SharpeR (version 1.4.0)

sric: Sharpe Ratio Information Coefficient

Description

Computes the Sharpe Ratio Information Coefficient of Paulsen and Soehl, an asymptotically unbiased estimate of the out-of-sample Sharpe of the in-sample Markowitz portfolio.

Usage

sric(z.s)

Value

The Sharpe Ratio Information Coefficient.

Arguments

z.s

an object of type sropt

Author

Steven E. Pav

Details

Let \(X\) be an observed \(T \times k\) matrix whose rows are i.i.d. normal. Let \(\mu\) and \(\Sigma\) be the sample mean and sample covariance. The Markowitz portfolio is $$w = \Sigma^{-1}\mu,$$ which has an in-sample Sharpe of \(\zeta = \sqrt{\mu^{\top}\Sigma^{-1}\mu}.\)

The Sharpe Ratio Information Criterion is defined as $$SRIC = \zeta - \frac{k-1}{T\zeta}.$$ The expected value (over draws of \(X\) and of future returns) of the \(SRIC\) is equal to the expected value of the out-of-sample Sharpe of the (in-sample) portfolio \(w\) (again, over the same draws.)

References

Paulsen, D., and Soehl, J. "Noise Fit, Estimation Error, and Sharpe Information Criterion." arxiv preprint (2016): https://arxiv.org/abs/1602.06186

See Also

Other sropt Hotelling: asnr_confint(), inference()

Examples

# generate some sropts
nfac <- 3
nyr <- 5
ope <- 253
# simulations with no covariance structure.
# under the null:
set.seed(as.integer(charToRaw("fix seed")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
asro <- as.sropt(Returns,drag=0,ope=ope)
srv <- sric(asro)