Minimum-Variance Portfolios Based on Covariance Matrices Using Implied Volatilities: Evidence from the German Market

摘要

This article compares the performance of minimum-variance portfolios based on four different covariance matrix estimators, using daily return data from the German stock market.To assess whether investing in ex ante minimum-variance portfolios is a recommendable way to achieve efficient portfolios in accordance with Markowitz's mean-variance optimization, the authors benchmark the four portfolios' performance against the German stock index DAX, which also determines the investable universe. This is the first study that uses not only historical volatility and covariance data, but also implied volatilities from the stock options market to estimate the covariance matrix.The article also analyzes how results change when the shrinkage method, suggested by Ledoit and Wolf in a 2003 article published in this journal, is applied to both the historical and the implied volatility estimators.The authors demonstrate that all minimum-variance portfolios outperform the DAX index. The implied-volatility estimator, modified by the shrinkage method, offered the best results in terms of volatility, return, and efficiency ratio. In contrast to previous empirical results, applying the shrinkage method to the historical sample covariance matrix yields little benefit, if any. However, applying the shrinkage method to the implied-volatility estimator significantly improves the quality of the covariance estimation, resulting in improved performance from the minimum-variance portfolio.