Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios?

Finance
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15 September, 2017

*Read the paper here.*

Simplicity is everything! According to **Ockham’s razor or** “**law of parsimony,**” among competing hypotheses, the one with the fewest assumptions should be selected. What can be simpler than an equal-weighted portfolio? — Probably nothing, and since ancient times financial advisors recommended splitting your wealth into equal parts, and put them in different assets. While after 1950s portfolio management has undergone a substantial revision in the form of the Markowitz modern portfolio theory, we see in the last two decades a vast development of various Smart Beta strategies, including a revival of the equal-weighted portfolio allocation.

Why is an equal-weighted portfolio becoming so popular? Why does it typically demonstrate better performance compared to traditional value- and price-weighted indices? Is the outperformance due to pure alpha or just a compensation of extra risk we are exposed to with the 1/N allocation?

These questions were in focus of the study that have claimed first prize (USD $50,000) in S&P Indices first annual SPIVA Awards program several years back. In short, it is an extremely meticulous investigation into the outperformance of equal-weighted portfolios. Using a broad array of statistical techniques, the paper demonstrates that the relative outperformance of equal weighting is driven not just by higher exposure to well-known systematic value and size factors, but via the built-in alpha of equal weighting approaches. An equal weight portfolio must be rebalanced periodically, in effect buying the losers and selling the winners.

It is important to understand the difference in performance of the equal- and value-weighted portfolios given the central role that the value-weighted market portfolio plays in asset pricing, for instance in the Capital Asset Pricing Model of Sharpe (1964), and also as a benchmark against which portfolio managers are evaluated. Our work is motivated by the finding in DeMiguel, Garlappi, and Uppal (2009) that the out-of-sample performance of an equal-weighted portfolio of stocks is significantly better than that of a value-weighted portfolio, and no worse than that of portfolios from a number of optimal portfolio selection models; Jacobs, Muller, and Weber (2010) extend this finding to other datasets and asset classes. Our objective in this paper is to compare the performance of the equal-weighted portfolio relative to the value- and price-weighted portfolios, and to understand the reasons for differences in performance across these three weighting rules. Our main contribution is to show that there are significant differences in the performance of equal-, value-, and price-weighted portfolios, and to explain that only a part of this is because of differences in exposure to systematic risk factors, and that a substantial proportion comes from the rebalancing required by the equal-weight portfolio.

To undertake our analysis, we construct equal-, value-, and price-weighted portfolios from 100 stocks randomly selected from the constituents of the S&P500 index over the last forty years. We find that the equal-weighted portfolio with monthly rebalancing outperforms the value- and price-weighted portfolios in terms of total mean return and four-factor alpha from the Fama and French (1993) and Carhart (1997) models. The total return of the equal-weighted portfolio is higher than that of the value- and price-weighted portfolios by 271 and 112 basis points per annum. The four-factor alpha of the equal-weighted portfolio is 175 basis points per year, which is more that 2.5 times the 60 and 67 basis points per year for the value- and price- weighted portfolios, respectively. The differences in total mean return and alpha are significant even after allowing for transactions costs of 50 basis points.

The equal-weighted portfolio, however, has a higher volatility (standard deviation) and kurtosis compared to the value- and price-weighted portfolios. The volatility of the return on the equal-weighted portfolio is 17.90% per annum, which is higher than the 15.83% and 16.46% for the value- and price-weighted portfolios; the kurtosis of 5.53 for the equal-weighted portfolio is also higher than the 4.83 and 5.36 for the value- and price-weighted portfolios. The skewness of the equal-weighted portfolio is less negative than the skewness of the value- and price-weighted portfolios: the skewness of the equal-weighted portfolio is 0.3266, compared to 0.3860 and 0.4996 for the value- and price-weighted portfolios, respectively.

Using the standard four-factor model (Fama and French (1993) and Carhart (1997)) to decompose the total returns of the equal-, value-, and price-weighted portfolios into a systematic component, which is related to factor exposure, and alpha, which is not related to factor exposure. We find that of the total excess mean return of 271 basis points per annum earned by the equal-weighted portfolio over the value-weighted portfolio, 42% comes from the difference in alpha and 58% from the excess systematic component. On the other hand, of the total excess mean return of 112 basis points earned by the equal-weighted portfolio relative to the price-weighted portfolio, 96% comes from the difference in alpha and only 4% from the difference in systematic return. The proportional split between systematic return and alpha is similar also after adjusting for transactions costs of 50 basis points. We find that the higher systematic return of the equal-weighted portfolio arises from its higher exposure to the market, size, and value factors; however, the equal- weighted portfolio has a more negative exposure to the momentum factor than the value- and price-weighted portfolios. We also extend the four-factor model by including the systematic reversal factor (constructed by K. French and available on his web site) and find that 11% of the four-factor alpha of the equal-weighted portfolio can be attributed to the exposure to the reversal factor. However, including the reversal factor does not affect the alphas of the value- and price-weighted portfolios, both of which stay insignificant.

Finally, we demonstrate through two experiments that the higher alpha and less negative skewness of the equal-weighted portfolio are a consequence of the monthly rebalancing to main- tain equal weights, which is implicitly a contrarian strategy that exploits the reversal in stock prices at the monthly frequency. In the first experiment, we reduce the rebalancing frequency of the equal-weighted portfolio. We find that as the rebalancing frequency decreases from 1 month to 6 months, the excess alpha earned by the equal-weighted portfolio decreases and the skewness of the portfolio return becomes more negative; when the rebalancing frequency is fur- ther reduced to 12 months, the alpha of the equal-weighted strategy is indistinguishable from that of the value- and price-weighted strategies. In the second experiment, we artificially keep the weights of the value- and price-weighted portfolios fixed so that they have the contrarian flavor of the equal-weighted portfolio, and we find that this increases their alpha and makes skewness less negative. If we keep the weights of the value- and price-weighted strategies fixed for 12 months, the alpha of these portfolios increases and is indistinguishable from that of the equal-weighted portfolio. An important insight from these two experiments is that it is not the initial weights of the equal-weighted portfolio, but the monthly rebalancing that is responsible for the alpha it earns, relative to the alphas for the value- and price-weighted portfolios.