Do cash distributions justify share prices
Do Cash Distributions Justify Share Prices?
Claudio Loderer and Lukas Roth * November 4, 2007
* Claudio Loderer is at the Universität Bern, Switzerland; Lukas Roth is at the Pennsylvania State University. We wish to thank Nancy Macmillan for the great editorial help. We have benefited from the helpful comments of Ingolf Dittmann, Jean Helwege, Petra Joerg, John Long, John McConnell, Urs Peyer, Cesare Robotti, Kurt Schmidheiny, Tim Simin, and John Wald. We would also like to thank the seminar participants at Pennsylvania State University, and the participants of the 2007 EWGFM Conference in Rotterdam, the CRSP Forum 2006 in Chicago, the 2006 European Finance Association Meetings in Zürich, the 2006 Eastern Finance Association Meetings in Philadelphia, the 2005 European Financial Management Association Meetings in Milan, the 2005 Financial Management Meetings in Chicago, and the 10th Symposium on Finance, Banking, and Insurance at the Universität Karlsruhe. Special thanks go to Philippe Mueller and Urs Waelchli for their substantial help in the early stages of the paper.
Abstract We ask whether corporations pay out the cash that shareholders anticipate and find consistent evidence. We study the firms traded on the NYSE, the AMEX, and the Nasdaq in 1926–2004. Over 30-year investment horizons, and ignoring taxes, corporate cash distributions yield returns commensurate with the contemporaneous risk-free rates and the risk premiums assessed in the literature, on average. Riskier stocks pay out more cash, although with greater volatility. Moreover, terminal stock prices decline in importance as the investment horizon grows longer. Relative to their prices, however, large firms appear to pay too much cash, and tiny firms too little.
Keywords: Market efficiency, equity risk premium, cash distributions, dividends JEL classification: G12, G14, G35
“Properly formulated, the dividend approach defines the current worth of a share as the discounted value of the stream of dividends to be paid on the share in perpetuity.” Miller and Modigliani (1961, p. 419) Much of finance theory rests on the assumption that stock prices are the present value of the future cash flows which shareholders expect to receive. That claim goes back to at least Williams (1938) and Gordon (1962). However, the vast majority of the tests of this proposition have focused on short-term dividends and subsequent resale prices. This paper inquires whether corporations themselves distribute enough cash over time to justify the investment that shareholders make. We take into account all forms of cash distribution, not just ordinary dividends. Stock market efficiency is a hotly debated subject with formidable advocates on either side of the issue. Whereas Fama (1970, 1991, 1998) claims the evidence favors efficient markets (see also Schwert, 2002, and the literature cited therein), other academics, especially behavioral finance specialists, think otherwise. According to Barberis and Thaler (2003), deviations from information efficiency occur because of limits to arbitrage and deviations from full investor rationality. Most studies concentrate on stock returns and their time-series and cross-sectional properties and are therefore concerned, as we said, with dividend yields and capital gains. A notable exception are Donaldson and Kamstra (1996), who compare the discounted value of dividend forecasts with the stock prices observed in the 1920s. 1 Another exception is the strand of literature, which, starting with LeRoy and Porter (1981) and Shiller (1981), has focused on
1
Foerster and Sapp (2005) examine the dividend discount model in a clinical study.
1
contrasting the volatility of stock price changes with that of future dividends. 2 These latter studies, however, do not make direct comparisons of cash distributions and stock prices— presumably to avoid the thorny issue of assessing the correct risk-adjusted discount rates. This paper conducts that experiment and asks whether the future value of the cash distributions yielded by an initial investment in equities matches the compounded value of that investment over the very long run. We are unable to avoid the problem of the appropriate risk-adjusted discount rates completely, but the propositions we test do not require a quantitative answer. Our approach is more intuitive than one that relies on present values because it reproduces possible investment strategies. We take into account all forms of cash payout and ignore the proceeds shareholders receive from selling to each other. We test various implications of a discounted-cash-flow (DCF) model of stock prices and find mostly consistent evidence. Ignoring taxes, the aggregate cash that firms distribute over investment horizons of 30 years yields internal rates of return equal to the contemporaneous riskfree rates plus the average equity risk premium reported in the recent literature for the years in question. Perhaps more impressive, riskier stocks at the time of the original investment yield more volatile yet larger cash distributions. There are also observations apparently inconsistent with a DCF model. The market seems to erroneously price firms with low dividend yields. Investors seem to be too optimistic about
2
Many studies report evidence of excess volatility. These tests have been questioned, however, because they
make various stationarity assumptions (at least the early ones; for tests that get around the stationarity problems, see West (1988), and Campbell and Shiller (1991)), assume constant discount rates (see the criticism, among others, of Fama (1991), and Schwert (1991)), or ignore non-dividend forms of cash distributions (see the criticism of Ackert and Smith (1993)). Yet according to the critics of the efficient market hypothesis, those reservations cannot account fully for the evidence (see, for example, Shiller (2002)).
