The CS Character and Limitations of the Sharpe Ratio
17 Pages Posted: 11 Oct 2010
Date Written: October 5, 2010
Abstract
Aside from mean return, the Sharpe ratio probably is the financial world’s most ubiquitous statistic (Sharpe 1966, 1994). Introduced forty years ago and widely used in portfolio construction and performance measurement of conventional equity and bond investments, the Sharpe ratio now is, to the chagrin of its creator, also routinely reported by hedge fund and fund of hedge fund managers.
This paper is the first of two that examine the limitations of the Sharpe ratio and introduces new statistics that provide simple and robust tests of financial data for indications that use of the Sharpe ratio is inappropriate. We provide a practical substitute for the Sharpe ratio using standard dispersion - a replacement for standard deviation - as a preferred common unit of risk.
In this paper, we examine the conditions under which one may expect the Sharpe ratio to reasonably measure and compare risk-adjusted returns in financial markets. This boils down to a single assumption: that standard deviation provides a common unit of risk among the various returns distributions. We show that, across a variety of randomly selected financial instruments such as equities, mutual funds, and equity indexes in developed and emerging markets, as well as hedge funds and hedge fund indexes, standard deviation fails to provide a common unit of risk.
Next we introduce the first CS character, a statistic that provides a simple test for the validity of the assumption that standard deviation provides a common unit of risk. Applied to our examples, the first CS character confirms observations and provides a simple test for the applicability of standard deviation as a risk measure. We discuss the first CS character’s genesis from our research into the properties of Omega functions and the natural statistics they generate. Then we consider the first CS character’s remarkable sampling properties and provide examples of its use that rely on these properties.
In the second paper, we outline the mathematical background of CS characters and standard dispersion. Replacing standard deviation with standard dispersion provides our generalization of the Sharpe ratio. We show in a number of examples that using standard dispersion produces significantly different results from the Sharpe ratio and that these results will impact portfolio construction and performance measurement.
Keywords: Standard Deviation, Standard Dispersion, CS Character
JEL Classification: G11, G14
Suggested Citation: Suggested Citation