test_MVSP

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 @BDOPS2021HDShOP.

Constructs shrinkage estimators of high-dimensional mean-variance portfolios and performs
high-dimensional tests on optimality of a given portfolio. The techniques developed in
Bodnar et al. (2018 <doi:10.1016/j.ejor.2017.09.028>, 2019 <doi:10.1109/TSP.2019.2929964>,
2020 <doi:10.1109/TSP.2020.3037369>, 2021 <doi:10.1080/07350015.2021.2004897>)
are central to the package. They provide simple and feasible estimators and tests for optimal
portfolio weights, which are applicable for 'large p and large n' situations where p is the
portfolio dimension (number of stocks) and n is the sample size. The package also includes tools
for constructing portfolios based on shrinkage estimators of the mean vector and covariance matrix
as well as a new Bayesian estimator for the Markowitz efficient frontier recently developed by
Bauder et al. (2021) <doi:10.1080/14697688.2020.1748214>.

Dmitry Otryakhin

HDShOP

High-Dimensional Shrinkage Optimal Portfolios

Taras Bodnar

Solomiia Dmytriv

Yarema Okhrin

Nestor Parolya

test_MVSP function

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

Arguments

Test for mean-variance portfolio weights — test_MVSP

<dl>

<dt>gamma</dt>
<dd>a numeric variable. Coefficient of risk aversion.</dd>


<dt>x</dt>
<dd>a p by n matrix or a data frame of asset returns. Rows represent
different assets, columns -- observations.</dd>


<dt>w_0</dt>
<dd>a numeric vector of tested weights.</dd>


<dt>beta</dt>
<dd>a significance level for the test.</dd>

</dl>

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

test_MVSP: Test for mean-variance portfolio weights

Description

Usage

Value

Arguments

Details

References

Examples