Using SharpeR

The SharpeR package provides basic functionality for testing signif-icance of the Sharpe ratio of a series of returns, and of the Markowitz portfolio on a number of possibly correlated assets.[15] The goal of the package is to make it simple to estimate profitability (in terms of risk-adjusted returns) of strategies or asset streams. 1 The Sharpe ratio and Optimal Sharpe ratio Sharpe defined the ‘reward to variability ratio’, now known as the ‘Sharpe ratio’, as the sample statistic ζ ̂ = µ̂ σ̂ where µ ̂ is the sample mean, and σ ̂ is the sample standard deviation. [15] The Sharpe ratio was later redefined to include a ‘risk-free ’ or ‘disastrous rate of return’: ζ ̂ = (µ̂ − r0) /σ̂. It is little appreciated in quantitative finance that the Sharpe ratio is iden-tical to the sample statistic proposed by Gosset in 1908 to test for zero mean when the variance is unknown. [5] The ‘t-test ’ we know today, which includes an adjustment for sample size, was formulated later by Fisher. [4] Knowing that the Sharpe ratio is related to the t-statistic provides a ‘natural arbitrage, ’ since the latter has been extensively studied. Many of the interesting properties of the t-statistic can be translated to properties about the Sharpe ratio. Also little appreciated is that the multivariate analogue of the t-statistic, Hotelling’s T 2, is related to the Markowitz portfolio. Consider the following portfolio optimization problem: max ν̂:ν̂⊤Σ̂ν̂≤R2 ν̂ µ̂ − r0√ ν