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Some Results on Bivariate Squared Maximum Sharpe Ratio

Author

Listed:
  • Samane Al-sadat Mousavi

    (Department of Statistics, College of Mathematics, Yazd University, Yazd P.O. Box 89195-741, Iran)

  • Ali Dolati

    (Department of Statistics, College of Mathematics, Yazd University, Yazd P.O. Box 89195-741, Iran)

  • Ali Dastbaravarde

    (Department of Statistics, College of Mathematics, Yazd University, Yazd P.O. Box 89195-741, Iran)

Abstract

The Sharpe ratio is a widely used tool for assessing investment strategy performance. An essential part of investing involves creating an appropriate portfolio by determining the optimal weights for desired assets. Before constructing a portfolio, selecting a set of investment opportunities is crucial. In the absence of a risk-free asset, investment opportunities can be identified based on the Sharpe ratios of risky assets and their correlation. The maximum squared Sharpe ratio serves as a useful metric that summarizes the performance of an investment opportunity in a single value, considering the Sharpe ratios of assets and their correlation coefficients. However, the assumption of a normal distribution in asset returns, as implied by the Sharpe ratio and related metrics, may not always hold in practice. Non-normal returns with a non-linear dependence structure can result in an overestimation or underestimation of these metrics. Copula functions are commonly utilized to address non-normal dependence structures. This study examines the impact of asset dependence on the squared maximum Sharpe ratio using copulas and proposes a copula-based approach to tackle the estimation issue. The performance of the proposed estimator is illustrated through simulation and real-data analysis.

Suggested Citation

  • Samane Al-sadat Mousavi & Ali Dolati & Ali Dastbaravarde, 2024. "Some Results on Bivariate Squared Maximum Sharpe Ratio," Risks, MDPI, vol. 12(6), pages 1-17, May.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:6:p:88-:d:1401095
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    References listed on IDEAS

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    1. Barillas, Francisco & Kan, Raymond & Robotti, Cesare & Shanken, Jay, 2020. "Model Comparison with Sharpe Ratios," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(6), pages 1840-1874, September.
    2. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    3. Dowd, Kevin, 2000. "Adjusting for risk:: An improved Sharpe ratio," International Review of Economics & Finance, Elsevier, vol. 9(3), pages 209-222, July.
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