Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

References

• Abhakorn P, Smith P, Wickens M (2013) What do the Fama-French factors add to C-CAPM? J. Empirical Finance 22:113–127.Crossref, Google Scholar
• Agarwal V, Naik N (2004) Risks and portfolio decisions involving hedge funds. Rev. Financial Stud. 17(1):63–98.Crossref, Google Scholar
• Ang A (2014) Asset Management: A Systematic Approach to Factor Investing (Oxford University Press, Oxford, UK).Crossref, Google Scholar
• Bacon C (2008) Practical Portfolio Performance Measurement and Attribution, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Bai J (2003) Testing parametric conditional distributions of dynamic models. Rev. Econom. Statist. 85(3):531–549.Crossref, Google Scholar
• Barasinska N, Schäfer D, Stephan A (2012) Individual risk attitudes and the composition of financial portfolios: Evidence from German household portfolios. Quart. Rev. Econom. Finance 52(1):1–14.Crossref, Google Scholar
• Baron D (1977) On the utility theoretic foundations of mean-variance analysis. J. Finance 32(5):1683–1697.Crossref, Google Scholar
• Bernard C, Vanduffel S (2014) Mean-variance optimal portfolios in the presence of a benchmark with applications to fraud detection. Eur. J. Oper. Res. 234(2):469–480.Crossref, Google Scholar
• Black F (1972) Capital market equilibrium with restricted borrowing. J. Bus. 45(3):444–455.Crossref, Google Scholar
• Board J, Sutcliffe C (1994) Estimation methods in portfolio selection and the effectiveness of short sales restrictions: UK evidence. Management Sci. 40(4):516–534.Link, Google Scholar
• Brockett P, Golden L (1987) A class of utility functions containing all the common utility functions. Management Sci. 33(8):955–964.Link, Google Scholar
• Cass D, Stiglitz JE (1970) The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds. J. Econom. Theory 2(2):122–160.Crossref, Google Scholar
• Chamberlain G (1983) A characterization of the distributions that imply mean-variance utility functions. J. Econom. Theory 29(1):185–201.Crossref, Google Scholar
• DeMiguel V, Garlappi L, Uppal R (2009) Optimal vs. naive diversification: How inefficient is the 1/N portfolio strategy? Rev. Financial Stud. 22(5):1915–1953.Crossref, Google Scholar
• Dexter A, Yu J, Ziemba W (1980) Portfolio selection in a lognormal market when the investor has a power utility function: Computational results. Dempster M, ed. Stochastic Programming (Academic Press, London), 507–523.Google Scholar
• Eling M, Schuhmacher F (2007) Does the choice of performance measure influence the evaluation of hedge funds? J. Banking Finance 31(9):2632–2647.Crossref, Google Scholar
• Elton E, Gruber M, Brown S, Goetzmann W (2007) Modern Portfolio Theory and Investment Analysis, 7th ed. (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Fama E, French K (2012) Size, value, and momentum in international stock returns. J. Financial Econom. 105(3):457–472.Crossref, Google Scholar
• Gao X, Nardari F (2018) Do commodities add economic value in asset allocation? New evidence from time-varying moments. J. Financial Quant. Anal. 53(1):365–393.Crossref, Google Scholar
• Gardner R, Pinder J, Wood R (1980) Monte Carlo estimation of percentiles for the multi-Smirnov test. J. Statist. Comput. Simulation 10(3-4):243–249.Crossref, Google Scholar
• Genton M, Loperfido N (2005) Generalized skew-elliptical distributions and their quadratic forms. Ann. Inst. Statist. Math. 57(2):389–401.Crossref, Google Scholar
• Green J, Hand J, Zhang X (2017) The characteristics that provide independent information about average U.S. monthly stock returns. Rev. Financial Stud. 30(12):4389–4436.Crossref, Google Scholar
• Grootveld H, Hallerbach W (1999) Variance vs downside risk: Is there really that much difference? Eur. J. Oper. Res. 114(2):304–319.Crossref, Google Scholar
• Grundy B, Lim B, Verwijmeren P (2012) Do option markets undo restrictions on short sales? Evidence from the 2008 short-sale ban. J. Financial Econom. 106(2):331–348.Crossref, Google Scholar
