## Abstract

Portfolios weighted by fundamental measures of company size, such as assets, dividends, sales, earnings, and employees, have recently attracted a lot of attention. Pioneering research has showed that these fundamental value–weighted portfolios, especially dividend-weighted portfolios, can achieve better mean returns and better Sharpe ratios than could be attained with the traditional market value– weighted portfolio. In this article, the authors examine three portfolios weighted by the additional fundamental measures of firm size—share repurchases, total payout, and earnings retention—and find that the repurchase-weighted portfolios and total payout–weighted portfolios have higher excess returns and higher Sharpe ratios than the other fundamental value–weighted portfolios, including the dividend-weighted portfolio. The repurchase-weighted portfolio shows a positive and statistically significant alpha of 2.77% after controlling for the Fama–French factors (market, size, and book-to-market) and Carhart’s momentum variable. The total payout–weighted portfolio also has a positive and significant alpha, albeit smaller than that of the repurchase-weighted portfolio.

A market value–weighted investment portfolio composed of all common stocks can be used as a proxy for the market portfolio. Based on the assumptions underlying the strong efficient market hypothesis, the value–weighted portfolio can be both efficient and one of the optimal portfolios. In recent years, a number of researchers have pointed out that the value–weighted portfolio may not be efficient if the market is not efficient. Arnott, Hsu, and Moore [2005] were the first to suggest portfolios weighted by fundamental measures of company size. Their path-breaking research showed that weighting portfolios according to assets, dividends, sales, earnings, employees, and other fundamental measures of company size resulted in better mean returns and better Sharpe ratios than could be attained with the traditional market value–weighted portfolio.^{1} Clever entrepreneurs recognized the value of these findings and quickly created exchange-traded funds (ETFs) based on indices formed from fundamental measures of the size of the issuing firm (see Siegel [2006]).

One of the most attractive features of portfolios weighted by fundamental size variables is the simplicity in construction. This simplicity makes fundamental size–weighted portfolios ideal for exchange-traded funds. The fundamental value^{®}–weighted portfolio that initially attracts the most attention is the cash dividend–weighted portfolio.^{2}
,Siegel [2006] argued that dividends represent the true payout to shareholders and, hence, dividend–weighted portfolios should perform better when the market is noisy. While dividends are one form of corporate payout, share repurchase by issuer has recently assumed a more important role than the other form of making corporate payouts (Skinner [2006]). In fact, Boudoukh et al. [2007] showed that payout yield is a better predictor of future asset prices than dividend yield.

Following the research of those who precede us, we study portfolios weighted by the dollar amount of shares repurchased by the issuing firms. We find that such portfolios usually have higher excess returns and higher Sharpe ratios. In fact, the excess returns and Sharpe ratios from the repurchase-weighted portfolios are higher than the corresponding statistics from the dividend–weighted portfolios. In addition to repurchase-weighted portfolios, we study portfolios weighted by total payout and retention. Given the fact that the repurchase-weighted and dividend–weighted portfolios both perform quite well in terms of excess return and Sharpe ratio, it is logical to study the effect of total payout, which is the sum of dividends and repurchases. The market may, however, value retention as a proxy for growth. In such a case, a portfolio weighted by retention, which is the difference between earnings and total payout, may display some interesting characteristics. We find that a total payout–weighted portfolio has a slightly higher excess return and Sharpe ratio than a dividend–weighted portfolio, while the retention-weighted portfolio underperforms the dividend–weighted portfolio.

In addition to studying these three new portfolios, we also analyze the alphas of all the fundamental-weighted portfolios. A number of researchers have argued that portfolios weighted by fundamental size variables are just repackaging existing ideas, such as value tilt in portfolio theory (see, for example, Asness [2006] and Perold [2007]). We investigate this issue by studying the alphas of these portfolios after controlling for known valuation factors, such as market, size, book-to-market, and Carhart’s momentum factor. We find that most of the fundamental size–weighted portfolios studied in Arnott, Hsu, and Moore [2005] have positive alphas, but the alphas are not significant. In contrast, the repurchase-weighted portfolio has an alpha of 2.77% per year, which is statistically and economically significant.

