Adjusting MV-efficient portfolio frontier bias for skewed and non-mesokurtic returns |
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| Institution: | 1. Department of Banking and Finance, National Chiayi University, No. 580, Sinmin Road, Chiayi City 60054, Taiwan;2. Department of Finance, National Yunlin University of Science & Technology, No. 123, University Road, Section 3, Douliou City 64002, Taiwan;3. Department of Wealth and Taxation Management, National Kaohsiung University of Applied Sciences, No. 415, Chien-Kung Road, Sanmin District, Kaohsiung City 80778, Taiwan;4. Graduate Institute of Finance, National Pingtung University of Science and Technology, No. 1, Hseuhfu Road, Neipu, Pingtung 91201, Taiwan;1. Department of Mathematics, University of Bayreuth, Germany;2. Department of Economics, University of Bayreuth, Germany;3. Public Choice Research Centre, University of Turku, Finland;1. Assistant Professor Department of Computer Science and Engineering Anna University Regional Office, Madurai, Tamilnadu, India;2. Professor Department of Information Technology K.L.N.College of Engineering, Pottapalayam, Sivaganga, Tamil Nadu, India;1. Rand Merchant Bank, 1 Merchant Place, Cnr Fredman Drive & Rivonia Road, Sandton 2196, South Africa;2. Research Associate, Faculty of Economics and Financial Sciences, Department of Finance and Investment Management, University of Johannesburg, PO Box 524, Aucklandpark, South Africa;3. Department of Finance and Investment Management, University of Johannesburg, Aucklandpark 2006, South Africa |
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| Abstract: | This study investigates the bias adjustment for mean–variance efficient portfolio frontiers due to population mean and variance estimation error in Taiwan stock market. Although Siegel and Woodgate (2007; Management Science, 53, 1005–1015) and Kan and Smith (2008; Management Science, 54, 1364–1380) suggested two portfolio frontiers that improved upon the out-of-sample performance of a traditional sample portfolio frontier. However, this study shows that, using the copula function and Gram-Charlier series, the two frontiers are theoretically biased toward the actual frontier unless returns behave normally, and the bias is related to the return skewness and kurtosis. Indeed, the two frontiers are empirically biased to the lower-left side of the actual ones, because the Taiwan stock returns are right-skewed and highly leptokurtic. Thus, this study thus proposes revised portfolio frontiers that are closer to the actual frontier than unrevised ones. This improvement may enhance the estimation accuracy of the capital market line, and hence this study can provide an effective investment reference. |
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| Keywords: | Mean–variance efficient Estimation error Portfolio frontier Copula function Gram-Charlier series |
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