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Last data update: 2014.03.03

R: test for optimal Sharpe ratio

sropt_test

R Documentation

test for optimal Sharpe ratio

Description

Performs one sample tests of Sharpe ratio of the Markowitz portfolio.

Usage

sropt_test(X,alternative=c("greater","two.sided","less"),
            zeta.s=0,ope=1,conf.level=0.95)

Arguments

`X`	a (non-empty) numeric matrix of data values, each row independent, each column representing an asset, or an object of class `sropt`.
`alternative`	a character string specifying the alternative hypothesis, must be one of `"two.sided"`, `"greater"` (default) or `"less"`. You can specify just the initial letter.
`zeta.s`	a number indicating the null hypothesis 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.
`conf.level`	confidence level of the interval. (not used yet)

Details

Suppose xi are n independent draws of a q-variate normal random variable with mean mu and covariance matrix Sigma. This code tests the hypothesis

H0: mu' Sigma^-1 mu = delta_0^2

The default alternative hypothesis is the one-sided

H1: mu' Sigma^-1 mu > delta_0^2

but this can be set otherwise.

Note there is no 'drag' term here since this represents a linear offset of the population parameter.

Value

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

`statistic`	the value of the T^2-statistic.
`parameter`	a list of 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.
`estimate`	the estimated optimal Sharpe, annualized
`null.value`	the specified hypothesized value of the optimal Sharpe.
`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

Examples


# test for uniformity
pvs <- replicate(128,{ x <- sropt_test(matrix(rnorm(1000*4),ncol=4),alternative="two.sided")
                        x$p.value })
plot(ecdf(pvs))
abline(0,1,col='red') 

# input a sropt objects:
nfac <- 5
nyr <- 10
ope <- 253
# simulations with no covariance structure.
# under the null:
set.seed(as.integer(charToRaw("be determinstic")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
asro <- as.sropt(Returns,drag=0,ope=ope)
stest <- sropt_test(asro,alternative="two.sided")

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/sropt_test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: sropt_test
> ### Title: test for optimal Sharpe ratio
> ### Aliases: sropt_test
> ### Keywords: htest
> 
> ### ** Examples
> 
> 
> # test for uniformity
> pvs <- replicate(128,{ x <- sropt_test(matrix(rnorm(1000*4),ncol=4),alternative="two.sided")
+                         x$p.value })
> plot(ecdf(pvs))
> abline(0,1,col='red') 
> 
> # input a sropt objects:
> nfac <- 5
> nyr <- 10
> ope <- 253
> # simulations with no covariance structure.
> # under the null:
> set.seed(as.integer(charToRaw("be determinstic")))
> Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
> asro <- as.sropt(Returns,drag=0,ope=ope)
> stest <- sropt_test(asro,alternative="two.sided")
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>