*Yuliya Plyakha, Raman Uppal and Grigory Vilkov discover a surprising crop of non-systematic alpha generated by the monthly rebalancing process*

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 objective was to compare the performance of the equal-weighted portfolio relative with 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 rebalancing the equal-weight portfolio.

To undertake our analysis, we constructed equal, value, and price-weighted portfolios from 100 stocks randomly selected from the constituents of the S&P 500 index over the past 40 years.

We found the equal-weighted portfolio with monthly rebalancing outperformed the value and price-weighted portfolios in terms of total mean return and four-factor alpha from the Fama & French and Carhart models.

The total return of the equal-weighted portfolio was higher than that of the value and price-weighted portfolios by 271 and 112 basis points a year. The four-factor alpha of the equal-weighted portfolio was 175 basis points a year, more than 2.5 times the 60 and 67 basis points a 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, had a higher standard deviation and kurtosis compared with the value and price-weighted portfolios. The volatility of the return on the equal-weighted portfolio was 17.90% a year, which was higher than the 15.83% and 16.46% for the value and price-weighted portfolios. However, the skewness of the equal-weighted portfolio was less negative than the skewness of the value and price-weighted portfolios.

Despite the unfavourable volatility and kurtosis, the Sharpe ratio of the equal-weighted portfolio at 0.4275 was higher than those of the value and price-weighted portfolios - 0.3126 and 0.3966, respectively.

The higher return and less negative skewness of the equal-weighted portfolio also led to a higher certainty-equivalent return, which, for an investor with power utility and relative risk aversion of two, was 0.0994 per annum for the equal-weighted portfolio, compared with 0.0793 and 0.0930 for the value and price-weighted portfolios, respectively.

These results imply that the source of the superior performance of the equal-weighted portfolio is its significantly higher mean return, along with its less-negatively skewed returns.

To understand the reasons for the superior performance of the equal-weighted portfolio, we first used the monotonicity tests developed by Patton & Timmermann to see if there was a relationship between a particular characteristic of stocks and the total return of the equal-weighted portfolio, relative to the value and price-weighted portfolios.

These tests indicated that the returns of the equal-weighted portfolios relative to the returns of the value and price-weighted portfolios were monotonically decreasing with size and price, and increasing with idiosyncratic volatility.

Book-to-market was monotonically related to the difference in returns of only the equal and value-weighted portfolios, while 12-month momentum was related to the difference in returns of only the equal and price-weighted portfolios.

Motivated by these findings, we used the standard four-factor model 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.

We found that of the total excess mean return of 271 basis points a year earned by the equal-weighted portfolio over the value-weighted portfolio, 42% came 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% came from the difference in alpha and only 4% from the difference in systematic return. The proportional split between systematic return and alpha was also similar after adjusting for transaction costs of 50 basis points.

We found the higher systematic return of the equal-weighted portfolio came from its higher exposure to the market, size, and value factors. However, the equal-weighted portfolio had a more negative exposure to the momentum factor than the value and price-weighted portfolios.

We also extended the four-factor model by including French's systematic reversal factor and found that 11% of the four-factor alpha of the equal-weighted portfolio could be attributed to exposure to the reversal factor. However, including the reversal factor did not affect the alphas of the value and price-weighted portfolios, both of which remained insignificant.

Finally, we demonstrated through two experiments that the higher alpha and less negative skewness of the equal-weighted portfolio were a consequence of the monthly rebalancing to maintain equal weights, an implicitly contrarian strategy that exploits the reversal in stock prices on a monthly frequency.

In the first experiment, we reduced the rebalancing frequency of the equal-weighted portfolio from one month to six months, and found the excess alpha earned by the equal-weighted portfolio decreased and the skewness of the portfolio return became more negative. When the rebalancing frequency was reduced to 12 months, the alpha of the equal-weighted strategy was indistinguishable from that of the value and price-weighted strategies.

In the second experiment, we kept the weights of the value and price-weighted portfolios artificially fixed so that they had the contrarian flavour of the equal-weighted portfolio, and we found this increased their alpha and made their skewness less negative. If we kept 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 equal weights of the equal-weighted portfolio, that is responsible for the alpha it earns, but the monthly rebalancing.

We checked the robustness of our results along a variety of dimensions. We considered not just one portfolio with 100 stocks but resampled to select 1,000 portfolios, and all the results we reported were based on the returns averaged across these 1,000 portfolios.

We also considered portfolios with 30, 50, 200, and 300 stocks (again, resampling more than 1,000 portfolios), mid-cap stocks from the S&P 400, and small-cap stocks from the S&P 600. We also carried out a number of tests using simulated data.

Finally, we studied the performance of the equal-weighted portfolio relative to the value- and price-weighted portfolios if one had invested in the strategy at the peak of the business cycle (March 2001 or December 2007) or the trough (November 2001). We found that our results were robust in all these variations.

The answer to the question, therefore, is that the equal-weighted portfolio outperforms the value and price-weighted portfolios partly because of its higher exposure to market, size, and value-risk factors, and partly because of its higher alpha.

The source of this alpha is the portfolio's monthly rebalancing that takes advantage of reversal, idiosyncratic volatility, and lead-lag characteristics of stock returns at the monthly frequency.

**Grigory Vilkov is assistant professor for derivatives and Yuliya Plyakha is a PhD candidate at the Goethe University, Frankfurt. Raman Uppal is professor of finance at the EDHEC Business School. This is a summary of a paper that won the $50,000 first prize in the 2011 Standard & Poor's Index Versus Active (SPIVA) Research Awards. The latest version of the paper can be downloaded from http://tinyurl.com/dy897t3**

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