By: Andy Dougan, director, research and analytics
Factor index construction is a topic widely discussed at the moment. A major area of debate concerns the construction of multi-factor indexes. Should construction be top-down where separate single factor indexes are created and then combined by averaging weights? Or should the construction be bottom-up where a single integrated top-down portfolio is formed by weighting stocks in consideration of their all factor characteristics simultaneously? In this theoretical paper we consider three approaches, one top-down and two bottom-up, that shed some light on this dilemma.
Any previous attempts to compare top-down versus bottom-up approaches focus only on the dimension of factor exposure, whereas we emphasize that to make precise like-for-like comparisons we must also consider another dimension, i.e., portfolio diversification. In other words, factor exposure can only really be compared when portfolios display equivalent levels of diversification. Alternatively, matching the factor exposures of alternative construction approaches allows one to sensibly compare levels of diversification.
Therefore, we argue that confusion around superiority for top-down and bottom-up approaches stems from not incorporating both of these dimensions. In particular, we demonstrate that a popular top-down approach consisting of a composite of single factor Selection and Weighting portfolios has a superior exposure-diversification trade-off to a bottom-up Selection and Weighting approach based on a composite multi-factor for diverse portfolios for highly positively correlated factors. For concentrated portfolios and negatively correlated factors, the opposite is true.
Finally, we demonstrate that the bottom-up approach of multiple tilt always displays a superior factor exposure-diversification trade-off compared to the top-down approach.
Chart 1. Multiple Tilt versus Composite Index
Source: FTSE Russell. All data is hypothetical and for illustrative purposes only. Please see important legal disclosures.
For more information, download FTSE Russell's theoretical paper on Alternative approaches to multi-factor index construction
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