• Hickernell F (1998) A generalized discrepancy and quadrature error bound. Math. Comput. 67(221):299–322.Crossref, Google Scholar
• Hlawitschka W (1994) The empirical nature of Taylor-series approximations to expected utility. Amer. Econom. Rev. 84(3):713–719.Google Scholar
• Homm U, Pigorsch C (2012) Beyond the Sharpe ratio: An application of the Aumann-Serrano index to performance measurement. J. Banking Finance 36(8):2274–2284.Crossref, Google Scholar
• Huffer F, Park C (2007) A test for elliptical symmetry. J. Multivariate Anal. 98(2):256–281.Crossref, Google Scholar
• Hunter J (1972) Independence, conditional expectation, and zero covariance. Amer. Statist. 26(5):22–24.Google Scholar
• Ingersoll JE (1987) Theory of Financial Decision Making, vol. 3 (Rowman & Littlefield, Lanham, MD).Google Scholar
• Jagannathan R, Ma T (2003) Risk reduction in large portfolios: Why imposing the wrong constraint helps. J. Finance 58(4):1651–1684.Crossref, Google Scholar
• Kapsos M, Christofides N, Rustem B (2014) Worst-case robust Omega ratio. Eur. J. Oper. Res. 234(2):499–507.Crossref, Google Scholar
• Kolm PN, Tütüncü R, Fabozzi FJ (2014) 60 years of portfolio optimization: Practical challenges and current trends. Eur. J. Oper. Res. 234(2):356–371.Crossref, Google Scholar
• Korkie B, Turtle H (2002) A mean-variance analysis of self-financing portfolios. Management Sci. 48(3):427–443.Link, Google Scholar
• Kroll Y, Levy H, Markowitz HM (1984) Mean-variance vs. direct utility maximization. J. Finance 39(1):47–61.Crossref, Google Scholar
• Kumar A, Lim S (2008) How do decision frames influence the stock investment choices of individual investors? Management Sci. 54(6):1052–1064.Link, Google Scholar
• Levy H, Levy M (2004) Prospect theory and mean-variance analysis. Rev. Financial Stud. 17(4):1015–1041.Crossref, Google Scholar
• Levy M, Kaplanski G (2015) Portfolio selection in a two-regime world. Eur. J. Oper. Res. 242(2):514–524.Crossref, Google Scholar
• Levy H, Markowitz HM (1979) Approximating expected utility by a function of mean and variance. Amer. Econom. Rev. 69(3):308–317.Google Scholar
• Li F, Tkacz G (2011) A consistent test for multivariate conditional distributions. Econometric Rev. 30(3):251–273.Crossref, Google Scholar
• Liang J, Fang K, Hickernell F (2008) Some necessary uniform tests for spherical symmetry. Ann. Inst. Statist. Math. 60(3):679–696.Crossref, Google Scholar
• Liang J, Ng K, Tian G (2019) A class of uniform tests for goodness-of-fit of the multivariate lp-norm spherical distributions and the lp-norm symmetric distributions. Ann. Inst. Statist. Math. 71(1):137–162.Crossref, Google Scholar
• Liang J, Fang K, Hickernell FJ, Li R (2001) Testing multivariate uniformity and its applications. Math. Comput. 70(233):337–355.Crossref, Google Scholar
• Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econom. Statist. 47(1):13–37.Crossref, Google Scholar
• Lwin KT, Qu R, MacCarthy BL (2017) Mean-VaR portfolio optimization: A nonparametric approach. Eur. J. Oper. Res. 260(2):751–766.Crossref, Google Scholar
• Mandelbrot B (1963) The variation of certain speculative prices. J. Bus. 36(4):394–419.Crossref, Google Scholar
• Manzotti A, Pérez F, Quiroz A (2002) A statistic for testing the null hypothesis of elliptical symmetry. J. Multivariate Anal. 81(2):274–285.Crossref, Google Scholar
• Markowitz H (1952) Portfolio selection. J. Finance 7(1):77–91.Google Scholar
• Markowitz H (1959) Portfolio Selection: Efficient Diversification of Investments (John Wiley & Sons, New York).Google Scholar
• Markowitz H (2000) Mean-Variance Analysis in Portfolio Choice and Capital Markets (Fabozzi Associates, New Hope, PA).Google Scholar
• Markowitz H (2014) Mean-variance approximations to expected utility. Eur. J. Oper. Res. 234(2):346–355.Crossref, Google Scholar
• McNeil AJ, Frey R, Embrechts P (2005) Quantitative Risk Management: Concepts, Techniques and Tools (Princeton University Press, Princeton, NJ).Google Scholar
• Meyer J (1987) Two moment decision models and expected utility maximization. Amer. Econom. Rev. 77:421–430.Google Scholar
