Description Usage Arguments Details Value Author(s) See Also Examples

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

1 2 | ```
sropt_test(X,alternative=c("greater","two.sided","less"),
zeta.s=0,ope=1,conf.level=0.95)
``` |

`X` |
a (non-empty) numeric matrix of data values, each row independent,
each column representing an asset, or an object of
class |

`alternative` |
a character string specifying the alternative hypothesis,
must be one of |

`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 |

`conf.level` |
confidence level of the interval. (not used yet) |

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.

A list with class `"htest"`

containing the following components:

`statistic` |
the value of the |

`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. |

Steven E. Pav [email protected]

Other sropt: `as.sropt`

,
`confint.sr`

, `dsropt`

,
`is.sropt`

, `pco_sropt`

,
`power.sropt_test`

,
`reannualize`

, `sropt`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# 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")
``` |

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