Higher moments portfolio Optimization with unequal weights based on Generalized Capital Asset pricing model with independent and identically asymmetric Power Distribution

Document Type: Research Paper

Authors

1 Department of Finance, Accounting and Management Faculty of Tehran University, Tehran, Iran

2 Economy Faculty of Tehran University, Tehran, Iran

3 Management Faculty of Shahrood University, Shahrood, Iran

10.22034/amfa.2020.1909590.1484

Abstract

The main criterion in investment decisions is to maximize the investors utility. Traditional capital asset pricing models cannot be used when asset returns do not follow a normal distribution. For this reason, we use capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) and capital asset pricing model with asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. When the assumption of normality is violated, the first and second moments lose their efficiency in optimization and we need to use the third and fourth moments. For the first time, we propose independent and identically asymmetric exponential power distributed with two tail parameters. Then, we use higher moments optimization with unequal weights to optimize portfolios. The results indicate that capital asset pricing model with independent and identically asymmetric power distributed (CAPM-IIAPD) is better than asymmetric independent and identically asymmetric exponential power distributed with two tail parameters(CAPM-AIEPD) to estimate return and risk. Adjusted Sharp ratio in portfolio optimization in second moments are higher than others. Adjusted returns to risk in third and fourth moments in the CAPM-IIAPD model significantly differ from the CAPM-AIEPD model and have a better performance.

Keywords


[1] Amiri, M., Mahboob Ghodsi, M., Fuzzy Linear Programming Model Optimum Portfolio Selection Problem, Quarterly Financial Engineering and Securities Management journal, 2015, 6(23), P.105-118 (in Persian). Doi:10.154/IJOR.2014.05849.

[2] Aracioglu, B., Demircan, F., Souyer, H., Mean-Variance-kewness-Kortusis Approach to Portfolio Optimization:An application in Istanbul Stock Exchange, Ege Academic Review, 2011, P.9-17.

[3] Aven, T., On The Meaning of a Black Swan In a Risk Context. Safety Science, 2013, 5(7), P. 44-51.
Doi: 10.1016/j.ssci.2013.01.016.

[4]  Bera, A.,   Park, S., Y.,. Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews,7, 2008,  P.484-512. Doi: 10.1080/07474930801960394.

[5]  Biglari , M., Multiperiod portfolio selection with  higher-order moment, Quarterly Financial Engineering and Securities Management journal , (2018), 9(37), P.1-22  (in Persian). Doi:www.sid.ir/en/journal/ViewPaper.aspx?id=667552.

[6]  Fallah ,M., Sina, A.,. Optimizing Portfolio through Extreme Value Theory in Tehran Stock Exchange, Quarterly Financial Engineering and Securities Management journal, 2019, 10(40), P.184-200 (in Persian).

[7]  Fama , F., Fisher, L., Jensen, C., Roll, R.  The adjustment of stock prices to new information. International Economic Review,  1969,10(1), P.1-21. Doi: 10.2307/2525569.

[8]   Hodgson , J., Linton, O., Vorkink,  K., Testing the capital asset pricing model efficiency under ellipiteal symmerty: A semiparametric appoach. J,Appl.Econ. 2002.17,P. 617-639. Doi: 102139/ssrn.283364 .

[9]  Hu, W., Kercheval, A,. Risk management with generalized hyperbolic distributions. Fourth IASTED International Conference on Financial Engineering and Applications. 2007. Doi:10.2139/ssrn.823986.

[10] Izadikhah, M., Deriving weights of criteria from inconsistent fuzzy comparison matrices by using the nearest weighted interval approximation, Advances in Operations Research, 2012, 2012 (574710), P. 1-17, Doi: 10.1155/2012/574710

[11] Jana, P., Roy, T., Mazumder, S., Multi-objective mean-variance-sekwness model for portfolio optimization , Advanced Modeling and Optimization, 2007,9,P.181-193.Doi: http://ssrn.com/abstract_id=18414311.

[12]  Kalantari,  M., Mohammadi, R., Saeidi, M., Fuzzy Goal Programming Model to Rolling Performance Based Budgeting by Productivity Approach, Journal of Advances in Mathematical Finance and Applications,  2018 , 3(3),  P.95-107. Doi: 0.22034/AMFA.2018.544952.

[13] Khaloozadeh, H., Jamshidi, E., The Tail Mean-Variance Model and Extended Efficient Frontier ,  Journal of Advances in Mathematical Finance and Applications,  2021 , 6(1),  P.185-199. Doi: 10.22034/AMFA.2020.1892182.1365.

