Sampling error and double shrinkage estimation of minimum variance portfolios

Shrinkage estimators of the covariance matrix are known to improve the stability over time of the Global Minimum Variance Portfolio (GMVP), as they are less error-prone. However, the improvement over the empirical covariance matrix is not optimal for small values of n, the estimation sample size. For typical asset allocation problems, with n small, this paper aims at proposing a new method to further reduce sampling error by shrinking once again traditional shrinkage estimators of the GMVP. First, we show analytically that the weights of any GMVP can be shrunk – within the framework of the ridge regression – towards the ones of the equally-weighted portfolio in order to reduce sampling error. Second, Monte Carlo simulations and empirical applications show that applying our methodology to the GMVP based on shrinkage estimators of the covariance matrix, leads to more stable portfolio weights, sharp decreases in portfolio turnovers, and often statistically lower (resp. higher) out-of-sample variances (resp. Sharpe ratios). These results illustrate that double shrinkage estimation of the GMVP can be beneficial for realistic small estimation sample sizes.