A large debate is ongoing about which portfolio is superior. Arnott, Hsu, and Moore [2005], Treynor [2005], Hsu [2006], Siegel [2006], and Arnott et al. [2007] are in favor of portfolios weighted by fundamental size measures. As explained in an excellent summary by Arnott et al. [2007], if the market price does not perfectly track the asset values and if the pricing errors are positively correlated with the market price, portfolios weighted by market capitalization are not efficient portfolios, and portfolios weighted by other fundamental measures of company size may be superior. Perold [2007] and Blitz and Swinkels [2008] argued that portfolios weighted by fundamental measures of company size do not necessarily outperform a value–weighted portfolio. To this debate, our contribution is the study of three additional fundamental-weighted portfolios: repurchase, total payout, and retention. We find that not only do repurchase-weighted and total payout–weighted portfolios have higher excess returns and Sharpe ratios than dividend–weighted portfolios, but they also have positive and significant alphas.

This article is organized as follows. The next section describes the data and method used in our tests. The third section presents the results, and the last section concludes.

**DATA AND METHODOLOGY**

We construct the portfolios based on data from CRSP and Compustat. To ensure that all the Compustat data are available at the time of the portfolio construction, we rebalance all portfolios at the end of June using company data from the previous year, as done by Fama and French [2007]. All portfolios are rebalanced only once a year, at the end of June. In this way we substantially reduce the impact of transaction costs by not rebalancing portfolios multiple times in a year. Note that our construction process does not equalize the transaction costs of the portfolios because the magnitude of the rebalancing at the end of June can vary depending on the weights used. For example, at rebalancing, value–weighted portfolios tend to incur the lowest transaction cost and equal-weighted portfolios tend to have the highest transaction cost.

Although we rebalance the portfolios annually, we measure the returns monthly. In particular, the return of portfolio *X* in month *i* is

where the sum is over all *j* = 1, 2, 3, … stocks in the portfolio, *r _{ji}
* is the return of stock

*j*in month

*i*, and

*w*is the weight of stock

_{ji}*j*in month

*i*. The weights are calculated as

where *tc* is the most recent portfolio rebalancing time (at the end of June of every year in our sample) and *c _{j,tc}
* is the initial weight assigned to stock

*j*.

The return of stock *j* in month *i* (*r _{ji}
*) is usually the monthly return including the dividend given in CRSP. If the stock is delisted during the month, we use the delisted return given by CRSP, if possible. Following Shumway [1997], we assume a 100% loss if the delisting code is negative. After delisting, a stock’s returns are proxied by filling in market value–weighted returns from CRSP.

The initial weights assigned to the stocks depend on the type of portfolio we construct. For an equal-weighted portfolio, the initial weights for all stocks are equal. For a market value–weighted portfolio, the initial weight for stock *j* is the market capitalization of stock *j* at the time of portfolio construction. Note that our equal-weighted portfolio assigns equal weights at the time of portfolio construction. But because we do not rebalance the portfolio from month to month, after an equal-weighted portfolio’s construction, the market values of the stocks in the portfolio can alter the portfolio’s weights. Our value–weighted portfolio is a little different from the CRSP value–weighted portfolio because our portfolio does not add new stocks between portfolio construction dates. We choose to construct equal-weighted and value-valued portfolios in this manner so that they are more comparable to our other portfolios.

We construct portfolios weighted by fundamental measures of firm size in the same fashion as Arnott, Hsu, and Moore [2005]. These fundamental measures of firm size for each stock are computed using information from COMPUSTAT annual data. At the time of portfolio construction (end of June), we use the data from the previous year to ensure all data are available to all investors. We construct portfolios weighted by assets, book equity, dividends, earnings, number of employees, cash flows, sales, repurchase, retention, and total payout by assigning the initial weights of the respective portfolios according to their respective financial statement values. The first seven portfolios have been studied by Arnott, Hsu and Moore [2005], but the last three—repurchase, retention, and total payout—portfolios have not been studied before.

