Shrinking the Covariance Matrix

The two-block covariance matrix and the CAPM

“…Specifically, we plan to evaluate the out-of-sample (ex-post) performance of the tangency portfolio that is constructed using a two-block covariance matrix. Stein, C. (1955) Ledoit and Wolf (2003), Jagannathan and Ma (2003), Disatnik and Benninga (2007), and DeMiguel et al (2009).…”

“…Namely, we are dealing here with relatively small-sized within-block covariances. Thus, like the shrinkage estimators advocated by Ledoit and Wolf (2003, 2004a, 2004b, and the portfolios of estimators advocated by Jagannathan and Ma (2000), Disatnik and Benninga (2007), and Fletcher (2009), the block matrix has the appealing property of covariance elements which are shrunk compared to the typically large covariances of the traditional sample matrix. Not only are the large covariances those responsible for the extreme short positions that are obtained so often when the mean-variance theory is implemented in practice, but as Michaud (1989) states, inverting the sample matrix with its large covariance elements also amplifies the sampling error.…”

“…Nevertheless, these short sale positions are still quite significant [see for example, Disatnik and Benninga (2007) and Disatnik and Katz (2012)]. …”

Estimation of Equicorrelated Diffusions from Incomplete Data

“…Some authors, like Wolf (2003, 2004) and Disatnik and Benninga (2007), however, argue that the estimation of the structured covariance matrix introduces specification errors, so propose a combination of structured and sample covariance. Wolf (2003, 2004) suggest shrinking extreme values of the sample covariance matrix toward the center.…”

A Comprehensive Portfolio Construction Under Stochastic Environment

“…But from an application point of view, Disatnik and Benninga, using historical data of NYSE stocks, showed that the optimal portfolios produced using the Shrinkage estimators are not significantly better than those produced using the traditional sample covariance matrix, see Disatnik and Benninga (2007).…”