sric {SharpeR}

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)

Arguments

z.s

an object of type sropt

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.)

Value

The Sharpe Ratio Information Coefficient.

Author(s)

Steven E. Pav [e-mail]

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)