Item 6 in the COMPUSTAT annual data is Assets. Cash Dividends is Item 21, the number of employees is Item 29, and sales is Item 12. Cash flows are calculated as Item 13 less Item 128. Following Kayhan and Titman [2003], we calculate book equity as total assets minus total liabilities minus preferred stock plus preferred tax and convertible debt; that is, Item 6 – Item 10 – Item 181 + Item 35 + Item 79. Following Fama and French [2001] and Skinner [2006], we measure repurchases as net repurchases. If the firm uses the treasury stock method for repurchases, we use the increase in common treasury stock (Item 226) as the net repurchase. If the firm uses the retirement method instead, which we infer from the fact that treasury stock is zero in the current and prior year, the repurchase is measured as the difference between stock purchases (Item 115) and stock issuances (Item 108). If either of these amounts is negative, repurchases are set to zero. Following Skinner [2006], we also adjust earnings for the effect of special items; that is, earnings = Item 18 – 60% of Item 17.^{3} The total payout is the sum of dividends and repurchases. The retention amount is the total earnings left after subtracting the total payout. If any of these values is negative, we set the value to zero.

**RESULTS**

We follow Arnott, Hsu, and Moore [2005] in using the largest 1,000 companies in each category and build portfolios weighted by these firms’ corresponding size values.^{4}
Exhibit 1 presents the summary results for these portfolios from 1973 to 2007. We start our sample period in 1973 because share repurchases first became possible around that time. In addition to the mean return and Sharpe ratio, we also regress each portfolio’s return on the market index return, the Fama and French SMB and HML factor returns, and Carhart’s momentum factor return (UMD). The intercept of the four-factor regression is the alpha, and the coefficients from the four factors are the four factor betas in Exhibit 1.

Exhibit 1 shows that the dividend–weighted portfolio has an annual return of 13% and an annualized Sharpe ratio of 0.529. This Sharpe ratio is the highest among all the portfolios studied by Arnott, Hsu, and Moore [2005], namely, equal-weighted and market value–weighted portfolios, and portfolios weighted by assets, sales, employees, earnings and cash flows. This result is consistent with the previous findings of Arnott, Hsu, and Moore [2005] and Siegel [2006]. The three additional portfolios considered in this study—repurchase-weighted, retention-weighted, and the total payout–weighted portfolios—show a different pattern. The portfolio weighted by repurchases has a mean annual return of 16.36% and a Sharpe ratio of 0.642; both are higher than the same measures for the dividend–weighted portfolio. The total payout–weighted portfolio also has a higher annual return and Sharpe ratio, at 13.51% and 0.554, respectively. The retention-weighted portfolio, however, has an annual return of 12.94% and a Sharpe ratio of 0.45. It appears that the portfolio weighted by retention performs worse than the portfolio weighted by dividends, but the portfolios weighted by repurchase and by total payout perform better.

When we run the four-factor regression on these portfolio returns, the results are quite interesting. None of the portfolios weighted by fundamental measures of firm size in the Arnott, Hsu, and Moore study have a significant alpha.^{5} The dividend–weighted portfolio, for example, has an alpha of 0.45% per year and is not statistically significantly different from zero. In terms of the factor betas, the dividend–weighted portfolio has a negative loading on SMB and UMD, but a positive loading on HML. In other words, the dividend–weighted portfolio is tilted toward large stocks, high-book-value stocks, and non-momentum stocks. But after taking these factors into account, the dividend–weighted portfolio does not show any significant positive excess return. Our result is consistent with the findings of Jun and Malkiel [2007]. They showed that an index return based on fundamental measures of firm size did not have a significant alpha after controlling for market, size, and book-to-market effects.

Unlike most other fundamental value–weighted portfolios, the repurchase-weighted portfolio has a positive and statistically significant alpha of 2.77% per year. The total payout–weighted portfolio has an alpha of 1.08% per year and is also significant at the 5% level.^{6} The retention-weighted portfolio does not show any significant alpha. In terms of betas, the total payout–weighted and retention-weighted portfolios show the same pattern as the dividend–weighted portfolio. The repurchase-weighted portfolio has a positive loading on SMB, while the other portfolios have negative loadings on SMB.