2
these firms. Moreover, compared to the prices they trade for, tiny firms seem to pay too little cash and very large firms disburse too much. Our experiment is similar in spirit to Fama and French (2002). They are interested in assessing the expected stock return on the basis of fundamentals, and in contrasting those estimates with the actual average stock return. We are interested in assessing whether the future value of the cash disbursed by firms is consistent with the prices investors pay. Since both papers ultimately rely on a DCF model, they share similarities. We have, however, a different perspective, and we take into account all forms of cash distribution. More important, we are interested in the cross-sectional aspects of those distributions, such as whether higher risk means more sizable and volatile cash distributions. In addition, we examine more than the S&P 500 index, namely all firms traded on the NYSE, the AMEX, and the Nasdaq. The issue we explore is not trivial. Even though there is a strong presumption that stock prices equal the current value of future cash distributions, equality is not automatic. The market needs an equilibrating mechanism when stock prices wander off the fundamental values. Arbitrage would seem to be such a mechanism. However, its effectiveness is compromised for the very reasons pointed out by Barberis and Thaler (2003). Arbitrage requires money and is risky. 3 Suppose in fact that stock prices were smaller than the present value of the expected future cash distributions. Arbitrageurs could then borrow to buy stocks and use the cash distributions to cover the interest on their liabilities. Eventually, they would make a profit. However, the cash distributions might not always be sufficient to cover the interest on the loans. Moreover, lenders might decide to call the loans prematurely and arbitrageurs’ expectations
3
might be wrong (Mitchell, Pulvino, and Stafford (2002)). Arbitrage is arguably an ineffective equilibrating mechanism in this case. Alternatively, investors could learn from their mistakes and adjust the prices they are willing to pay. They would have to wait a long time to recognize mistakes, however. Learning under those circumstances would be difficult if not impossible. The paper is organized as follows. The next section presents the experiment in more detail and derives testable implications. Section 2 discusses the data and their source. Section 3 presents the results. Our initial focus is on a buy-and-hold strategy. Thereafter, we replicate our analysis under a buy-and-participate strategy, where the hypothetical investor participates in all share buybacks. Section 4 draws the conclusions.
1. Test design Most of our analysis involves a hypothetical investor who buys and holds shares without ever selling (buy-and-hold strategy). For better understanding, let us illustrate the strategy formally. We begin with an initial investment of I0 at time 0 and invest it in one stock. We assume that all cash distributions are made at year-end and ignore personal taxes. For simplicity, we also ignore stock splits, stock dividends, liquidations, mergers, and delistings that would only complicate the exposition. We address these issues in the empirical section. n years after the initial investment, the value of the cash flows generated by our strategy, reinvested at a rate of return k, equals:
3
That is typically the case of real-world arbitrage. See De Long, Shleifer, Summers, and Waldman (1990),
Shleifer and Summers (1990), Shleifer and Vishny (1997), Mitchell, Pulvino, and Stafford (2002), and Liu and Longstaff (2004).
4
VnS =
I0 ⎡ n (n − j) ⎤ × ⎢ ∑ c j × (1 + k ) ⎥, P0 ⎣ j=1 ⎦
(1)
where
I0 P0 P0
cj
= number of shares purchased with the initial investment I0 at time 0; = stock price at time 0;
= annual cash per share distributed by the firm at the end of year j.
The amount of money we will have after n years equals the number of shares originally bought (I0/P0) times the sum of the reinvested annual cash distributions per share. To find out whether the firm’s cash distributions justify the initial investment, we compare the value of our buy-and-hold strategy with the value of the initial I0, if we invest and roll it over at a rate of return k every year. After n years, the resulting value, VnF , will equal: VnF = I 0 × (1 + k ) . n
(2)
To measure how quickly, if at all, the total cash distributions made by the firm to its shareholders exceed the initial investment, we compute the ratio of VnS and VnF and call it the distribution-toinvestment ratio (DIR):
I0 ⎡ n n− j ⎤ c 1 k × × + ( ) ⎢ ∑ ⎥ j VnS P0 ⎣ j=1 ⎦. DIR n = F = n Vn I0 × (1 + k )
(
)
Equations (1) to (3) assume we invest in one stock only. We made this simplification for purposes of illustration. In the empirical analysis, we invest in portfolios of stocks. Section 3.1.1. will explain our investment strategy in that context.
