mean_bs {HDShOP}

Bayes-Stein shrinkage estimator of the mean vector

Description

Bayes-Stein shrinkage estimator of the mean vector as suggested in Jorion (1986). The estimator is given by

\hat \mu_{BS} = (1-\beta) \bar x + \beta Y_0 1,

where \bar x is the sample mean vector, \beta and Y_0 are derived using Bayesian approach (see Eq.(14) and Eq.(17) in Jorion (1986)).

Usage

mean_bs(x)

Arguments

x

a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.

Value

a numeric vector containing the Bayes-Stein shrinkage estimator of the mean vector

References

Jorion P (1986). “Bayes-Stein estimation for portfolio analysis.” Journal of Financial and Quantitative Analysis, 279–292.

Examples

n <- 7e2 # number of realizations
p <- .5*n # number of assets
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)
mm <- mean_bs(x=x)