Equities Risk

Optimal Number of Statistical Factors

A principal-component diagnostic for estimating the number of latent statistical factors in Australian equity returns.

Purpose

The objective is to estimate how many latent statistical factors are needed to summarise the common variation in Australian equity returns. This diagnostic uses information criteria proposed by Bai and Ng (2002), applied to rolling five-year return panels.

Interpretation

Lower values of the criterion indicate a more favourable balance between explanatory power and model complexity. The selected number of factors is the value that minimises the criterion. based on the analyses, we estimate a maximum of four statistical factors. These statistical factors are considered in addition to observable factors like firm attributes, loadings on economic factors, and industry membership.

Bai and Ng criterion 1 values for alternative numbers of principal components — Figure 1. Bai and Ng (2002) criterion 1 applied to the Australian equities return panel.

Bai and Ng criterion 2 values for alternative numbers of principal components — Figure 2. Bai and Ng (2002) criterion 2 applied to the Australian equities return panel.

See Bai, J. & Ng, S. (2002). Determining the number of factors in approximate factor models, Econometrica, 70(1), 191–221.