Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes

Oops! I Shrunk the Sample Covariance Matrix Again: Blockbuster Meets Shrinkage

Journal of Financial Econometrics ◽

10.1093/jjfinec/nbaa020 ◽

2020 ◽

Author(s):

Gianluca De Nard

Keyword(s):

Covariance Matrix ◽

Historical Data ◽

State Of The Art ◽

General Structure ◽

Asset Returns ◽

Linear Shrinkage ◽

Shrinkage Estimator ◽

Sample Covariance ◽

Optimal Linear ◽

Asset Classes

Abstract Existing shrinkage techniques struggle to model the covariance matrix of asset returns in the presence of multiple-asset classes. Therefore, we introduce a Blockbuster shrinkage estimator that clusters the covariance matrix accordingly. Besides the definition and derivation of a new asymptotically optimal linear shrinkage estimator, we propose an adaptive Blockbuster algorithm that clusters the covariance matrix even if the (number of) asset classes are unknown and change over time. It displays superior all-around performance on historical data against a variety of state-of-the-art linear shrinkage competitors. Additionally, we find that for small- and medium-sized investment universes the proposed estimator outperforms even recent nonlinear shrinkage techniques. Hence, this new estimator can be used to deliver more efficient portfolio selection and detection of anomalies in the cross-section of asset returns. Furthermore, due to the general structure of the proposed Blockbuster shrinkage estimator, the application is not restricted to financial problems.

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The Covariance Matrix between Real Assets

The Journal of Portfolio Management ◽

10.3905/jpm.2018.45.1.085 ◽

2018 ◽

Keyword(s):

Covariance Matrix ◽

Private Equity ◽

Investment Risk ◽

Cross Sectional ◽

Time Variance ◽

The Matrix ◽

Trade Prices ◽

Asset Classes ◽

The Cross ◽

Real Assets

For real assets such as private equity, infrastructure, and real estate, computing the time-variance of trade prices is of limited interest because there is not much trading in these assets. The author argues that it is more meaningful to use variance measures over the cross section as indicators for investment risk. In a large database of funds invested in sparsely traded assets, the cross-sectional variance—or dispersion—of fund performances is measured within and between the asset classes in which they are invested. The covariance matrix that is estimated in this way has features similar to the matrix between regularly traded assets that is computed over time. The author argues that the matrix provides a practical framework for analyzing risk and constructing portfolios invested in real assets with the same methods that are habitually employed on liquid assets.

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