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

Performs a hypothesis test of equality of Sharpe ratios of p assets given paired observations.

1 2 3 4 |

`X` |
an |

`type` |
which approximation to use. |

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

`contrasts` |
an |

`vcov.func` |
a function which takes a model of class lm (one of
the form x ~ 1), and produces a variance-covariance matrix.
The default is |

Given *n* *i.i.d.* observations of the excess returns of
*p* strategies, we test

*H0: sr1 = sr2 = ...*

using the method of Wright, et. al.

More generally, a matrix of constrasts, *E* can be given, and we can
test

*H0: E s = 0,*

where *s* is the vector of Sharpe ratios of the *p* strategies.

When *E* consists of a single row (a single contrast), as is the
case when the default contrasts are used and only two strategies are
compared, then an approximate t-test can be performed against the
alternative hypothesis *Ha: E s > 0*

Both chi-squared and F- approximations are supported; the former is
described by Wright. *et. al.*, the latter by Leung and Wong.

Object of class `htest`

, a list of the test statistic,
the size of `X`

, and the `method`

noted.

Steven E. Pav [email protected]

Sharpe, William F. "Mutual fund performance." Journal of business (1966): 119-138. http://ideas.repec.org/a/ucp/jnlbus/v39y1965p119.html

Wright, J. A., Yam, S. C. P., and Yung, S. P. "A note on the test for the equality of multiple Sharpe ratios and its application on the evaluation of iShares." J. Risk. to appear. http://www.risk.net/journal-of-risk/technical-paper/2340067/a-test-for-the-equality-of-multiple-sharpe-ratios

Leung, P.-L., and Wong, W.-K. "On testing the equality of multiple Sharpe ratios, with application on the evaluation of iShares." J. Risk 10, no. 3 (2008): 15–30. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=907270

Memmel, C. "Performance hypothesis testing with the Sharpe ratio." Finance Letters 1 (2003): 21–23.

Ledoit, O., and Wolf, M. "Robust performance hypothesis testing with the Sharpe ratio." Journal of Empirical Finance 15, no. 5 (2008): 850-859. http://www.ledoit.net/jef2008_abstract.htm

Lo, Andrew W. "The statistics of Sharpe ratios." Financial Analysts Journal 58, no. 4 (2002): 36-52. http://ssrn.com/paper=377260

Other sr: `as.sr`

, `confint.sr`

,
`dsr`

, `is.sr`

,
`plambdap`

, `power.sr_test`

,
`predint`

, `print.sr`

,
`reannualize`

, `se`

,
`sr_test`

, `sr_unpaired_test`

,
`sr_vcov`

, `sr`

,
`summary`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | ```
# under the null
rv <- sr_equality_test(matrix(rnorm(500*5),ncol=5))
# under the alternative (but with identity covariance)
ope <- 253
nyr <- 10
nco <- 5
rets <- 0.01 * sapply(seq(0,1.7/sqrt(ope),length.out=nco),
function(mu) { rnorm(ope*nyr,mean=mu,sd=1) })
rv <- sr_equality_test(rets)
## Not run:
# using real data
if (require(quantmod)) {
get.ret <- function(sym,...) {
OHLCV <- getSymbols(sym,auto.assign=FALSE,...)
lrets <- diff(log(OHLCV[,paste(c(sym,"Adjusted"),collapse=".",sep="")]))
lrets[-1,]
}
get.rets <- function(syms,...) { some.rets <- do.call("cbind",lapply(syms,get.ret,...)) }
some.rets <- get.rets(c("IBM","AAPL","NFLX","SPY"))
pvs <- sr_equality_test(some.rets)
}
# test for uniformity
pvs <- replicate(1024,{ x <- sr_equality_test(matrix(rnorm(400*5),400,5),type="chisq")
x$p.value })
plot(ecdf(pvs))
abline(0,1,col='red')
## End(Not run)
## Not run:
if (require(sandwich)) {
set.seed(as.integer(charToRaw("0b2fd4e9-3bdf-4e3e-9c75-25c6d18c331f")))
n.manifest <- 10
n.latent <- 4
n.day <- 1024
snr <- 0.95
latent.rets <- matrix(rnorm(n.day*n.latent),ncol=n.latent) %*%
matrix(runif(n.latent*n.manifest),ncol=n.manifest)
noise.rets <- matrix(rnorm(n.day*n.manifest),ncol=n.manifest)
some.rets <- snr * latent.rets + sqrt(1-snr^2) * noise.rets
# naive vcov
pvs0 <- sr_equality_test(some.rets)
# HAC vcov
pvs1 <- sr_equality_test(some.rets,vcov.func=vcovHAC)
# more elaborately:
pvs <- sr_equality_test(some.rets,vcov.func=function(amod) {
vcovHAC(amod,prewhite=TRUE) })
}
## End(Not run)
``` |

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