# predint: prediction interval for Sharpe ratio In SharpeR: Statistical Significance of the Sharpe Ratio

## Description

Computes the prediction interval for Sharpe ratio.

## Usage

 ```1 2``` ```predint(x,oosdf,oosrescal=1/sqrt(oosdf+1),ope=NULL,level=0.95, level.lo=(1-level)/2,level.hi=1-level.lo) ```

## Arguments

 `x` a (non-empty) numeric vector of data values, or an object of class `sr`. `oosdf` the future (or 'out of sample', thus 'oos') degrees of freedom. In the vanilla Sharpe case, this is the number of future observations minus one. `oosrescal` the rescaling parameter for the future Sharpe ratio. The default value holds for the case of unattributed models ('vanilla Shape'), but can be set to some other value to deal with the magnitude of attribution factors in the future period. `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 to take the same `ope` from the input `x` object, if it is unambiguous. `level` the confidence level required. `level.lo` the lower confidence level required. `level.hi` the upper confidence level required.

## Details

Given n_0 observations xi from a normal random variable, with mean mu and standard deviation sigma, computes an interval [y_1,y_2] such that with a fixed probability, the sample Sharpe ratio over n future observations will fall in the given interval. The coverage is over repeated draws of both the past and future data, thus this computation takes into account error in both the estimate of Sharpe and the as yet unrealized returns.

## Value

A matrix (or vector) with columns giving lower and upper confidence limits for the parameter. These will be labelled as level.lo and level.hi in %, e.g. `"2.5 %"`

## Author(s)

Steven E. Pav [email protected]

## 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

`confint.sr`.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# should reject null etc <- predint(rnorm(1000,mean=0.5,sd=0.1),oosdf=127,ope=1) etc <- predint(matrix(rnorm(1000*5,mean=0.05),ncol=5),oosdf=63,ope=1) # check coverage mu <- 0.0005 sg <- 0.013 n1 <- 512 n2 <- 256 p <- 100 x1 <- matrix(rnorm(n1*p,mean=mu,sd=sg),ncol=p) x2 <- matrix(rnorm(n2*p,mean=mu,sd=sg),ncol=p) sr1 <- as.sr(x1) sr2 <- as.sr(x2) ## Not run: # takes too long to run ... etc1 <- predint(sr1,oosdf=n2-1,level=0.95) is.ok <- (etc1[,1] <= sr2\$sr) & (sr2\$sr <= etc1[,2]) covr <- mean(is.ok) ## End(Not run) ```

SharpeR documentation built on Oct. 8, 2018, 1:05 a.m.