5
(3)
The strategy we just described is one of buy and hold. Other investment strategies are conceivable, including one that participates in all share repurchases. If firms switch from paying dividends to repurchasing shares (Fama and French (2001), Grullon and Michaely (2002)), tendering in share repurchases could be more beneficial than simply buying and holding. The empirical section therefore also investigates the alternative of buying and participating in share repurchases on a pro-rata basis (buy-and-participate strategy). Whatever strategy investors follow, the hypothesis that corporate cash distributions justify the prices that shareholders pay implies the following six testable propositions. Proposition 1. Over time, the reinvested value of the cash distributions grows and exceeds
the compounded value of the initial investment at rates of return (k) between the risk-free rate ( R F ) and the required rate of return (μ). Put differently, the distribution-to-investment ratio (DIR) should grow and eventually exceed one for R F ≤ k < μ as the investment horizon grows. When the reinvestment return is μ, DIR asymptotically approaches the value of one from below. The proof is in the Appendix. Since we are unable to assess the required rate of return (μ) correctly, we test whether the predicted regularity between DIR and k holds as k grows farther from the risk-free rate. Figure 1 illustrates this proposition by plotting various DIRs as a function of different reinvestment rates of return. For simplicity, we assume an initial investment of $100 and a constant annual perpetuity of $10. For all reinvestment rates of return smaller than the required rate of return of 10%, the DIRs grow with the investment horizon and eventually exceed one. They all asymptotically approach a given value above one. For example, for k = 8%, the DIR reaches the value of one after 21 years and then asymptotically approaches the value of 1.25.
6
When k = 10%, the DIR asymptotically moves toward the value of one from below, and when k = 11%, it tends to 0.91 without ever reaching the value of one. Proposition 2. The preceding logic also implies that the greater k, the smaller the DIR for a
given investment horizon T. Figure 1 illustrates this phenomenon. For any investment horizon, the highest DIR is that computed when the reinvestment return equals the risk-free rate (5%), and the lowest DIR is that associated with a reinvestment return of 10%. Proposition 3. Riskier stocks should eventually make higher cash distributions than stocks
that are less risky. If we invest the same amount of money in two different stocks, the investment with higher risk will eventually have to make higher cash distributions—larger cash flows are needed to offset higher discount rates. It follows that, as we extend the investment horizon T, the DIRs of riskier stocks should eventually be higher (keeping the reinvestment rate of return the same). This is probably the most restrictive test of market rationality we perform, since it requires that investors predict both future cash distributions and risk over long time horizons. Since companies change capital structure, products, and markets over time, predicting risk would seem like a daunting task. Proposition 4. Riskier stocks at the time of the investment should subsequently yield more
volatile cash distributions. Proposition 5. Terminal stock prices should decline in importance over time (Fama and
Miller (1972)). To illustrate this implication, we restate the DCF model using the stock price at time T, PT, and write:
7
T
P0 = ∑ t =1
ct PT + t (1 + μ) (1 + μ)T
(4)
P0 should converge to a finite limit as T approaches infinity. But this requires that the value of PT as a proportion of the compounded future value of the cash distributions decline with T, on average. Proposition 6. Stocks with the same risk should have the same distribution-to-investment
ratios in the long run regardless whether they distribute cash from the beginning or initiate payouts only later. This follows from equation (3) above with the appropriate rearrangements.
