Papers
Topics
Authors
Recent
Search
2000 character limit reached

Uniform Pessimistic Risk and its Optimal Portfolio

Published 2 Mar 2023 in q-fin.PM, cs.LG, stat.CO, and stat.ML | (2303.07158v3)

Abstract: The optimal allocation of assets has been widely discussed with the theoretical analysis of risk measures, and pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model. The α\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 a computationally tractable model. In this study, we propose an integral of α\alpha-risk called the \textit{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. Real data analysis of three stock datasets (S&P500, CSI500, KOSPI200) demonstrates the usefulness of the proposed risk and portfolio model.

Authors (2)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (39)
  1. Carlo Acerbi. Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking & Finance, 26(7):1505–1518, 2002.
  2. Expected shortfall: a natural coherent alternative to value at risk. Economic notes, 31(2):379–388, 2002.
  3. Spectral risk measures and portfolio selection. Journal of Banking & Finance, 32(9):1870–1882, 2008.
  4. Coherent measures of risk. Mathematical finance, 9(3):203–228, 1999.
  5. Pessimistic portfolio allocation and choquet expected utility. Journal of financial econometrics, 2(4):477–492, 2004.
  6. Beyond value-at-risk: Gluevar distortion risk measures. Risk Analysis, 34(1):121–134, 2014.
  7. Financial risk and heavy tails. Elsevier, 2003.
  8. Robust actionable prescriptive analytics. Available at SSRN 4106222, 2022.
  9. An introduction to statistical modeling of extreme values, volume 208. Springer, 2001.
  10. Extremiles: A new perspective on asymmetric least squares. Journal of the American Statistical Association, 114(527):1366–1381, 2019.
  11. Optimal versus naive diversification: How inefficient is the 1/n portfolio strategy? The review of Financial studies, 22(5):1915–1953, 2009.
  12. What is the best risk measure in practice? a comparison of standard measures. Journal of Risk, 18(2):31–60, 2015.
  13. Probabilistic forecasting with spline quantile function rnns. In The 22nd International Conference on Artificial Intelligence and Statistics, pages 1901–1910. PMLR, 2019.
  14. Sara A Geer. Empirical Processes in M-estimation, volume 6. Cambridge university press, 2000.
  15. Strictly proper scoring rules, prediction, and estimation. Journal of the American statistical Association, 102(477):359–378, 2007.
  16. Comparing density forecasts using threshold-and quantile-weighted scoring rules. Journal of Business & Economic Statistics, 29(3):411–422, 2011.
  17. Expected probability weighted moment estimator for censored flood data. Advances in water resources, 34(8):933–945, 2011.
  18. Package ‘quantreg’. Cran R-project. org, 2018.
  19. Shigeo Kusuoka. On law invariant coherent risk measures. pages 83–95, 2001.
  20. Supervised learning with general risk functionals. In International Conference on Machine Learning, pages 12570–12592. PMLR, 2022.
  21. Kernel density estimation based distributionally robust mean-cvar portfolio optimization. Journal of Global Optimization, 84(4):1053–1077, 2022.
  22. Harry Markowitz. Portfolio selection. The journal of finance, 7(1):77–91, 1952.
  23. Scoring rules for continuous probability distributions. Management science, 22(10):1087–1096, 1976.
  24. Christoph Memmel. Performance hypothesis testing with the sharpe ratio. Available at SSRN 412588, 2003.
  25. Expected pinball loss for quantile regression and inverse CDF estimation. Transactions on Machine Learning Research, 2024.
  26. On tracking portfolios with certainty equivalents on a generalization of markowitz model: the fool, the wise and the adaptive. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pages 73–80, 2011.
  27. Georg Ch Pflug. Some remarks on the value-at-risk and the conditional value-at-risk. Probabilistic constrained optimization: Methodology and applications, pages 272–281, 2000.
  28. Distributionally robust optimization: A review. arXiv preprint arXiv:1908.05659, 2019.
  29. Conditional value-at-risk for general loss distributions. Journal of banking & finance, 26(7):1443–1471, 2002.
  30. Optimization of conditional value-at-risk. Journal of risk, 2:21–42, 2000.
  31. Judith Rousseau. Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparametric estimation of the density. The Annals of Statistics, 38(1):146–180, 2010.
  32. Optimization of convex risk functions. Mathematics of operations research, 31(3):433–452, 2006.
  33. Alexander Shapiro. Minimax and risk averse multistage stochastic programming. European Journal of Operational Research, 219(3):719–726, 2012.
  34. Alexander Shapiro. On kusuoka representation of law invariant risk measures. Mathematics of Operations Research, 38(1):142–152, 2013.
  35. Improving robustness via risk averse distributional reinforcement learning. In Learning for Dynamics and Control, pages 958–968. PMLR, 2020.
  36. Statistically efficient construction of α𝛼\alphaitalic_α-risk-minimizing portfolio. Advances in Decision Sciences, 2012.
  37. Aad W Van der Vaart. Asymptotic statistics, volume 3. Cambridge university press, 2000.
  38. Shaun S Wang. A class of distortion operators for pricing financial and insurance risks. Journal of risk and insurance, pages 15–36, 2000.
  39. A synthesis of risk measures for capital adequacy. Insurance: mathematics and Economics, 25(3):337–347, 1999.
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Tweets

Sign up for free to view the 7 tweets with 4 likes about this paper.

Sign Up for Free