se: Standard error computation

In SharpeR: Statistical Significance of the Sharpe Ratio

Standard error computation

Description

Estimates the standard error of the Sharpe ratio statistic.

Usage

se(z, type)

## S3 method for class 'sr'
se(z, type = c("t", "Lo", "Mertens", "Bao"))

Arguments

z	an observed Sharpe ratio statistic, of class sr.
type	estimator type. one of "t", "Lo", "Mertens", "Bao"

Details

For an observed Sharpe ratio, estimate the standard error. The following methods are recognized:

t

The default, based on Johnson & Welch, with a correction for small sample size. Also known as 'Lo'.

Mertens

An approximation to the standard error taking into skewness and kurtosis of the returns distribution.

Bao

An even higher accuracty approximation using higher order moments.

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

See ‘The Sharpe Ratio: Statistics and Applications’, sections 2.5.1 and 3.2.3.

Value

an estimate of standard error.

Note

The units of the standard error are consistent with those of the input sr object.

Author(s)

Steven E. Pav [e-mail]

References

Sharpe, William F. "Mutual fund performance." Journal of business (1966): 119-138. https://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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/31.3-4.362")}

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

Bao, Yong. "Estimation Risk-Adjusted Sharpe Ratio and Fund Performance Ranking Under a General Return Distribution." Journal of Financial Econometrics 7, no. 2 (2009): 152-173. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/jjfinec/nbn022")}

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

Pav, S. E. "The Sharpe Ratio: Statistics and Applications." CRC Press, 2021.

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

See Also

sr-distribution functions, dsr, sr_variance.

Other sr: as.sr(), confint.sr(), dsr(), is.sr(), plambdap(), power.sr_test(), predint(), print.sr(), reannualize(), sr, sr_equality_test(), sr_test(), sr_unpaired_test(), sr_vcov(), summary.sr

Examples

asr <- as.sr(rnorm(128,0.2))
anse <- se(asr,type="t")
anse <- se(asr,type="Lo")

SharpeR documentation built on April 3, 2025, 7:36 p.m.