A hybrid approach to the discrepancy in financial performance’s robustness
Tóm tắt
Performance measurement is a crucial ingredient in the industry of investment funds. Mainly grounded on indices of risk-adjusted returns, it requires historical data to estimate the relevant statistics such as the Sharpe ratio. Therefore the measurement process is sensitive to outliers in the time series underlying historical data. Since alternative measures are available for performance evaluation, we propose an iterative methodology for a set of eleven indices (including the Sharpe ratio) in order to: (a) quantify their intrinsic degree of statistical robustness; (b) find different sensitivity to alternative outliers configuration. This methodology is a combination of a reasonable definition of breakdown point and the definition of discrepancy of a finite point set. A suitable Monte Carlo simulation provides numerical evidence of changing sensitivity among all considered performance measures, instead the classical definition of breakdown point only shows lack of robustness among all indices without further specification. Our approach may be useful in choosing the most robust performance measure to be employed in investment management, especially when robust portfolio optimization has to be used.
Tài liệu tham khảo
Acerbi C (2002) Spectral measures of risk: a coherent representation of subjective risk aversion. J Bank Finance 26:1505–1518
AIMR: Performance Evaluation, Benchmarks, and Attribution Analysis. AIMR (CFA Institute), ICFA Continuining Education, First Edition (1995)
AIMR: Performance Presentation Standards Handbook (The AIMR-PPS Standards with Commentary and Interpretation). AIMR (CFA Institute), Second Edition (1997)
Amenc N, Le Sourd V (2003) Portfolio theory and performance analysis. Wiley, Hoboken
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertainty data. Math Program 88:411–424
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton
Bertsimas D, Brown DB (2009) Constructing uncertainty sets for robust linear optimization. Oper Res 57:1483–1495
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53
Bertsimas D, Sim M (2011) Theory and applications of robust optimization. SIAM Rev 53:464–501. https://doi.org/10.1080/1351847X.2021.1960404
Best MJ, Grauer RR (1991) On the sensitivity of mean-variance efficient portfolios to changes in asset means: some analytical and computational results. Rev Financ Stud 4(2):315–342
Black F, Litterman R (1991) Asset allocation: combining investor views with market equilibrium. J Fixed Income 1(2):7–18
Bradrania R, Pirayesh Neghab D (2021) State-dependent asset allocation using neural networks. Eur J Finance. https://doi.org/10.1080/1351847X.2021.1960404
Caporin M, Jannin GM, Lisi F (2014) A survey on the four families of performance measures. J Econ Surv 28(5):917–942
Chan LKC, Karceski J, Lakonishok J (1999) On portfolio optimization: forecasting covariances and choosing the risk model. Rev Financ Stud 12(5):937–974
Chang T-J, Yang S-C, Chang K-J (2009) Portfolio optimization problems in different risk measures using genetic algorithm. Expert Syst Appl 36(7):10529–10537
Chopra VK, Ziemba WT (1993) The effect of errors in means, variances, and covariances on optimal portfolio choice. J Portfolio Manag Winter 19(2):6–11. https://doi.org/10.3905/jpm.1993.409440
Christopherson JA, Cariño DR, Ferson WE (2009) Portfolio performance measurement and benchmarking. McGraw-Hill, New york
Cogneau P, Hübner G (2015) The prediction of fund failure through performance diagnostics. J Bank Finance 50:224–241
Cont R, Deguest R, Scandolo G (2010) Robustness and sensitivity analysis of risk measurement procedures. Quant Finance 10(6):593–606
Davies PL, Gather U (2005) Breakdown and groups. Ann Stat 33(3):977–988
De Capitani L, Pasquazzi L (2015) Inference for performance measures for financial assets. Metron 73(1):73–98. https://doi.org/10.1007/s40300-014-0055-y
Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper Res 58(3):596–612
Deng G, Dulaney T, McCann C, Wang O (2013) Robust portfolio optimization with value-at-risk-adjusted sharpe ratios. J Asset Manag 14(5):293–305
Donnelly C, Embrechts P (2010) The devil is in the tails: actuarial mathematics and the subprime mortgage crisis. ASTIN Bull J Int Actuar Assoc 40(01):1–33
Dowd K (2000) Adjusting for risk: an improved Sharpe ratio. Int Rev Econ Financ 9(3):560–577
El Gahoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper Res 51(4):543–556
Fabozzi FJ, Kolm PN, Pachamanova D, Focardi SM (2007) Robust portfolio optimization and management. Wiley, Hoboken
