SharpeR (version 1.3.0)

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 [email protected]

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: 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)