[14]  Komunjer, l., Asymmetric Power distribution:Theory and applications to risk      measurement .J.Appl.Econ.   2007, 22, P.891-921. Doi:10.1002/jae.961.

[15]  Kordloei,  H., Ahmadi, R., The Effect of Financial Distress on the Investment Behavior of Companies Listed on Tehran Stock Exchange , Journal of Advances in Mathematical Finance and Applications  ,  2018 , 3(4),  P.17-28.

 [16] Li, L., Lin, M., Analysis of French stock Market's CAPM based on asymmetric exponential power distribution.Int. J.Appl.Math.Stat, , 2014, 52, P.84-95. Doi: 10.4236/tel.2014.48085.

[17]   Liu, Y., Risk forecasting and portfolio optimization with GARCH,  skewed t distributions and multiple timescales: The Florida State University, 2012 Doi:http://purl.flvc.org/fsu/fd/FSU_migr_etd-4998.

[18]  Luo, C., Stochastic Correlation and Portfolio Optimization by Multivariate Garch, University of Toronto (Canada), 2016. Doi: http://hdl.handle.net/1807/73049.

[19] Ngailo, E., Javed, F., Higher order moments of the estimated tangency portfolio weights,
JournalJournal of Applied Statistics, 2020. Doi: 10.1080/02664763.2020.1736523.

 [20]  Rahnamay Roodposhti,F., & Mirghafar,R., Portfolio Performance in Tehran stock Exchange:Value at risk application , Quarterly Financial Engineering and Securities Management journal , 2011, 2(8),P.51-78 (In  Persian).

[21]   Rostami , M., Behzadi , A.,  Higher moments optimization in fuzzy environment , Quarterly Financial Engineering and Securities Management journal , 2015, 9(24),  2018, P.41-61.(In   Persian).
Doi:10.1016/j.camwa.2010.10.039https://doi.org/10.1016/j.camwa.2010.10.039.

[22]   Bao, T., Diks , C., Li , H.,. A generalized CAPM with asymmetric power distributed errors with an application to portfolio construction , Economic Modeling, 2017, 32-48.  Doii:10.1016/j.econmod.2017.03.035.

[23]   Thomas,R., Gup, B.E., The valuation handbook:valuation techniques from today's top practitioners, JohnWiley &Sons,Inc., Hoboken,  2010 .

[24] Waqar, N,. Iqbal, K,. Shahid,. R., Sustainable Portfolio Optimization with Higher-Order Moments of Risk,  Economic and Business Aspects of Sustainability, 2020, 12.  Doi:10.3390/su12052020.

  [25] Wilcox, J., Better portfolios with higher moments, Journal of Asset Management, 2020.
Doi:10.1057/s41260-020-00170-5.

[26]  Willems, J., Van Holle, F., Cornilly, D.,  Algorithmic portfolio tilting to harvest higher moment gains , Heliyon, 2020,6,3. Doi:10.1016/j.heliyon.2020.e03516.

[27]  Xiong, J. X.,  Idzorek, T. M.,  The impact of skewness and fat tails on the asset allocation decision. Financial Analysts Journal, 2018, 67(2), P.23-35. Doi:10.2307/23031987.

[28]  Yunyun, S., Jiangshan H., Fang M., A Possibilistic Portfolio Model with Fuzzy Liquidity Constraint , Complexity, 2020, 10 .  Doi:10.1155/2020/3703017.

[29] Zhai,J.Bai,M.&Wu,H.(2018). Mean-risk-skewness models for portfolio optimization based on uncertain measure, Journal of Mathematical Programming and Operations Research, 67(5), https://doi.org/10.1080/02331934.2018.1426577.

[30]  Zhang,  X.,  Creal,  D.,  Koopman, S.J.,  Lucas,  A.,  Modeling dynamic volatilities and correlations under skewness and fat tails. Technical Report, Tinbergen Institute,Amesterdam, 2011, P.11-78. Doi:10.2139/ssrn.1920839.

 [31]  Zhu, D.,  Galbraith, J.W.,  A generalized asymmetric student-t distribution with application to financial econometrics, Econ.157, 2010, P.297-305.  Doi:10.1016/j.jeconom.2010.01.013.

[32]  Zhu,D.,  Zinde-Walsh, V.,  Properties and estimation of asymmetric exponential power distribution, 148,   2009, P.86-99. Doi: 10.1016/j.jeconom.2008.09.038.

[33]  Zinoviy, L., Tomer , S., Analytic solution to the portfolio optimization problem in a mean-variance-skewness model ,   The European Journal of Finance, 2020, P.165-178. Doi:10.1080/1351847X.2019.1618363.