# se: Standard error computation In SharpeR: Statistical Significance of the Sharpe Ratio

## Description

Estimates the standard error of the Sharpe ratio statistic.

## Usage

 ```1 2 3 4``` ```se(z, type) ## S3 method for class 'sr' se(z, type = c("t", "Lo")) ```

## Arguments

 `z` an observed Sharpe ratio statistic, of class `sr`. `type` estimator type. one of `"t", "Lo", "exact"` `...` further arguments to be passed to or from methods.

## Details

For an observed Sharpe ratio, estimate the standard error. There are two methods:

• The default, `t`, based on Johnson & Welch, with a correction for small sample size, also known as `Lo`.

• A method based on the exact variance of the non-central t-distribution, `exact`.

There should be very little difference between these except for very small sample sizes.

## Value

an estimate of standard error.

## Note

Eventually this should include corrections for autocorrelation, skew, kurtosis.

## 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

Johnson, N. L., and Welch, B. L. "Applications of the non-central t-distribution." Biometrika 31, no. 3-4 (1940): 362-389. http://dx.doi.org/10.1093/biomet/31.3-4.362

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

Opdyke, J. D. "Comparing Sharpe Ratios: So Where are the p-values?" Journal of Asset Management 8, no. 5 (2006): 308-336. http://ssrn.com/paper=886728

Walck, C. "Hand-book on STATISTICAL DISTRIBUTIONS for experimentalists." 1996. http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf

sr-distribution functions, `dsr`
Other sr: `as.sr`, `confint.sr`, `dsr`, `is.sr`, `plambdap`, `power.sr_test`, `predint`, `print.sr`, `reannualize`, `sr_equality_test`, `sr_test`, `sr_unpaired_test`, `sr_vcov`, `sr`, `summary`
 ```1 2 3``` ```asr <- as.sr(rnorm(128,0.2)) anse <- se(asr,type="t") anse <- se(asr,type="Lo") ```