Money, finances and credit

Further examination of the 1/N portfolio rule: a comparison against Sharpe-optimal portfolios under varying constraints

Economic Annals-XXI

Economic Annals-ХХI: Volume 166, Issue 7-8, Pages: 56-60

Citation information:
Nor, S. M., & Islam, S. M. N. (2017). Further examination of the 1/N portfolio rule: a comparison against Sharpe-optimal portfolios under varying constraints. Economic Annals-XXI, 166(7-8), 56-60. doi: https://doi.org/10.21003/ea.V166-11

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Safwan Mohd Nor
PhD (Finance),
UMT Fund Manager,
University of Malaysia Terengganu
21030 Kuala Nerus, Terengganu, Malaysia
Research Associate,
Victoria Institute of Strategic Economic Studies,
Victoria University
Melbourne, Victoria 3000, Australia
safwan@umt.edu.my;
safwan.mohdnor@live.vu.edu.au
ORCID ID: http://orcid.org/0000-0003-0791-2363

Sardar M. N. Islam
PhD (Quantitative Methods and Economics),
Professor,
Victoria Institute of Strategic Economic Studies,
Victoria University
Melbourne, Victoria 3000, Australia
sardar.islam@vu.edu.au
ORCID ID: https://orcid.org/0000-0001-9451-7390

Further examination of the 1/N portfolio rule: a comparison against Sharpe-optimal portfolios under varying constraints

Abstract. Practical trading constraints (such as asset bounds and transaction costs) are known to affect the efficient frontier of an investment portfolio. In this study, we investigate out-of-sample trading performances of tangency portfolios against the naïve 1/N policy under varying constraints. Our aim is to deliberate if such constraints are influential to the relative (individual) performances between (of) the two competing strategies. Using FTSE Bursa Malaysia KLCI constituent stocks of 30 companies listed, we form several portfolios with different Ns and constraint specifications. Sample period spans 2006 through 2015, in order to alleviate possible confounding affects on risk/return dynamics caused by the 1MDB financial scandal and the U.S. Federal Reserve increasing its key interest rate starting from December 2015. Performance metrics exhibit sensitivity of portfolios to the degree (variability) of constraints, specifically floor, ceiling and the consideration of trading cost.

Among other valuable findings, it has been found out that in all the cases researched the simple 1/N portfolio selection rule offers superior outcome as compared to the tangency portfolios. Generally stated, the naïve policy outperforms the more sophisticated portfolio optimization model in terms of the Sharpe criterion, information ratio and maximum drawdown during the period under investigation. Relative performances remain consistent regardless of the number of stocks included in the portfolio.

Keywords: Portfolio Optimization; Sharpe Ratio; Information Ratio; Maximum Drawdown; Naïve Diversification; Practical Constraints

JEL Classifications: G11; C60

Acknowledgments: The authors would like to thank participants of the 2016 International Conference on Management and Operations Research in Beijing, China (August 12-14) and Associate Professor Adrian Cheung from Curtin University, Australia, for their comments and suggestions.

