test_MVSP: Test for mean-variance portfolio weights

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

Test for mean-variance portfolio weights

Description

A high-dimensional asymptotic test on the mean-variance efficiency of a given portfolio with the weights \rm{w}_0. The tested hypotheses are

H_0: w_{MV} = w_0 \quad vs \quad H_1: w_{MV} \neq w_0.

The test statistic is based on the shrinkage estimator of mean-variance portfolio weights \insertCite@see Eq.(44) of @BDOPS2021HDShOP.

Usage

test_MVSP(gamma, x, w_0, beta = 0.05)

Arguments

gamma	a numeric variable. Coefficient of risk aversion.
x	a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.
w_0	a numeric vector of tested weights.
beta	a significance level for the test.

Details

Note: when gamma == Inf, we get the test for the weights of the global minimum variance portfolio as in Theorem 2 of \insertCiteBDPS2019;textualHDShOP.

Value

Element	Description
alpha_hat	the estimated shrinkage intensity
alpha_sd	the standard deviation of the shrinkage intensity
alpha_lower	the lower bound for the shrinkage intensity
alpha_upper	the upper bound for the shrinkage intensity
T_alpha	the value of the test statistic
p_value	the p-value for the test

References

\insertAllCited

Examples

n<-3e2 # number of realizations
p<-.5*n # number of assets
b<-rep(1/p,p)
gamma<-1

x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)

T_alpha <- test_MVSP(gamma=gamma, x=x, w_0=b, beta=0.05)
T_alpha

HDShOP documentation built on May 29, 2024, 2:20 a.m.