Fundamental indexation via smoothed cap weights

If prices of individual stocks are unbiased but noisy approximations to fundamental values, there will be a gap in returns between the standard cap-weighted market portfolio and the one based on fundamentals. The discrepancy occurs because, relative to fundamentals, cap-weights are too large (small) for stocks with positive (negative) deviations from fundamental values. It follows that the usual cap-weighted portfolio will underperform relative to the fundamental-based portfolio as long as prices revert to fundamental values. This has led Arnott et al. to propose new market indices based on a firm's fundamental size as measured by its revenues, number of employees, and so on. In this paper we follow the same principle but propose to estimate fundamental weights using a smoothed average of standard cap-weights. Since the putative excess returns of a fundamentals-weighted portfolio requires reversion to fundamental values, and because fundamental values are likely to change slowly, we can estimate current fundamentals by smoothing the time series of a stock's noisy prices. The determination of fundamental size in terms of accounting data is thereby replaced by a simple estimate based on price history. We derive expressions for expected returns of the market capitalization-based and fundamentals-based portfolios under various assumptions about (i) the random deviations from fundamental values and (ii) the change in fundamentals over time. We present empirical comparisons between portfolios and find the returns of the fundamentals-based portfolios exceed the standard indices by an amount comparable to the prior estimates that used accounting data to determine size.