By Greenbackd

Yesterday I took a look at the different ways of structuring an index suggested by Joel Greenblatt.

Greenblatt finds that an equal-weight portfolio far outperforms a market capitalization weight portfolio.

And for good reason. Greenblatt says that **market cap weighted indexes suffer from a systematic flaw – they increase the amount they own of a particular company as that company’s stock price increases.** So they **systematically invest too much in stocks when they are overpriced and too little in stocks when they are priced at bargain levels.** The equal weight index corrects this systematic flaw *to a degree *(the small correction is still worth 2.7 percent per year in additional performance). **An equally-weighted index will still own too much of overpriced stocks and too little of bargain-priced stocks, but in other cases, it will own more of bargain stocks and less of overpriced stocks. Since stocks in the index aren’t affected by price, errors will be random and average out over time.**

There is some good research on the structuring of indices. In a Janaury 2012 paper Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios? Yuliya Plyakha, Raman Uppal and Grigory Vilkov examine the performance of equal-, value-, and price-weighted portfolios of stocks in the major U.S. equity indices over the last four decades (note that here “value” weight is used in the academic sense, meaning “market capitalization weight”).

The researchers find **find that the equal-weighted portfolio with monthly rebalancing outperforms the value- and price-weighted portfolios in terms of total mean return, four factor alpha, Sharpe ratio, and certainty-equivalent return, even though the equal-weighted portfolio has greater portfolio risk.**(It’s interesting that they find the equal-weighted index possesses alpha. I think that says more about the calculation of alpha than it does about the equal-weight index, but I digress.)

They find that total return of the equal-weighted portfolio exceeds that of the value- and price-weighted because the equal-weighted portfolio has both a**higher return for bearing systematic risk and a higher alpha measured using the four-factor model. **The higher systematic return of the equal-weighted portfolio arises from its higher exposure to the market, size, and value factors.

They seem to agree with Greenblatt when they find that the higher alpha of the equal-weighted portfolio **arises from the monthly rebalancing** required to maintain equal weights, which is **a “contrarian strategy that exploits reversal and idiosyncratic volatility of the stock returns;** thus, **alpha depends only on the monthly rebalancing and not on the choice of initial weights.”**

[We demonstrate that the source of this extra alpha of the equal-weighted portfolio is the “contrarian” rebalancing each month that is required to maintain equal weights, which

exploits the “reversal” in stock prices that has been identified in the literature(see, for instance, Jegadeesh (1990) and Jegadeesh and Titman (1993, 2002)).To demonstrate our claim, we consider two experiments, which are in opposite directions. In the first experiment, we

reduce the frequency for rebalancing the equal-weighted portfolio from 1 month, to 6 months and then to 12 months.If our claim is correct, thenas we reduce the rebalancing frequency, we should see the alpha of the equal-weighted portfolio decrease toward the level of the alpha of the value- and price-weighted portfolios, which do not entail any rebalancing.In the second experiment,

we reverse the process and artificially fix the weights of the value- and price-weighted portfolios to give them the contrarian flavor of the equal-weighted portfolio.For instance, consider the case where the rebalancing frequency is t = 12 months. Then each month we change the weights of the value- and price-weighted portfolios so that they are the same as the initial weights at t = 0. Only after 12 months have elapsed, do we set the weights to be the true value and price weights. Then, again for the next 12 months, we keep the weights of the value- and price-weighted portfolios constant so that they are equal to the weights for these portfolios at the 12-month date. Only after another 12 months have elapsed do we set the weights to be the true value and price-weighted weights at t = 24 months. We undertake this experiment for rebalancing frequencies of 6 and 12 months. If our claim is correct, then as we keep fixed the weights of the value- and price-weighted portfolios for 6 months and 12 months, the alphas of these two portfolios should increase toward the alpha of the equal-weighted portfolio.

The results of both experiments confirm our hypothesis that it is the monthly rebalancing of the equal-weighted portfolio that generates the alpha for this strategy.Table 4 shows thatas we reduce the rebalancing frequency of the equal-weighted portfolio from the base case of 1 month to 6 months and then to 12 months, the per annum alpha of the equal-weighted portfolio drops from 175 basis points to 117 basis points and then to 80 basis points.Once the rebalancing frequency of the equal-weighted portfolio is 12 months, the difference in the alpha of the equal-weighted portfolio and that of the value- and price-weighted portfolios is no longer statistically significant (the p-value for the difference in alpha of the equal- and value-weighted portfolios is 0.96 and for the difference of the equal- and price-weighted portfolios is 0.98).Similarly, for the second experiment we see from Table 5 that once we hold constant the weights of the value- and price-weighted portfolios for 12 months and rebalance the weights only after 12 months, the differences in alphas for the equal-weighted portfolio relative to the value- and price-weighted portfolios is statistically insignificant (with the p-values being 0.65 and 0.30).

An important insight from these experiments is that the higher alpha of the equal-weighted portfolio arises, not from the choice of equal weights, but from the monthly rebalancing to maintain equal weights, which is implicitly a contrarian strategy that exploits reversal that is present at the monthly frequency. Thus, alpha depends on only the rebalancing strategy and not on the choice of initial weights.

**Table 4** (Click to embiggen)

**Table 5 **(click to embiggen)

And two charts showing size and book-to-market measures:

**Conclusion**

Equal-weighting is a **contrarian strategy** that **exploits the “reversal” in stock prices **and eliminates some of the errors in market capitalization-weighted indices.

The **monthly rebalancing** of the equal-weighted portfolio **generates the alpha**for this strategy. As we **reduce the rebalancing frequency** of the equal-weighted portfolio from the base case of 1 month to 6 months and then to 12 months, the per annum **alpha of the equal-weighted portfolio drops **from 175 basis points to 117 basis points and then to 80 basis points.

For me, the most important part of the study is the finding that “The**nonparametric monotonicity** **relation test** indicates that the differences in the total return of the equal-weighted portfolio and the value- and price-weighted portfolios is **monotonically related to size, price, liquidity and idiosyncratic volatility**.” (Kidding, I’ve got no idea what that means.)