sr_unpaired_test {SharpeR} | R Documentation |
test for equation on unpaired Sharpe ratios
Description
Performs hypothesis tests on a single equation on k independent samples of Sharpe ratio.
Usage
sr_unpaired_test(
srs,
contrasts = NULL,
null.value = 0,
alternative = c("two.sided", "less", "greater"),
ope = NULL,
conf.level = 0.95
)
Arguments
srs |
a (non-empty) list of objects of class |
contrasts |
an array of the constrasts, the |
null.value |
the constant null value, the |
alternative |
a character string specifying the alternative hypothesis,
must be one of |
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 |
conf.level |
confidence level of the interval. |
Details
For 1 \le j \le k
, suppose you have n_j
observations of a normal random variable with mean \mu_j
and
standard deviation \sigma_j
, with all observations
independent. Given constants a_j
and value b
, this
code tests the null hypothesis
H_0: \sum_j a_j \frac{\mu_j}{\sigma_j} = b
against two or one sided alternatives.
See ‘The Sharpe Ratio: Statistics and Applications’, section 3.3.1.
Value
A list with class "htest"
containing the following components:
statistic |
The Wald statistic. |
parameter |
The degrees of freedom of the Wald statistic. |
p.value |
the p-value for the test. |
conf.int |
a confidence interval appropriate to the specified alternative hypothesis. |
estimate |
the estimated equation value, just the weighted sum of the sample Sharpe ratios. Annualized |
null.value |
the specified hypothesized value of the sum of Sharpes. |
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. https://ideas.repec.org/a/ucp/jnlbus/v39y1965p119.html
Pav, S. E. "The Sharpe Ratio: Statistics and Applications." CRC Press, 2021.
See Also
sr_equality_test
, sr_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_test()
,
sr_vcov()
,
sr
,
summary.sr
Examples
# basic usage
set.seed(as.integer(charToRaw("set the seed")))
# default contrast is 1,-1,1,-1,1,-1
etc <- sr_unpaired_test(as.sr(matrix(rnorm(1000*6,mean=0.02,sd=0.1),ncol=6)))
print(etc)
etc <- sr_unpaired_test(as.sr(matrix(rnorm(1000*4,mean=0.0005,sd=0.01),ncol=4)),
alternative='greater')
print(etc)
etc <- sr_unpaired_test(as.sr(matrix(rnorm(1000*4,mean=0.0005,sd=0.01),ncol=4)),
contrasts=c(1,1,1,1),null.value=-0.1,alternative='greater')
print(etc)
inp <- list(as.sr(rnorm(500)),as.sr(runif(200)-0.5),
as.sr(rnorm(30)),as.sr(rnorm(100)))
etc <- sr_unpaired_test(inp)
inp <- list(as.sr(rnorm(500)),as.sr(rnorm(100,mean=0.2,sd=1)))
etc <- sr_unpaired_test(inp,contrasts=c(1,1),null.value=0.2)
etc$conf.int