The Sharpe Ratio’s Upper Bound of the Portfolios in the Presence of a Benchmark: Application to the US Financial Market

Abstract

[1] analyzed the performance of Madoff’s investment strategy using the Sharpe ratio. Going a further step, [2] calculated the upper bound of the Sharpe ratio given different conditions. The upper bound is the maximum of the Sharpe ratio that a portfolio can realize. The US financial market is one of the well developed and diversified market across the globe. Significant numbers of funds are based on the broader market index and its derivatives. In this article, the upper bound of the Sharpe ratio for the portfolio depending on the broader index is calculated. The upper bound estimated in this study will help investors and regulators in US and across the globe in general to evaluate the Sharpe ratio with caution and identify investment vehicles that are promising fictitious returns.