|
Fundamental Indexation via Smoothed Cap Weights Authors: Chen Chen, Rong Chen, Gilbert W. Basset Source: Journal of Banking & Finance, vol. 31 Date: 2007 |
Cap-weighted indices were developed on the assumption that the market portfolio is mean-variance efficient. As the validity of this assumption has not been confirmed, however, alternative weighting systems have been proposed. Among them are the fundamental indices introduced by Arnott, Hsu, and Moore (2005). The underlying idea is that stock prices are noisy, which causes cap-weighted indices to over-weight over-valued stocks and under-weight under-valued stocks. So, Arnott, Hsu, and Moore propose instead an estimate of stock fundamental values to weight the indices, using accounting data as proxies for the fundamental values. In the present article, Chen, Chen, and Basset also propose fundamental indices, but with a statistical approach to deriving fundamental values from past stock prices. The underlying idea is that the observed prices are an unbiased but noisy representation of fundamental values and that fundamental values change slowly over time. So they propose a moving average of past prices as an estimate of fundamental prices.
The authors first provide a simple example with only two stocks to illustrate that fundamental weighting earns higher returns than capitalisation weighting, though fundamental weighting may under-perform during some time periods. They then provide the theoretical justifications for their approach. They show that the expected return of a fundamental-weighted portfolio is higher than that of a cap-weighted portfolio and that the spread between the two returns is related to the variance of the noise of stock prices. They then show that the fundamental-weighted portfolio’s outperformance of the cap-weighted portfolio depends on the size of the window of the moving average used to estimate the fundamental values, as well as on the evolution of fundamental value over time. They also establish that the returns of the portfolio derived with estimated fundamental weights are close to those obtained with exact fundamental weights.
To validate their method, they realised empirical tests over the period from January 1962 to December 2003 using CRSP data. They compare a cap-weighted index (CWI) and a fundamental-weighted index estimated using the median of the capitalisation weights over a twelve-month period. They refer to this latter index as the smoothed cap-weighted index (SCWI). This portfolio is rebalanced every twelve months. They show that the cap-weighted index puts greater weight on new economy stocks, while the smoothed cap-weighted index puts greater weight on old economy stocks. Index performance improves with longer estimation windows. In addition, the return volatility of the SCWI is lower than that of the cap-weighted index and this index outperforms the cap-weighted index.
The authors conclude that their approach provides similar results to those obtained by Arnott, Hsu, and Moore, with a different method. In addition, they observe that their approach is easier to implement and contains an analytical justification.
References
Arnott, R. D., J. C. Hsu, and P. Moore “Fundamental Indexation”, Financial Analysts Journal, vol. 61, n°2, 2005, p. 83-99.
