test_MVSP {HDShOP}

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 (see Eq.(44) of Bodnar et al. 2021).

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 Bodnar et al. (2019).

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

Bodnar T, Dmytriv S, Okhrin Y, Parolya N, Schmid W (2021). “Statistical Inference for the Expected Utility Portfolio in High Dimensions.” IEEE Transactions on Signal Processing, 69, 1-14.

Bodnar T, Dmytriv S, Parolya N, Schmid W (2019). “Tests for the weights of the global minimum variance portfolio in a high-dimensional setting.” IEEE Transactions on Signal Processing, 67(17), 4479–4493.

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