2. Data
We study the NYSE, the AMEX, and the Nasdaq. The sample period covers the years 1926 to 2004 and the data are from CRSP. We compile all cash distributions that firms make to their shareholders ignoring for the moment share buybacks (Section 3.3. drops that restriction when investigating the buy-and-participate strategy). This involves the cash (or the cash value of property) paid out as ordinary and liquidating dividends, and all cash paid out as part of exchanges and reorganizations. Ordinary dividends are annual, semiannual, quarterly, and monthly cash dividends, year-end and special cash dividends, interim and nonrecurring cash dividends, and cash dividends with unknown frequency. We keep all distributions of common stock, such as stock splits and stock dividends, and add them to our initial shares. 4 Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash
4
We do, however, sell preemptive rights. We have no simple alternative, since CRSP does not report a price-
adjustment factor for rights issues. Selling preemptive rights is in principle inconsistent with our plan of focusing
8
generated by these stock distributions is added to the proceeds from investing in the original stock. One complication we have to deal with is delisting events. When a stock is delisted, it is dropped from CRSP. That happens, in particular, when a company goes private, when it switches to an exchange other than NYSE, AMEX, and Nasdaq, and when the company ceases to comply with stock exchange regulations or SEC rules. In those cases, we include the CRSP delisting amount as a final distribution. That amount is either an off-exchange price or pricequote, or the sum of cash distributions. All other delisting cases, including mergers and liquidations, are treated as any other form of cash or stock distribution. Strictly taken, delisting amounts are not necessarily cash distributions by the firm. The results do not change, however, when we ignore these payments. Table 1 provides descriptive statistics about the frequency of cash distributions as well as their value over time and by exchange. As one can see from Panel A, there are 570,279 distribution events, 553,621 of which are ordinary dividends, 4,753 are liquidating dividends, 7,451 are delisting distributions, and 4,454 are exchanges and reorganizations. The aggregate dollar amount in question is 9,939 billion constant 2004 dollars; roughly 75% of this amount is ordinary dividends, 4% reflects liquidating dividends and delisting distributions, and 21% comprises exchanges and reorganizations (keep in mind we are ignoring share buybacks for the moment). For 967 dividend payments, no payment date is specified on the CRSP tapes. In these cases, we use the ex-dividend dates as proxies. According to Panel B, NYSE firms make up roughly 87% of the total corporate cash disbursement, compared with 3% for AMEX, and 10%
on the cash distributed by firms and ignoring the cash received from other investors. Fortunately, rights issues are fairly rare—they represent only 0.1% of the value of all distributions by CRSP firms in the 1926–2004 period.
9
by Nasdaq firms. Industrial firms are responsible for about 72% of the aggregate sum; utilities and financials pay out the rest.
3. Results
We begin with an analysis of distribution-to-investment ratios for different firm-size portfolios under buy-and-hold. We use these data to test our six propositions. We start with a univariate analysis and then reexamine our conclusions in a multivariate context. Finally, we replicate the analysis under a buy-and-participate strategy.
3.1. Buy-and-hold: Univariate analysis 3.1.1. Portfolio formation and characteristics
We compute distribution-to-investment ratios for investments in equity portfolios. To form these portfolios, we rank firms on the CRSP tapes on any given month by market capitalization and assign them to ten buckets in descending order. Portfolios are then established by spreading an initial $100 equally across all the firms available in each bucket. Portfolio 1 combines the largest firms, portfolio 10 the smallest ones. We form the first portfolios in January of 1926. For each of the ten portfolios, we compute the cash payouts each individual stock in the portfolio yields during the following years. Portfolio composition remains the same until 2004. Stocks of firms that are taken over for cash or liquidated make a last payment and drop out of the portfolio. For exchanges of stock, we take the new stock and add it to the portfolio. In the first part of our analysis, we reinvest all cash distributions we receive at the risk-free rate observed at the end of a particular month. The proxy
10
for the risk-free rate is the one-month T-bill rate from the CRSP Fama Risk Free Rate Files. Later, we replicate our analysis by reinvesting at risk-adjusted rates of return. Alternatively, we put the same initial $100 in one-month T-bills in 1926 and renew that investment every month. That computation yields the value of our original investment under risk-free compounding over time. At given points in time, namely 15, 20, and 30 years after 1926, we then compute distribution-to-investment ratios (DIR) by dividing the aggregate compounded value of the cash distributions to a given portfolio by the compounded value of our original investment. We compute these ratios for each size portfolio. In January of 1927, we start a new round of investments. We rank firms by market capitalization and assign them again to ten buckets in descending order. We then invest in the various firms in each size bucket (and, alternatively, in the risk-free asset). Again, for each equally weighted stock portfolio, we compute DIRs 15, 20, and 30 years thereafter. In January of 1928, we start yet another round of investments. We repeat this procedure until the end of the sample period in 2004. To identify DIRs by the time elapsed since the underlying portfolios were formed, we add the corresponding numeral—DIR15, for instance, denotes DIRs 15 years after portfolio formation. The last DIRs observed in 2004 refer to portfolios established in 1990 (DIR15), 1985 (DIR20), and 1975 (DIR30), respectively. Because we start new portfolios every year, and because the CRSP firm population and firm value change over time, the composition of our newly created size portfolios generally changes from one year to the next as well. For example, the portfolio 1 we start in 1955 does not necessarily include the same firms as the portfolio 1 we start in 1956. The composition of existing portfolios, however, remains the same (unless firms are delisted).
