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Last data update: 2014.03.03

R: test for Sharpe ratio

sr_test

R Documentation

test for Sharpe ratio

Description

Performs one and two sample tests of Sharpe ratio on vectors of data.

Usage

sr_test(x,y=NULL,alternative=c("two.sided","less","greater"),
        zeta=0,ope=1,paired=FALSE,conf.level=0.95)

Arguments

`x`	a (non-empty) numeric vector of data values, or an object of class `sr`, containing a scalar sample Sharpe estimate.
`y`	an optional (non-empty) numeric vector of data values, or an object of class `sr`, containing a scalar sample Sharpe estimate. Only an unpaired test can be performed when at least one of `x` and `y` are of class `sr`
`alternative`	a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`zeta`	a number indicating the null hypothesis offset value, the S value.
`ope`	the number of observations per 'epoch'. For convenience of interpretation, The Sharpe ratio is typically quoted in 'annualized' units for some epoch, that is, 'per square root epoch', though returns are observed at a frequency of `ope` per epoch. The default value is 1, meaning the code will not attempt to guess what the observation frequency is, and no annualization adjustments will be made.
`paired`	a logical indicating whether you want a paired test.
`conf.level`	confidence level of the interval.
`...`	further arguments to be passed to or from methods.

Details

Given n observations xi from a normal random variable, with mean mu and standard deviation sigma, tests

H0: mu/sigma = S

against two or one sided alternatives.

Can also perform two sample tests of Sharpe ratio. For paired observations xi and yi, tests

H0: mu_x sigma_y = mu_y sigma_x

against two or one sided alternative, via sr_equality_test.

For unpaired (and independent) observations, tests

H0: mu_x / sigma_x - mu_y / sigma_y = S

against two or one-sided alternatives via the upsilon distribution.

Value

A list with class "htest" containing the following components:

`statistic`	the value of the t- or Z-statistic.
`parameter`	the degrees of freedom for the statistic.
`p.value`	the p-value for the test.
`conf.int`	a confidence interval appropriate to the specified alternative hypothesis. NYI for some cases.
`estimate`	the estimated Sharpe or difference in Sharpes depending on whether it was a one-sample test or a two-sample test. Annualized
`null.value`	the specified hypothesized value of the Sharpe or difference of Sharpes depending on whether it was a one-sample test or a two-sample test.
`alternative`	a character string describing the alternative hypothesis.
`method`	a character string indicating what type of test was performed.
`data.name`	a character string giving the name(s) of the data.

Author(s)

Steven E. Pav shabbychef@gmail.com

References

Sharpe, William F. "Mutual fund performance." Journal of business (1966): 119-138. http://ideas.repec.org/a/ucp/jnlbus/v39y1965p119.html

Pav, Steven. "Inference on the Sharpe ratio via the upsilon distribution.' Arxiv (2015). http://arxiv.org/abs/1505.00829

Examples

# should reject null
x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="greater")
x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="two.sided")
# should not reject null
x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="less")

# test for uniformity
pvs <- replicate(128,{ x <- sr_test(rnorm(1000),ope=253,alternative="two.sided")
                        x$p.value })
plot(ecdf(pvs))
abline(0,1,col='red') 
# testing an object of class sr
asr <- as.sr(rnorm(1000,1 / sqrt(253)),ope=253)
checkit <- sr_test(asr,zeta=0)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(SharpeR)

Attaching package: 'SharpeR'

The following object is masked from 'package:base':

    summary

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SharpeR/sr_test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: sr_test
> ### Title: test for Sharpe ratio
> ### Aliases: sr_test
> ### Keywords: htest
> 
> ### ** Examples
> 
> # should reject null
> x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="greater")
> x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="two.sided")
> # should not reject null
> x <- sr_test(rnorm(1000,mean=0.5,sd=0.1),zeta=2,ope=1,alternative="less")
> 
> # test for uniformity
> pvs <- replicate(128,{ x <- sr_test(rnorm(1000),ope=253,alternative="two.sided")
+                         x$p.value })
> plot(ecdf(pvs))
> abline(0,1,col='red') 
> # testing an object of class sr
> asr <- as.sr(rnorm(1000,1 / sqrt(253)),ope=253)
> checkit <- sr_test(asr,zeta=0)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>