Alternative Approaches to Multi-Factor Index Construction: Like-for-Like Comparisons
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In this paper we undertake a theoretical comparison of the exposure and diversification outcomes of multi-factor portfolios that use a Composite Index, a Composite Factor and a Multiple Tilt approach to index construction. A Composite Index is characterized as a “Top-down” methodology in which the multifactor portfolio is formed as a weighted average of separate single factor (or “sleeve”) portfolios. In contrast the Composite Factor and Multiple Tilt methods are characterized as “Bottom-up” techniques. The Composite Factor approach combines all factor values into a single score, which is then used to construct the multi-factor portfolio. The Multiple Tilt converts factor values into scores that are then multiplied together to determine the weights of stocks in the multi-factor portfolio. We construct Composite Index and Composite Factor outcomes using a simple and commonly employed multi-factor portfolio construction methodology; Selection and Weighting. Here single factor sleeve portfolios are created by selecting a given proportion of some initial stock universe which has been scored and ranked by a factor value. The resulting set of stocks may then be weighted according to the factor value itself, or on some other criteria concerned with capacity (e.g. market capitalization weighting), diversification (e.g. equal weighting) or risk (e.g. inverse volatility weighting), or a combination thereof. A Top-down Composite Index portfolio is constructed by averaging the single factor portfolio sleeves. A Bottom-up Composite Factor portfolio arises from the application of the same selection and weighting mechanism to a single composite or average multi-factor score
