INVESTED: In Markets, in the Future, and in Society.

As an investor building a portfolio, your primary concern should be understanding the relationships between various assets within an investment universe. By seeking to understand these relationships, you’ll gain insight into the effects of various changes (like adding a new asset or changing overall asset weightings) on the aggregate risk and return of a portfolio.

This is important regardless of your portfolio construction approach, whether it be fundamental and discretionary, or quantitative and systematic. In the case of the latter “quantitative” approach, an accurate estimation will determine the extent to which a portfolio can capture its intended exposures.
Enter the covariance matrix: a mathematical device which captures the correlations and relative volatilities between different assets or asset classes. In layman’s terms, it gives us insight into the movement of asset prices in relation to one another. It provides an input for optimization frameworks, such as mean variance optimization and risk parity. While future returns are difficult to estimate with any degree of accuracy (though many attempt to), correlations and asset volatilities are more stable and predictable, making risk-driven portfolio construction attractive for quant managers.

Decades of academic and practitioner research have gone into improving the estimation of covariances so that they can be both accurate and responsive to market shifts. Statistical shrinkage is one of the techniques widely used in financial markets to accomplish this. It combines an estimate of the sample covariance matrix (a reactive, yet relatively inaccurate measure of the true covariance matrix) with a target matrix, which is easier to estimate and is more representative of the true covariance matrix. Shrinkage then adaptively adjusts the weight allocations between the target matrix and the sample matrix using statistical considerations.

In this interactive whitepaper (no sweat – the complexity has been stratified to match your comfort level with the material; you can do a deep dive or quickly skim the surface), the Viewpoint research team discusses the underlying assumptions of shrinkage methods along with their strengths and drawbacks. Its use is considered for multiple types of portfolios, showing how the opportunity set can have a significant impact on accuracy. In conclusion, using a composite estimator can utilize the short-term reactivity of shrinkage methods while avoiding the significant, long-term, and systemic biases of asset allocation.