• Meyer J, Rasche RH (1992) Sufficient conditions for expected utility to imply mean-standard deviation rankings: Empirical evidence concerning the location and scale condition. Econom. J. (London) 102(410):91–106.Google Scholar
• Miller F Jr, Quesenberry C (1979) Power studies of tests for uniformity, ii. Comm. Statist. Simulation Comput. 8(3):271–290.Crossref, Google Scholar
• Mossin J (1966) Equilibrium in a capital asset market. Econometrica 34(4):768–783.Crossref, Google Scholar
• Neyman J (1937) Smooth test for goodness of fit. Scandinavian Actuarial J. (3-4):149–199.Crossref, Google Scholar
• Owen J, Rabinovitch R (1983) On the class of elliptical distributions and their applications to the theory of portfolio choice. J. Finance 38(3):745–752.Crossref, Google Scholar
• Paolella M (2019) Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Peiró A (1999) Skewness in financial returns. J. Banking Finance 23(6):847–862.Crossref, Google Scholar
• Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32(1/2):122–136.Crossref, Google Scholar
• Pulley LB (1983) Mean-variance approximations to expected logarithmic utility. Oper. Res. 31(4):685–696.Link, Google Scholar
• Quesenberry C, Miller F Jr (1977) Power studies of some tests for uniformity. J. Statist. Comput. Simulation 5(3):169–191.Crossref, Google Scholar
• Ray P, Jenamani M (2016) Mean-variance analysis of sourcing decision under disruption risk. Eur. J. Oper. Res. 250(2):679–689.Crossref, Google Scholar
• Schott J (2002) Testing for elliptical symmetry in covariance-matrix-based analyses. Statist. Probab. Lett. 60(4):395–404.Crossref, Google Scholar
• Schuhmacher F (2012) The Sharpe ratio is better than you may think. J. Bus. Econom. 82(6):685–705.Google Scholar
• Schuhmacher F, Auer BR (2014) Sufficient conditions under which SSD- and MR-efficient sets are identical. Eur. J. Oper. Res. 239(3):756–763.Crossref, Google Scholar
• Sharpe W (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. J. Finance 19(3):425–442.Google Scholar
• Shushi T (2016) A proof for the conjecture of characteristic function of the generalized skew-elliptical distributions. Statist. Probab. Lett. 119:301–304.Crossref, Google Scholar
• Shushi T (2018) Generalized skew-elliptical distributions are closed under affine transformations. Statist. Probab. Lett. 134:1–4.Crossref, Google Scholar
• Simaan Y (1993a) Portfolio selection and asset pricing-three-parameter framework. Management Sci. 39(5):568–577.Link, Google Scholar
• Simaan Y (1993b) What is the opportunity cost of mean-variance investment strategies? Management Sci. 39(5):578–587.Link, Google Scholar
• Simaan Y (2014) The opportunity cost of mean-variance choice under estimation risk. Eur. J. Oper. Res. 234(2):382–391.Crossref, Google Scholar
• Sinn H-W (1983) Economic Decisions Under Uncertainty (North-Holland Publishing Company, New York).Google Scholar
• Statman M (1987) How many stocks make a diversified portfolio? J. Financial Quant. Anal. 22(3):353–363.Crossref, Google Scholar
• Stephens M (1970) Use of the Kolmogorov Smirnov, Cramér-von Mises and related statistics without extensive tables. J. Roy. Statist. Soc. B. 32(1):115–122.Google Scholar
• Strang G (2009) Introduction to Linear Algebra, 4th ed. (Wellesley-Cambridge Press, Wellesley, MA).Google Scholar
• Tobin J (1958) Liquidity preference as behavior toward risk. Rev. Econom. Stud. 25(2):65–86.Crossref, Google Scholar
• Vassalos M, Dillon C, Childs P (2012) Empirically testing for the location-scale condition: A review of the economic literature. J. Risk Model Validation 6(3):51–66.Crossref, Google Scholar
• Watson G (1961) Goodness-of-fit tests on a circle. Biometrika 49(1-2):109–114.Crossref, Google Scholar
• Watson G (1962) Goodness-of-fit tests on a circle. ii. Biometrika 49(1-2):57–63.Crossref, Google Scholar
• Zakamouline V, Koekebakker S (2009) Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance. J. Banking Finance 33(7):1242–1254.Crossref, Google Scholar