When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

Abstract

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of nine improved covariance estimation procedures using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between the estimation period T and the number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than that obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover, many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary, when short selling is not allowed and T > N, the considered methods are unable to outperform the sample covariance in terms of realized risk, but can give much more diversified portfolios than that obtained with the sample covariance. When T < N, the use of the sample covariance matrix and of the pseudo-inverse gives portfolios with very poor performance.Portfolio optimization, Correlation structures, Statistical methods, Econophysics,

An adaptively managed dynamic portfolio selection model using a time-varying investment target according to the market forecast

“…Hui et al (1993) showed that for cases in which short sales were not allowed, the empirical performance of portfolios constructed using a Bayes estimator to improve estimation accuracy was no different from the performance of those using the sample mean. More recently, Pantaleo et al (2011) compared the empirical performance of various estimation procedures using a database including daily returns of 90 assets for a period of 11 years. Comparing the performance of 10 different covariance matrix estimators (including the sample covariance estimator), they showed that when short sales were not allowed and the length of the estimation time horizon was greater than the number of assets, portfolios using various sophisticated and complex methods did not significantly outperform those using the sample covariance estimator.…”

“…The AIS outlines steps for adaptive management of an investment portfolio constructed from the DPSM, rebalancing the portfolio according to a predetermined cycle, which is not necessarily fixed to 1 month, and estimating input parameters that are responsive to recent changes in the market on each rebalancing date. The simple sample mean and sample covariance matrix is used, based on the results of recent research (Hui et al, 1993;Pantaleo et al, 2011), while implementing the EWMA estimator for estimating input parameters. In this study, the performance of the AIS is empirically tested against benchmark indices in 10 different stock markets around the world.…”

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“…Use of alternative estimators has focused on the covariance matrix. Here, there are a multiplicity of approaches that are possible (e.g., see Pantaleo et al [29] for a study comparing nine different covariance estimators). Generic approaches used here include the following:…”

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“…In Markowitz portfolio optimsations, if the number of stocks (N) is greater than the number of historical returns per stock (T ), then estimating the sample covariance matrix is subject to significant error and is dominated by noise (Jagannathan and Ma 2003;Tola et al 2008) and using a sample covariance in such cirumstances can lead to a portfolio with very poor performance (Pantaleo et al 2010). The dimension ratio T /N must always exceed 1 in order to begin to mitigate this.…”