sr_variance: sr_variance .

In SharpeR: Statistical Significance of the Sharpe Ratio

Description

Computes the variance of the sample Sharpe ratio.

Usage

sr_variance(snr, n, cumulants)

Arguments

snr	the population Signal Noise ratio. Often one will use the population estimate instead.
n	the sample size that the Shapre ratio is observed on.
cumulants	a vector of the third through fourth, or the third through seventh population cumulants of the random variable. More terms are needed for the higher accuracy approximation.

Details

The sample Sharpe ratio has variance of the form

V = \frac{1}{n}≤ft(1 + \frac{ζ^2}{2}\right) +\frac{1}{n^2}≤ft(\frac{19ζ^2}{8} + 2\right) -γ_1ζ≤ft(\frac{1}{n} + \frac{5}{2n^2}\right) +γ_2ζ^2≤ft(\frac{1}{4n} + \frac{3}{8n^2}\right) +\frac{5γ_3ζ}{4n^2} +γ_1^2≤ft(\frac{7}{4n^2} - \frac{3ζ^2}{2n^2}\right) +\frac{39γ_2^2ζ^2}{32n^2} -\frac{15γ_1γ_2ζ}{4n^2} +o≤ft(n^{-2}\right),

where ζ is the population Signal Noise ratio, n is the sample size, γ_1 is the population skewness, and γ_2 is the population excess kurtosis, and γ_3 through γ_5 are the fifth through seventh cumulants of the error term. This form of the variance appears as Equation (4) in Bao.

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

Value

the variance of the sample statistic.

Author(s)

Steven E. Pav [e-mail]

References

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. doi: 10.1093/jjfinec/nbn022

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

See Also

sr_bias.

Examples

# variance under normality:
sr_variance(1, 100, rep(0,5))

SharpeR documentation built on Aug. 18, 2021, 5:08 p.m.