Estimation of growth in fund models

TL;DR

This paper analyzes how estimation errors affect growth in fund models, proposing a shrinkage method that improves stability and growth potential in empirical settings.

Contribution

It introduces a shrinkage estimation technique for fund models that reduces growth loss and enhances stability compared to traditional Bayesian estimates.

Findings

Loss of growth is proportional to the number of funds.

Shrinkage estimates outperform unrestricted Bayesian estimates in empirical tests.

Growth loss increases with the size of the investment universe.

Abstract

Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as models where the global growth-optimal portfolio only involves investment in the aforementioned funds. The loss of growth due to estimation error in fund models under local frequentist estimation is determined entirely by the number of funds. Furthermore, under a general filtering framework for Bayesian estimation, the loss of growth increases as the investment universe does. A shrinkage method that targets maximal growth with the least amount of deviation is proposed. Empirical evidence suggests that shrinkage gives a stable estimate that more closely follows growth potential than an unrestricted Bayesian estimate.