11
Since we form new portfolios every year, their DIRs cover overlapping periods. For example, the portfolios we form in 1927 cover the same years as the portfolios we form in 1926 (except for 1926). Consequently, even if the composition of our portfolios is not necessarily the same from one year to the next, the distribution-to-investment ratios will tend to be serially correlated. The DIR15s, for example, are highly correlated, although they do not seem to necessarily follow the same stochastic process (not shown). To deal with the overlapping data, the significance tests involving the distribution-toinvestment ratios rely on a Newey-West autocorrelation consistent covariance estimator approach. In the multivariate analysis, we address the serial correlation problem with a PraisWinsten approach that has the merit of also allowing for panel-corrected standard errors.
3.1.2. Distribution-to-investment ratios: Testing Propositions 1, 3, and 4
The various panels of Table 2 provide descriptive statistics for the distribution-to-investment ratios of different size portfolios and over different investment horizons. All ratios are computed assuming reinvestment at the risk-free rate. For ease of interpretation, the next-to-last column in each panel reports the relative size of each portfolio, computed by dividing the average market capitalization of firms in that portfolio by the average market capitalization of the largest firms (portfolio 1). Note that the smallest firms have an average size that is only 0.3% of the average size of the largest firms. The last column reports the average standard deviation of return on each size portfolio. Panel A refers to distribution-to-investment ratios fifteen years after portfolio creation. Because we form the first portfolios at the beginning of 1926, we observe the first DIR15s at the end of 1940. From then until 2004, there are 64 additional DIR15 values we observe for each
12
portfolio. Across all portfolios, the average DIR15 is greater than one. Hence, it takes 15 years for an investment in stocks to generate sufficient cash to justify the initial outlay under riskless compounding (remember, however, that we ignore the possible liquidation proceeds). The individual portfolios’ average DIR15s are between 0.909 (for portfolio 1) and 1.177 (for portfolio 9). With the exception of portfolio 1, we cannot reject the hypothesis that these DIR15s equal one at customary levels of significance (not shown). We also see that DIR and firm size are inversely correlated. The smaller firm size, the higher the distribution-to-investment ratio. Portfolio 10, however, does not have the highest DIR. This seems to contradict Proposition 3, since riskier portfolios should distribute more cash over time. We assume that risk is inversely related to market capitalization—and the volatility figures in the last column of the panel support that assumption. It could be that the smallest size portfolio includes young firms that originally pay little cash and have therefore fallen behind in their payouts compared with other firms. As predicted by Proposition 4, the dispersion of distribution-to-investment ratios within each portfolio is inversely correlated with firm size. That is true for both the spread between the minimum and the maximum values and the standard deviation. Portfolio 1, for example, has a minimum DIR15 of 0.344 and a maximum of 1.586 with a standard deviation of 0.293. In comparison, portfolio 10 has a minimum of 0.124 and a maximum of 4.772 with a standard deviation of 0.822. Panel B shows the distribution-to-investment ratios 20 years after portfolio formation. As predicted by Proposition 1, all DIR20s have increased from what they were five years before and are larger than one. Moreover, the inverse relation between firm size and DIR predicted by
13
Proposition 3 is monotonic. And so is the relation between firm size and the DIR dispersion measures, which confirms Proposition 4. The same comments apply to the distribution characteristics of DIR30 in Panel C. Average and median DIRs have increased uniformly from the level they had ten years before. All average DIRs have increased by at least 50% compared with the DIR20 values. The first quartiles of the distributions of DIR30 are larger than one, and all third quartiles are close to or exceed three (portfolios 1 and 2 are the exceptions). The dispersion of DIR values within each portfolio has also increased substantially, and it is still a monotonic function of risk. The standard deviation, for example, has about doubled in all size portfolios. The only observation not fully in line with our predictions is the impact of risk on DIR value. Contrary to Proposition 3, the inverse relation between firm size and DIR is not monotonic over the full domain. Portfolio 10 has a smaller DIR than the preceding three size portfolios. Overall, Table 2 therefore supports almost all our predictions. The DIRs grow to values larger than one over time. The relation between risk and DIR dispersion is uniformly positive. And risk and the distribution-to-investment ratios are positively correlated. However, the smallest firms do not have the highest DIRs, whether we look at short or long horizons. The same conclusion follows if we measure risk by return variance or CAPM-beta rather than firm value (not shown). The smallest firms seem to pay too little cash. All these results are confirmed when we replicate the analysis by dropping all AMEX and Nasdaq firms or when we focus only on industrial firms. Consequently, the regularities we observe, including that the smallest firms do not have the highest DIRs, are not driven by the presence of AMEX and Nasdaq firms—nor by that of financials and utilities.