DOI: https://doi.org/10.21003/ea.V166-11

References

  1. Investment Company Institute (ICI) (2017). Worldwide Regulated Open-End Fund Assets and Flows Second Quarter 2017.
    Retrieved from https://www.ici.org/research/stats/worldwide/ww_q2_17
  2. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
    doi: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
  3. DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: how inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915-1953.
    doi: https://doi.org/10.1093/rfs/hhm075
  4. Kritzman, M., Page, S., & Turkington, D. (2010). In defense of optimization: the fallacy of 1/N. Financial Analysts Journal, 66(2), 1-9.
    doi: https://doi.org/10.2469/faj.v66.n2.6
  5. Levy, H. & Duchin, R. (2010). Markowitz’s mean–variance rule and the Talmudic diversification recommendation. In J. B. Guerard (Ed.), Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques (pp. 97-123). New York: Wiley.
  6. Nor, S. M., & Islam, S. M. N. (2016). Beating the market: Can evolutionary based portfolio optimisation outperform the Talmudic diversification strategy. International Journal of Monetary Economics and Finance, 9(1), 90-99.
    doi: https://doi.org/10.1504/IJMEF.2016.074584
  7. Benartzi, S., & Thaler, R. H. (2001). Naive diversification strategies in defined contribution saving plans. American Economic Review, 91(1), 79-98.
    doi: https://doi.org/10.1257/aer.91.1.79
  8. Huberman, G. & Jiang, W. (2006). Offering versus choice in 401(k) plans: equity exposure and number of funds. Journal of Finance, 61(2), 763-801.
    doi: https://doi.org/10.1111/j.1540-6261.2006.00854.x
  9. Sharpe, W. F. (1963). A simplified model of portfolio analysis. Management Science, 9(2), 277-293.
    doi: https://doi.org/10.1287/mnsc.9.2.277
  10. Yoshimoto, A. (1996). The mean-variance approach to portfolio optimization subject to transaction costs. Journal of the Operations Research Society of Japan, 39(1), 99-117.
    doi: https://doi.org/10.15807/jorsj.39.99
  11. Mei, X., DeMiguel, V., & Nogales, F. J. (2016). Multiperiod portfolio optimization with multiple risky assets and general transaction costs. Journal of Banking and Finance, 69, 108-120.
    doi: https://doi.org/10.1016/j.jbankfin.2016.04.002
  12. Ruiz-Torrubiano, R., & Suárez, A. (2015). A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs. Applied Soft Computing, 36, 125-142.
    doi: https://doi.org/10.1016/j.asoc.2015.06.053
  13. Xue, H.-G., Xu, C.-X., & Feng, Z.-X. (2006). Mean-variance portfolio optimal problem under concave transaction cost. Applied Mathematics and Computation, 174(1), 1-12.
    doi: https://doi.org/10.1016/j.amc.2005.05.005
  14. Guidi, F., & Gupta, R. (2013). Market efficiency in the ASEAN region: evidence from multivariate and cointegration tests. Applied Financial Economics, 23(4), 265-274.
    doi: http://doi.org/10.1080/09603107.2012.718064
  15. Soon, S.-V., Baharumshah, A. Z., & Chan, T.-H. (2015). Efficiency market hypothesis in an emerging market: does it really hold for Malaysia? Jurnal Pengurusan, 42, 31-42.
    Retrieved from http://ejournal.ukm.my/pengurusan/article/view/9208
  16. Nor, S. M., & Wickremasinghe, G. (2014). The profitability of MACD and RSI trading rules in the Australian stock market. Investment Management and Financial Innovations, 11(4), 194-199.
    Retrieved from https://businessperspectives.org/journals/investment-management-and-financial-innovations/issue-4-cont-9/the-profitability-of-macd-and-rsi-trading-rules-in-the-australian-stock-market
  17. Shahzad, S. J. H., Nor, S. M., Mensi, W., & Kumar, R. R. (2017a). Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches, Physica A: Statistical Mechanics and its Applications, 471, 351-363.
    doi: https://doi.org/10.1016/j.physa.2016.12.037
  18. Jobson, J. D., & Korkie, B. M. (1981). Performance hypothesis testing with the Sharpe and Treynor measures. Journal of Finance, 36(4), 889-908.
    doi: https://doi.org/10.1111/j.1540-6261.1981.tb04891.x
  19. Memmel, C. (2003). Performance hypothesis testing with the Sharpe ratio. Finance Letters, 1(1), 21-23.
  20. Baur, D. G., & Löffler, G. (2016). Is contagion infecting your portfolio? A study of the euro sovereign debt crisis. The Journal of Fixed Income, 25(3), 46-57.
    doi: https://doi.org/10.3905/jfi.2016.25.3.046
  21. Cai, X. J., Tian, S., Yuan, N., & Hamori, S. (2017). Interdependence between oil and East Asian stock markets: Evidence from wavelet coherence analysis. Journal of International Financial Markets, Institutions and Money, 48, 206-223.
    doi: https://doi.org/10.1016/j.intfin.2017.02.001
  22. Han, Y., Gong, P., & Zhou, X. (2016). Correlations and risk contagion between mixed assets and mixed-asset portfolio VaR measurements in a dynamic view: an application based on time varying copula models. Physica A: Statistical Mechanics and its Applications, 444, 940-953.
    doi: https://doi.org/10.1016/j.physa.2015.10.088
  23. Low, R. K. W., Faff, R., & Aas, K. (2016). Enhancing mean-variance portfolio selection by modeling distributional asymmetries. Journal of Economics and Business, 85, 49-72.
    doi: https://doi.org/10.1016/j.jeconbus.2016.01.003
  24. Shahzad, S. J. H., Nor, S. M., Ferrer, R., & Hammoudeh, S. (2017b). Asymmetric determinants of CDS spreads: U.S. industry-level evidence through the NARDL approach. Economic Modelling, 60, 211-230.
    doi: https://doi.org/10.1016/j.econmod.2016.09.003
  25. Shahzad, S. J. H., Nor, S. M., Hammoudeh, S., & Shahbaz, M. (2017c). Directional and bidirectional causality between U.S. industry credit and stock markets and their determinants. International Review of Economics & Finance, 47, 46-61.
    doi: https://doi.org/10.1016/j.iref.2016.10.005
  26. Shahzad, S. J. H., Nor, S. M., Kumar, R. R., & Mensi, W. (2017d). Interdependence and contagion among industry-level US credit markets: an application of wavelet and VMD based copula approaches. Physica A: Statistical Mechanics and its Applications, 466, 310-324.
    doi: https://doi.org/10.1016/j.physa.2016.09.008
  27. Bodnar, T., & Zabolotskyy, T. (2013). Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization. Economic Annals-XXI, 11-12(1), 110-113.
    Retrieved from https://ea21journal.world/index.php/ea-v135-28/
  28. Cesarone, F., Moretti, J., & Tardella, F. (2016). Optimally chosen small portfolios are better than large ones. Economics Bulletin, 36(4), 1876-1891.
    Retrieved from http://www.accessecon.com/Pubs/EB/2016/Volume36/EB-16-V36-I4-P183.pdf
  29. Moosa, I. A., & Al-Deehani, T. M. (2009). The myth of international diversification. Economia Internazionale, 62, 383-406.
    Retrieved from http://www.iei1946.it/RePEc/ccg/MOOSA%20AL%20DEEHANI%20383_406.pdf
  30. Zhang, P. (2015). Multi-period possibilistic mean semivariance portfolio selection with cardinality constraints and its algorithm. Journal of Mathematical Modelling and Algorithms in Operations Research, 14(2), 239-253.
    doi: https://doi.org/10.1007/s10852-014-9268-6
  31. Zhang, P. (2016). An interval mean-average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints. Soft Computing, 20(3), 1203-1212.
    doi: https://doi.org/10.1007/s00500-014-1583-3
  32. Nor, S. M. & Wickremasinghe, G. (2017). Market efficiency and technical analysis during different market phases: further evidence from Malaysia. Investment Management and Financial Innovations, 14(2), 359-366.
    doi: https://doi.org/10.21511/imfi.14(2-2).2017.07

Received 10.06.2017

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