How risky is the optimal portfolio which maximizes the Sharpe ratio?

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• 作者：Taras Bodnar ; Taras Zabolotskyy
• 关键词：Tangent portfolio ; Sharpe ratio ; Value ; at ; Risk ; Parameter uncertainty ; Elliptically contoured distributions
• 刊名：AStA Advances in Statistical Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：101
• 期：1
• 页码：1-28
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Econometrics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1863-818X
• 卷排序：101

文摘

In this paper, we investigate the properties of the optimal portfolio in the sense of maximizing the Sharpe ratio (SR) and develop a procedure for the calculation of the risk of this portfolio. This is achieved by constructing an optimal portfolio which minimizes the Value-at-Risk (VaR) and at the same time coincides with the tangent (market) portfolio on the efficient frontier which is related to the SR portfolio. The resulting significance level of the minimum VaR portfolio is then used to determine the risk of both the market portfolio and the corresponding SR portfolio. However, the expression of this significance level depends on the unknown parameters which have to be estimated in practice. It leads to an estimator of the significance level whose distributional properties are investigated in detail. Based on these results, a confidence interval for the suggested risk measure of the SR portfolio is constructed and applied to real data. Both theoretical and empirical findings document that the SR portfolio is very risky since the corresponding significance level is smaller than 90 % in most of the considered cases.