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Sample and realized minimum variance portfolios: Estimation, statistical inference, and tests

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Abstract The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. The estimation of the GMVP weights is therefore of much importance for financial investors. The GMVP weights depend only on the inverse covariance matrix of returns on financial risky assets, for this reason the estimated GMVP weights are subject to substantial estimation risk, especially in high‐dimensional portfolio settings. In this paper we review the recent literature on traditional sample estimators for the unconditional GMVP weights which are typically based on daily asset returns, as well as on modern realized estimators for the conditional GMVP weights based on intraday high‐frequency returns. We present various types of GMVP estimators with the corresponding stochastic results, discuss statistical tests and point on some directions for further research. Our empirical application illustrates selected properties of realized GMVP weights. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Models > Multivariate Models
Markowitz mean–variance efficient frontier in (σ − μ)‐space and the GMVP as its starting point
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The p‐value plots for the tests as in (19) and (20) whether the target weights computed as in (f), (g), (h), (i) from above to below, are valid proxies for the original realized GMVP weights
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The p‐value plots for the tests as in (19) and (20) whether the target weights computed as in (a), (b), (c), (d), (e) from above to below, are valid proxies for the original realized GMVP weights
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Envelope time series plots of realized GMVP weights ωt, ω(zc),t, ω(ec),t. The solid lines are 5%‐, median (50%) and 95%‐sample quantiles of k = 100 GMVP weight series for each time point
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Statistical Models > Multivariate Models
Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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