14
3.1.3. Distribution-to-investment ratios with risk-adjusted reinvestment rates: Testing Propositions 2 and 3
Table 3 repeats the analysis with reinvestment returns higher than the risk-free rate. To choose a meaningful equity risk premium, we invoke the literature. For 1900 to 2002, Dimson, Marsh, and Staunton (2003) measure a real premium relative to bills of 7.2% (arithmetic mean); Fama and French (2002) report a 5.57% premium relative to commercial paper for 1872 to 2000; 5 Pastor and Stambaugh (2001) offer estimates “based on reasonable priors” that fluctuate between 3.9% and 6.0% since 1834; and the data in Ibbotson Associates (2000) imply a premium of 7.5% between 1926 and 1999 ???. We therefore investigate the value of distribution-toinvestment ratios over a 30-year investment horizon with nominal premiums between 0% and 8%. We do not claim to have the correct risk-adjusted discount rates. All we want to do is test the predicted regularities 2 and 3 for reinvestment rates reasonably close to their correct values. The evidence is generally consistent with the propositions in question. In agreement with Proposition 2, the cross-sectional average DIR30 drops with the risk premium we impose—it equals 2.575 for a risk premium of 0%, and 0.888 for one of 8%. The same results hold for the individual size portfolios. More importantly, the average DIR30 exceeds one for risk premiums up to 6%, equals one (statistically) for a 7% premium, and falls below one for an 8% premium. Since 7% is in the ballpark range of the premium estimates reported in the literature for the years in question, this evidence fails to reject the claim that firms disburse payments commensurate with the prices that shareholders pay, on average.
5
For the same period, Fama and French (2002) also compute an equity premium using dividend growth rates of
3.54%. Since that figure is imputed from dividend data, and since we use dividend data ourselves, relying on that estimate would involve a circular argument.
15
The numbers are mostly supportive also of the hypothesis that, for a given investment horizon, the distribution-to-investment ratios go up with risk (Proposition 3). A look at the table shows that the DIR30 for each portfolio increases almost monotonically with the risk premium— the exceptions are Portfolios 9 and 10. Note that, if one is willing to assume market efficiency, one can follow a logic similar to that in Fama and French (2002) to assess the risk premiums appropriate for the various size portfolios. As implied by Proposition 1, distribution-to-investment ratios reach one asymptotically for reinvestment rates equal to the required rate of return. The table tells us roughly where that is the case for each individual portfolio. The implied risk premiums go from 5% (Portfolio 1) to 8% (Portfolios 6–10). We shaded the corresponding values in the table.
3.1.4. The importance of the terminal stock price: Testing Proposition 5
In our computation, we have omitted the liquidation proceeds at the end of the investment horizon. In computing DIR15, for instance, we disregard the money investors would receive if they sold their portfolios after 15 years. The rationale is that we want to measure only the cash that firms actually disburse to shareholders rather than the cash that shareholders receive from selling to each other. What follows explores the importance of that omission and tests whether, as predicted by Proposition 5, the relevance of the terminal stock price falls with the investment horizon. Table 4 examines the importance of terminal stock prices for investment horizons of 15 and 30 years. The reinvestment return equals the risk-free interest plus a 7%-risk premium. Column (1) lists the average DIR15s without liquidation proceeds (these DIR15s are those reported in Table 2); in contrast, column (2) documents what value the DIR15s would have, on average, if
16
we liquidated the investment after 15 years and added the liquidation proceeds to the cash distributions. The inclusion of terminal stock prices about doubles the overall average DIR15 (from 0.644 to 1.202). The average terminal stock price itself is between 75% and 96% of the reinvested cash distributions in the individual size portfolios, with an overall average value of 81% (column 3). The right-hand side of the table replicates the analysis for a 30-year investment horizon and confirms Proposition 5. Doubling the horizon cuts the terminal stock price’s importance from 81% to 24%. For the individual size portfolios, their value is now between 20% and 31% of the cash distributions. Even after 30 years, the liquidation proceeds remain fairly sizable. A spreadsheet calculation shows that ignoring them does not significantly affect our conclusions, however. Given the initial $100-investment, a nominal discount rate of 11%, 6 and the observed 24%-ratio of terminal stock price to accumulated cash distributions, omitting the liquidation proceeds affects the implied-yield-to-maturity by a mere 80 basis points. Table 4 also helps us understand the small-firm puzzle a bit better. As we have seen, the smallest size portfolio seems to pay too little cash. The table shows that this is not because tiny firms postpone their distributions. In fact, if we look at the table’s last column, we see that the ratio of terminal stock price to aggregate distributions for the top three portfolios is at least 27%; for the smallest firms, it is 25%. If investors truly believed that tiny firms deliberately defer their cash distributions for more than 30 years, their ratio would be higher rather than lower than 27%.
