Higher Moments Portfolio Optimization with Entropy Based Polynomial Goal Programming

Document Type : Research Paper

Authors

1 Assistant Prof., Faculty of Management, Kharazmi University, Tehran, Iran.

2 Ph.D Candidate, Department of Financial Engineering, Faculty of Management, University of Tehran, Tehran, Iran

Abstract

Objective: Portfolio selection is a critical factor in investment. Having considered a number of risky assets, fund
 managers must choose the optimum portfolio. Stock values can be affected by different types of events
 such as governmental crises, economic turmoil and industrial improvements. Due to the vague nature
 of these events, it is difficult to estimate the future value of stocks. However, Markowitz’s Modern
 portfolio theory, which is principally focused on portfolio risk, has introduced a novel model for stock
 diversification. When the normality assumption
 of return series of assets are not valid, higher moments can also be added to ensure the efficiency of
 the Markowitz model. On other hand, entropy can be used as diversification creteria in portfolio theory. In this paper, the affect of simulatnus usage higher moment and entropy is examined. Methods: In this paper, a polynomial goal programming based on the model of meanvariance-skidding-elongation-entropy and direct search algorithms is used. For estimation of entropy, Shannon and Ginny Simpson criteria have been used.  Results: Tehran Stock Exchange data was used to evaluate the models. The findings indicate portfolio performance measure is enhanced by using the proposed approach. Conclusion: Using a combination of higher moments and entropy, although it does not improve some of the target functions, but generally improves the performance of the portfolios.  
 

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References

References
Aksaraylı, M., & Pala, O. (2018). A polynomial goal programming model for portfolio optimization based on entropy and higher moments. Expert Systems with Applications, 94:185-192.
Arditti, F. (1971). Another look at mutual fund performance. Journal of Financial and Quantitative Analysis, 6(3): 909-912.
Bera, A. K. & S. Y. Park (2008). Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews, 27(4-6): 484-512.
Chow, K. V. and K. C. Denning (1994). On variance and lower partial moment betas the equivalence of systematic risk measures. Journal of Business Finance & Accounting, 21(2): 231-241.
Chunhachinda, P., K. Dandapani, S. Hamid & A. J. Prakash (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance, 21(2): 143-167.
DeMiguel, V. & Nogales, F. J. (2009). Portfolio selection with robust estimation. Operations Research, 57(3): 560-577.
Fama, E. F. (1965). Portfolio analysis in a stable Paretian market. Management science, 11(3): 404-419.
Grootveld, H. & Hallerbach, W. (1999). Variance vs downside risk: Is there really that much difference?. European Journal of operational research, 114(2): 304-319.
Harvey, C. R., Liechty, J. C., Liechty, M. W. and P. Müller. (2010). Portfolio selection with higher moments. Quantitative Finance, 10(5): 469-485.
Harvey, C. and Sediqque. (2000). Conditional skewness in asset pricing tests. Journal of finance, 55: 1263–1295.
Israelsen, C. L. (2005). A refinement to the Sharpe ratio and information ratio. Journal of Asset Management, 5(6), 423-427.
Jarque, C. M. & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review/Revue Internationale de Statistique: 163-172.
Jost, L. (2006). Entropy and diversity. Oikos, 113(2), 363-375.
Kostakis, A., Muhammad, K. & Siganos, A.(2012). Higher co-moments and asset pricing on London Stock Exchange. Journal banking and finance. 36(3): 913-922
Kraus, A. & Litzenberger, R. H. (1976). Skewness Preference and the Valuation of Risk Assets. The Journal of Finance ,31(4): 1085-1100.
Lai, K. K., Yu, L., & Wang, S. (2006, June). Mean-variance-skewness-kurtosis-based portfolio optimization. In First International Multi-Symposiums on Computer and Computational Sciences (IMSCCS'06) (Vol. 2, pp. 292-297). IEEE.
Liu, S., Wang, S. & Qiu, W. (2003). Mean-variance-skewness model for portfolio selection with transaction costs. International Journal of Systems Science, 34(4): 255-262.
Machado, C., & Brandão, A. (2000). Skewness in financial returns: Evidence from the portuguese stock market, Minho University (Portugal), Management Research Group Working Paper
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1): 77-91.
Ray, A. & S. K. Majumder. (2017). Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization. OPSEARCH: 1-27.
Rom, B. M. & Ferguson, K. W. (1994). Post-modern portfolio theory comes of age. The Journal of Investing, 3(3): 11-17.
Simkowitz, M. A. & Beedles, W. L. (1978). Diversification in a three-moment world. Journal of Financial and Quantitative Analysis, 13(5): 927-941.
Škrinjarić, T. (2013). Portfolio Selection with Higher Moments and Application on Zagreb Stock Exchange. Zagreb International Review of Economics & Business, 16(1): 65-78.
Tayi, G. K. & Leonard, P. A. (1988). Bank balance-sheet management: An alternative multi-objective model. Journal of the Operational Research Society, 39(4): 401-410.
Usta, I. and Kantar, Y. M. (2011). Mean-variance-skewness-entropy measures: a multi-objective approach for portfolio selection. Entropy, 13(1): 117-133.
Yue, W. and Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465: 124-140.
Zhang, W.-G., Y.-L. Wang, Z.-P. Chen and Z.-K. Nie (2007). "Possibilistic mean–variance models and efficient frontiers for portfolio selection problem." Information Sciences 177(13): 2787-2801.
 
 
 
Financial Research Journal
Volume 20, Issue 2
2018
Pages 193-210

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