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

Bodnar, Taras; Zabolotskyy, Taras

doi:10.1007/s10182-016-0270-3

Cited by 18 publications

(12 citation statements)

References 27 publications

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“…For example, Alexander and Baptista [3,4] suggested the application of the VaR and the CVaR as measures of the risk in Markowitz's optimization problem instead of the variance and examined the economic implications of a mean-VaR model for portfolio selection. A brief connection between the TP and the minimum VaR portfolio has been drawn by Bodnar and Zabolotskyy [19] while focusing mainly on the riskiness of an optimal portfolio which maximizes the Sharpe ratio. Following the lines of Bodnar et al [18], we obtain explicit relations of minimum VaR and minimum CVaR portfolio weights in terms of estimated tangency portfolio weights, where these higher moments come into play their role.…”

Section: Application Implications Of Main Resultsmentioning

confidence: 99%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

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In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order noncentral and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

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Section: Application Implications Of Main Resultsmentioning

confidence: 99%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

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“…The distribution ofŵ I when sampling from a Gaussian distribution is well established (Okhrin and Schmid 2006;Bodnar and Zabolotskyy 2017). In particular, the estimator S −1 is, by the law of large numbers, a consistent estimator of −1 and the consistency of (3) follows directly.…”

Section: Preliminariesmentioning

confidence: 99%

A risk perspective of estimating portfolio weights of the global minimum-variance portfolio

2019

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The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n). Keywords Global minimum-variance portfolio • Portfolio theory • High dimensional • Risk functions JEL Classification C13 • C18 • C44 • G11 We thank two anonymous reviewers for their insightful comments and helpful suggestions and the session participants at the German Statistical Society conference in Augsburg 2016 and those attending the seminar at the European University Viadrina in January 2017 for useful suggestions. The usual disclaimer applies.

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“…This model gives the opportunities, especially for individual investors to monitor their portfolio by getting higher returns instead of lower risk (Ivanova & Dospatliev, 2017;Vo et al, 2019). Moreover, the SRM model contributed to the efficient frontier in the Markowitz optimisation problem and also gave a strong opinion to minimise the risk of the portfolio (Bodnar & Zabolotskyy, 2017). Although constructed portfolio was less diversified compared to Naïve (1/N) allocation, the composition of portfolio weights of the constructed portfolio was able to achieve high annual returns per unit of risk that was suitable for individual investors (Hoe & Siew, 2016).…”

Section: Portfolio Optimisationmentioning

confidence: 99%

Market Timing and Stock Selection Strategies in Shariah- Compliant Stock Portfolio

Halim¹,

Elias²,

Kamil³

2021

JSSH

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This study focuses on market timing and stock selection strategies that could be implemented by individual investors of Shariah-compliant equity using the top ten constituents of the FTSE Bursa Malaysia Hijrah Shariah Index. Investors are assumed to enter and exit the stock market following the buy-and-sell signal from Moving Average Crossover. Meanwhile, for stock selection, this study aims to construct the optimal portfolio using the Sharpe Ratio Maximisation model and Naïve (1/N) portfolio. The level of market timing and selectivity skills of individual investors following the suggested investment strategies will be measured by using the Treynor-Mazuy model. The empirical results showed that the best Moving Average Crossover gave plausible trading frequencies and provided the most return to investors was the (1, 100, 0.01) strategy. Albeit, the stock allocation for the constructed portfolio was less diversified compared to the Naïve (1/N) portfolio, the composition of portfolio weights of the constructed portfolio was able to offer a more than average risk to reward ratio. Furthermore, in the out-of-sample framework, both portfolios outperformed the market benchmark. Unlike previous studies, this study backed tests the strategy and found that it was beneficial for individual investors of Shariah-compliant equities to enhance market timing and selectivity skills in stock investment.

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

Cited by 18 publications

References 27 publications

Higher order moments of the estimated tangency portfolio weights

Higher order moments of the estimated tangency portfolio weights

A risk perspective of estimating portfolio weights of the global minimum-variance portfolio

Market Timing and Stock Selection Strategies in Shariah- Compliant Stock Portfolio

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