6
For the years in question, Ibbotson Associates (2000) report an annualized return on equities of 11.3 percent.
17
3.1.5. The importance of the delisting amounts
The preceding analysis treats the delisting amounts reported on the CRSP tapes as corporate cash distributions. In some cases, however, these “distributions” are simply off-exchange prices or price-quotes. We therefore retrace the steps of our analysis and investigate what happens when we ignore these fictitious corporate payments (not shown). The results are qualitatively the same. The only difference is that, without delisting amounts, the DIRs are lower, especially for the smallest firms, since they are the ones most likely to delist. With a 5%-risk premium, for example, the smallest size portfolio has a DIR30 of 1.398 when we include the delisting amounts and one of 1.093 when we don’t.
3.1.6. Summary and conclusions
Overall, the evidence uncovered so far supports the prediction that distribution-toinvestment ratios grow with the investment horizon and eventually exceed one for reinvestment returns smaller than the firm’s required rate of return (Proposition 1); moreover, they are inversely related to the magnitude of the reinvestment return (Proposition 2). Also, the evidence confirms that riskier portfolios (as measured by size) have more volatile cash distributions (Proposition 4) and that the importance of terminal stock prices falls with the investment horizon (Proposition 5). Perhaps most importantly, we document that, using a common reinvestment rate of return, the distribution-to-investment ratios are a positive and monotone function of risk (Proposition 3). The exception is the smallest firms. This finding, however, is the result of a univariate analysis and therefore potentially misleading, since risk (firm value, in our analysis) might be correlated with other variables. We therefore reexamine Proposition 3 in a multivariate context.
18
3.2. Buy-and-hold: Multivariate analysis 3.2.1. General considerations
The purpose of our multivariate analysis is to test the propositions that average distributionto-investment ratios: a)
Increase with risk (Proposition 3). Remember, we compute our DIRs assuming a common reinvestment rate of return. Consequently, the higher portfolio risk the higher its DIR. We measure risk alternatively as CAPM-beta, standard deviation of return, and firm size. We should point out that we have to assess risk at the time of portfolio formation, just as investors have to. Firm size could also be a proxy for market liquidity. According to the evidence, the two are directly related (see, among others, Amihud and Mendelson (1986), Amihud (2002), Pástor and Stambaugh (2003), and Loderer and Roth (2005)). If so, illiquid firms would have to yield higher DIRs on average. The logic is similar to that used to justify the relation between DIRs and risk;
b)
Correlate with the dividend payout at the time we assemble our portfolios. All else being equal, higher current dividend yields should not imply higher distribution-to-investment ratios (Proposition 6);
c)
Are abnormal for either very large or very small firms. The preceding tables suggest that tiny firms differ from the rest. The null hypothesis is that there is no difference;
d)
Change over time. Time effects could occur because of different sample composition after 1962 and 1972, the years in which CRSP adds AMEX and Nasdaq companies, respectively,
19
to its tapes. Alternatively, time effects could capture changes in risk premiums (Fama and French (2002)). If so, our DIRs should be lower after 1962.
We focus on distribution-to-investment ratios computed over 30 years. We assume reinvestment returns equal the risk-free interest (we relax this assumption when examining the robustness of our results). Since valuable information might be lost by aggregating firms into large portfolios, we repeat the calculations by sorting firms not in 10 but rather in 100 portfolios in descending order of firm size. With either sample, we estimate the following regression:
LNDIR30i,t = α 0 + α1RISK i,t + α 2 LNSIZEi,t + α 3DYi,t + α 4 D-LARGE-10%i,t
(5)
+ α 5 D-SMALL-10%i,t + α 6 REPTODISTi,t +α 7 D-1963i,t + ε i,t , where the subscript i refers to a given size portfolio, the subscript t is the year in which we observe the DIR in question, and εi,t is an error term. LNDIR30 is the natural logarithm of DIR30. The results remain the same without the logarithmic transformation. ‹D-› in front of a variable labels it as a binary variable equal to one if a certain condition applies, and equal to zero otherwise. Variable definitions, descriptive statistics, and expected sign of their coefficients are shown in Table 5. The variable REPTODIST is added for control purposes. REPTODIST assesses the relative market-wide importance of share repurchases as a form of cash distribution in a given calendar year. If firms replace dividend payments with share repurchases, its coefficient should be negative, since the cash distributions under our buy-and-hold investment policy omit all share repurchases.