Note that the market value–weighted portfolio has an alpha of 0.51% per year. Although the magnitude is not large, it is nonetheless statistically significant. The main reason for the statistical significance is that we use the largest 1,000 companies to construct our value–weighted portfolio. Previous research by Cremers, Petajisto, and Zitzewitz [2008] also found a similar effect for the S&P 500 and Russell 1000 indices. Another reason for the statistical significance is related to the way we construct portfolios. Unlike the typical way of calculating market index returns, we rebalance the portfolio once a year and then hold it constant through the remainder of that year. As mentioned previously, the fundamental measure of a firm size–weighted portfolio is not exactly the same as the market value–weighted index.

We also construct portfolios using all the companies included in both the CRSP and Compustat databases. The results are presented in Exhibit 2. With the exception of the equal-weighted portfolio, the other portfolios (in Exhibit 1) display the same pattern as their counterparts constructed using the largest 1,000 companies in each category. This result is not surprising given that the largest 1,000 companies in each portfolio constitute a significant weight in the all-company portfolios that are based on fundamental measures of firm size. For the opposite reason, the equal-weighted portfolio using all companies shows some difference from the equal-weighted portfolio using only the 1,000 largest companies.

To conduct further inquiries, we split our total sample from 1973 to 2007 into four subsamples. Exhibit 3 reports the performance of portfolios weighted by fundamental measures of firm size in each of our four subperiods. Note that the repurchase-weighted portfolio performs best in terms of mean return, Sharpe ratio, and alpha in three of the four subsamples. Only in the last subsample, from 2000 to 2007, does the dividend–weighted portfolio outperform the repurchase-weighted portfolio in terms of mean return and Sharpe ratio. We hypothesize that the outperformance of the dividend–weighted portfolio in the last subsample might be due to a dollar of cash dividends being valued like a “bird in the hand,” but a dollar of share repurchases being valued like “a bird in the bush.” Stated differently, a change in investors’ intertemporal preferences in the latest subsample made them prefer a dollar of cash dividends over a dollar’s worth of repurchased shares, whereas the two quantities were viewed more equally during the preceding three subsamples.

**CONCLUSION**

This article studies three portfolios weighted by three different fundamental measures of firm size that have not been previously examined: a portfolio based on share repurchases, a portfolio based on total payouts, and a portfolio based on retention. We find that the repurchase-weighted and total payout–weighted portfolios have higher excess returns and larger Sharpe ratios than the more commonly used cash dividend–weighted portfolio. We also study the alphas of all the fundamental size–weighted portfolios initially suggested in the insightful paper by Arnott, Hsu, and Moore [2005], plus the three new weightings suggested in this article. While the alphas for the fundamental-weighted portfolios in Arnott, Hsu, and Moore [2005] are not significant, the repurchase-weighted portfolio has an alpha of 2.77% after controlling for market, size, book-to-market, and Carhart’s momentum factors. The total payout–weighted portfolio also has a positive and significant alpha of 1.08%, somewhat smaller than that of the repurchase-weighted portfolio. Given our findings and given that portfolios weighted by fundamental measures of firm size are easy to construct, it is interesting to consider the future possibilities for ETFs or index funds that are weighted by the repurchase dollar amount and/or the total payout.

## ENDNOTES

↵

^{1}We would like to extend special thanks to Robert Arnott, the reviewer, for insightful comments on this article.↵

^{2}The Fundamental Index trade name and patent pending concept are the exclusive property of Research Affiliates^{®}.↵

^{3}We also measured earnings without the adjustment and our results did not change.↵

^{4}Equal-weighted portfolios are constructed by equally weighting the largest 1,000 companies (ranked by their market values) at the time of portfolio construction.↵

^{5}The fact that these portfolios, which are weighted by fundamental measures of firm size, do not have a statistically significant alpha is acknowledged in Arnott, Hsu, and Moore [2005].↵

^{6}Boudoukh et al. [2007] also studied portfolios constructed from stocks with high-payout yields, and they found that these portfolios have significant positive alphas. While our results are consistent with their findings, our portfolio construction is different. We use repurchase dollars and total payout dollars to weight our portfolios and they used payout yield to select the stocks and then used equal weighting to construct the portfolios.

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