test for Sharpe ratio

Description

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

Usage

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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

See Also

reannualize

sr_equality_test, sr_unpaired_test, t.test.

Other sr: as.sr, confint.sr, dsr, is.sr, plambdap, power.sr_test, predint, print.sr, reannualize, se, sr_equality_test, sr_unpaired_test, sr_vcov, sr, summary

Examples

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# 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)

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