sr_test: 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

a (non-empty) numeric vector of data values, or an object of class sr, containing a scalar sample Sharpe estimate.

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 epoc

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.

`Value`

A list with class "htest" containing the following components:
statisticthe value of the t- or Z-statistic.
parameterthe degrees of freedom for the statistic.
p.valuethe p-value for the test.
conf.inta confidence interval appropriate to the specified alternative hypothesis. NYI for some cases.
estimatethe estimated Sharpe or difference in Sharpes depending on whether it was a one-sample test or a two-sample test. Annualized
null.valuethe specified hypothesized value of the Sharpe or difference of Sharpes depending on whether it was a one-sample test or a two-sample test.
alternativea character string describing the alternative hypothesis.
methoda character string indicating what type of test was performed.
data.namea character string giving the name(s) of the data.

`Details`

Given $n$ observations $x_i$ from a normal random variable,
with mean $\mu$ and standard deviation $\sigma$, tests
$$H_0: \frac{\mu}{\sigma} = S$$
against two or one sided alternatives.
Can also perform two sample tests of Sharpe ratio. For paired observations
$x_i$ and $y_i$, tests
$$H_0: \frac{\mu_x}{\sigma_x} = \frac{\mu_u}{\sigma_y}$$
against two or one sided alternative, via
sr_equality_test.
For unpaired (and independent) observations, tests
$$H_0: \frac{\mu_x}{\sigma_x} - \frac{\mu_u}{\sigma_y} = S$$
against two or one-sided alternatives via the upsilon distribution.

`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

`See Also`

reannualize
sr_equality_test, sr_unpaired_test, t.test.
Other sr: as.sr,
  as.sr.data.frame,
  as.sr.default, as.sr.lm,
  as.sr.matrix,
  as.sr.timeSeries, as.sr.xts;
  confint.del_sropt,
  confint.sr, confint.sropt;
  dsr, psr, qsr,
  rsr; is.sr;
  plambdap, qlambdap,
  rlambdap; power.sr_test;
  predint; print.del_sropt,
  print.sr, print.sropt;
  reannualize, reannualize.sr,
  reannualize.sropt; se,
  se.sr; sr_equality_test;
  sr_unpaired_test; sr_vcov;
  sr

`Examples`

Run this code# 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)
Run the code above in your browser using DataLab