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Determination the Parameters of Markowitz Portfolio Optimization Model

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  • Ertugrul Bayraktar
  • Ayse Humeyra Bilge

Abstract

The main purpose of this study is the determination of the optimal length of the historical data for the estimation of statistical parameters in Markowitz Portfolio Optimization. We present a trading simulation using Markowitz method, for a portfolio consisting of foreign currency exchange rates and selected assets from the Istanbul Stock Exchange ISE 30, over the period 2001-2009. In the simulation, the expected returns and the covariance matrix are computed from historical data observed for past n days and the target returns are chosen as multiples of the return of the market index. The trading strategy is to buy a stock if the simulation resulted in a feasible solution and sell the stock after exactly m days, independently from the market conditions. The actual returns are computed for n and m being equal to 21, 42, 63, 84 and 105 days and we have seen that the best return is obtained when the observation period is 2 or 3 times the investment period.

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  • Ertugrul Bayraktar & Ayse Humeyra Bilge, 2012. "Determination the Parameters of Markowitz Portfolio Optimization Model," Papers 1210.5859, arXiv.org.
    • Handle: RePEc:arx:papers:1210.5859
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    1. repec:oup:jfinec:v:10:y:2012:i:1:p:164-197 is not listed on IDEAS
    2. Bertille Antoine, 2010. "Portfolio Selection with Estimation Risk: A Test-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 10(1), pages 164-197, 2012 10 1.
    3. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    4. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
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    1. Pagnoncelli, Bernardo K. & Cifuentes, Arturo & Denis, Gabriela, 2017. "A two-step hybrid investment strategy for pension funds," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 574-583.
    2. Gutierrez, Tomás & Pagnoncelli, Bernardo & Valladão, Davi & Cifuentes, Arturo, 2019. "Can asset allocation limits determine portfolio risk–return profiles in DC pension schemes?," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 134-144.

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