Fliege J, Werner R (2014) Robust multiobjective optimization and applications in portfolio optimization. Eur J Oper Res 234:422–433
Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization. Eur J Oper Res 235:471–483
Genton MG, Lucas A (2003) Comprehensive definitions of breakdown points for independent and dependent observations. J R Stat Soc B 65(1):81–94
Ghahtarani A Saif A, Ghasemi A (2022) Robust portfolio selection problems: a comprehensive review. Operational. Res Int J. https://doi.org/10.1007/s12351-022-00690-5
Goldfarb D, Iyengar G (2003) Robust portfolio selection problems. Math Oper Res 28:1–38
Goel A, Sharma A, Mehra A (2017) Robust optimization of mixed CVaR starr ratio using copulas. J Comput Appl Math 347:62–83
Gregory C, Darby-Dowman K, Mitra G (2011) Robust optimization and portfolio selection: the cost of robustness. Eur J Oper Res 212:417–428
Huber PJ, Ronchetti EM (2009) Robust statistics. Wiley, Hoboken
Israelsen CL (2005) A refinement to the sharpe ratio and information ratio. J Asset Manag 5:423–427
Jagannathan R, Ma T (2003) Risk reduction in large portfolios: why imposing the wrong constraints helps. J Finance 58(4):1651–1683
Ji R, Lejeune MA, Prasad SY (2017) Properties, formulations, and algorithms for portfolio optimization using mean-Gini criteria. Ann Oper Res 248(1–2):305–343
Ji R, Lejeune MA, Fan Z (2022) Distributionally robust portfolio optimization with linearized STARR performance measure. Quant Finance. https://doi.org/10.1080/14697688.2021.1993623
Kaspos M, Christofides N, Rustem B (2014) Worst-case robust omega ratio. Eur J Oper Res 234(2):499–507
Krätschmer V, Schied A, Zhäle H (2014) Comparative and Qualitative Robustness for Law-Invariant Risk Measures. Finance Stochast 18:271–295. https://doi.org/10.1007/s00780-013-0225-4
Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market. Manage Sci 37:519–531
Lauprete GJ, Samarov AM, Welsch RE (2002) Robust portfolio optimization. Metrika 55:139–149
León A, Navarro L, Nieto B (2019) Screening rules and portfolio performance. North Am J Econ Finance 48:642–662
Lo AW (2002) The statistics of sharpe ratios. Financ Anal J 58:36–52
Lu Z (2006) A new cone programming approach for robust portfolio selection. Department of Mathematics, Simon Fraser University, Burnaby, BC, Tech. Rep
Lu Z (2011) Robust portfolio selection based on a joint ellipsoidal uncertainty set. Opt Methods Softw 26(1):89–104
Mamatzakis E, Tsionas MG (2021) Testing for persistence in US mutual funds’ performance: a Bayesian dynamic panel model. Ann Oper Res 299(1):1203–1233
Maronna RA, Martin RD, Yohai VJ (2006) Robust Statistics. Wiley, Hoboken
Markowitz H (1952) Portfolio selection. J Financ 7:77–91
Momen O, Esfahanipour A, Seifi A (2020) A robust behavioral portfolio selection. Operational. Res Int J 20:427–446
Niederreiter H (1992) Random number generation and quasi-monte carlo methods. CBMS-NSF regional conference series in applied mathematics, SIAM
Pinar MÇ, Paç AB (2014) Mean semi-deviation from a target and robust portfolio choice under distribution and mean return ambiguity. J Comput Appl Math 259:394–405
Rachev ST, Stoyanov SV, Fabozzi FJ (2008) Advanced stochastic models, risk assessment, and portfolio optimization. Wiley, Hoboken
Rossello D (2015) Ranking of investment funds: acceptability versus robustness. Eur J Oper Res 245(3):828–836
Roy B (2010) Robustness in operational research and decision aiding: a multi-faceted issue. Eur J Oper Res 200:629–638
Scutellà M, Recchia R (2013) Robust portfolio asset allocation and risk measures. Ann Oper Res 204(1):145–169
Sharma A, Utz S, Mehra A (2017) Oemga-CVaR portfolio optimization and its worst case analysis. OR Spect 39(2):505–539
Tsay RT (2010) Analysis of financial time series. Wiley, Hoboken
Tong X, Wu F (2014) Robust reward-risk ratio optimization with application in allocation of generation asset. Optimization. https://doi.org/10.1080/02331934.2012.672419
Tütüncü RH, Koening M (2004) Robust assect allocation. Ann Oper Res 132:157–187
Ytzhaki S (1983) On an extension of the Gini inequality index. Int Econ Rev 24(3):617–628
Zakamouline V, Koekebakker S (2009) Portfolio performance evaluation with generalized sharpe ratios: beyond the mean and variance. J Bank Finance 33(7):1242–1254
Zhao Q, Chen L, Wu J (2021) Robust and efficient estimation of GARCH models based on Hellinger distance. J Appl Stat. https://doi.org/10.1080/02664763.2021.1970120
Zhu S, Fukushima M (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper Res 57(5):1155–1168