Portfolios Weighted by Repurchase and Total Payout

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_ji is the weight of stock 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.