 2015. "Improved Portfolio Choice Using Second-Order Stochastic Dominance," Review of Finance, European Finance Association, vol. 19(4), pages 1623-1647.
    22. Porter, R Burr, 1974. "Semivariance and Stochastic Dominance: A Comparison," American Economic Review, American Economic Association, vol. 64(1), pages 200-204, March.
    23. Levy, Haim, 1973. "Stochastic Dominance, Efficiency Criteria, and Efficient Portfolios: The Multi-Period Case," American Economic Review, American Economic Association, vol. 63(5), pages 986-994, December.
    24. Haim Shalit & Shlomo Yitzhaki, 1994. "Marginal Conditional Stochastic Dominance," Management Science, INFORMS, vol. 40(5), pages 670-684, May.
    25. Vinod, H D, 1985. "Measurement of Economic Distance between Blacks and Whites," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 78-88, January.
    26. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
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    Cited by:

    1. H. D. Vinod, 2024. "May 2024 Buy-Sell Guide for Dow Jones 30 Stocks and Modified Omega Criterion," JRFM, MDPI, vol. 17(8), pages 1-13, August.

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    More about this item

    Keywords

    Portfolio choice; Cumulative density; Bootstrap; Step-function; Expected utility theory;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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