20
The regression is a pooled cross-section time-series regression. We estimate it with a PraisWinsten approach with panel-corrected standard errors (PCSE), as specified in the Stata software. 7 In implementing this approach, we allow for disturbances with different standard deviations across panels (heteroskedasticity across panels). Also, we permit contemporaneous correlation in disturbances across panels, and autocorrelation of order one in the disturbances within panels. Unless otherwise specified, statistical significance is with confidence 0.95 in a two-sided test.
3.2.2. Estimation results
The results are reported in Table 6. Columns (1) and (2) sort firms in 10 size portfolios, and columns (3) and (4) in 100 size portfolios. Column (1) refers to the regression specification in equation (6) using return volatility (VOLA) as the measure of investment risk. With 63%, this regression specification has fairly large explanatory power. The coefficient on VOLA is positive and statistically significant with confidence better than 0.99. Similarly, the coefficient associated with firm size (LNSIZE) has a negative and highly significant coefficient. Both observations are consistent, in principle, with Proposition 3, according to which higher risk leads to higher DIRs. Firm size, however, could also capture the effect of market liquidity. We also find that the variable DY, which gauges the importance of ordinary cash dividends, has a positive and significant coefficient. Hence, the cash distributions of firms with a lower ordinary dividend yield at the time the portfolio is created do not catch up with the payoffs of firms that
7
StataCorp. 2007. Stata Statistical Software: Release 9.2. College Station, TX: Stata Corporation. The method
of panel corrected standard errors was developed by Beck and Katz (1995). See also Beck (2001).
21
pay a higher ordinary dividend from the start. Taken at face value, this is inconsistent with Proposition 6. The coefficient of the binary variable D-LARGE-10% is positive and significant; that of the binary variable D-SMALL-10% is negative and significant. These two findings are also difficult to explain. Very large firms seem to distribute abnormally more cash, whereas tiny firms appear to do the opposite. Thus, very large firms would seem to be under- and tiny firms overpriced. One possible explanation for the result involving the very small firms is that investors may look upon them as gambles. 8 Given their high return volatility (see Table 2), 9 investors might regard these equities as unique chances to strike it rich, even if the probability of doing so is small. Investors might therefore be willing to pay more than these firms are worth. That leaves us with the puzzle, however, of why very large firms appear to be underpriced. The variable REPTODIST has a negative and statistically insignificant coefficient, apparently inconsistent with the claim that share repurchases are a partial substitute for cash dividends in the firm’s payout policy. Finally, the negative and significant coefficient of the binary variable D-1963 suggests that portfolios of firms created during the last four decades of the sample period yield distribution-toinvestment ratios that are lower than those of previous periods. As mentioned above, this could reflect the secular decline in equity risk premiums postulated by Fama and French (2002). Column (2) of the table repeats the estimation by replacing return volatility with CAPMbeta. This new risk proxy has a coefficient that is insignificantly different from zero at
8
For papers that discuss this notion, see, among others, Dwyer and Barnhart (2002), Statman (2002), Barberis
and Huang (2007), and Mitton and Vorkink (2007). 9
The smallest firms have an average standard deviation of return that is twice as large as that of the largest firms
(Table 2).
22
conventional levels of confidence. The remaining results are in line with what we observe under the preceding specification. The explanatory power of the regression is almost unchanged, too. Columns (3) and (4) perform the same analysis by splitting firms into 100 rather than 10 size portfolios. All variables have significant coefficients with the sign observed in the first two columns. The coefficient of BETA, in particular, becomes positive and significant. The explanatory power of these regressions is generally lower. Going from 10 to 100 portfolios therefore seems to add a significant amount of noise to our experiment, but it confirms our conclusions.
3.2.3. Robustness checks
To assess the robustness of our findings we replicate the analysis with alternative variable definitions and estimation approaches (not shown in separate tables). First, we ignore all delisting amounts. The results are identical. Second, we examine a shorter time horizon of 15 years. We observe essentially the same results. The main difference is that, except for firm size, our risk measures have statistically insignificant coefficients, regardless whether we form 10 or 100 size portfolios. One possible explanation is that 15 years is too short a time period for the cash distributions of riskier firms to catch up. The analysis in Table 6 assumes reinvestment at the risk-free rate. To probe the importance of that assumption, we repeat the computations under the assumption of different risk premiums. With minor changes in the coefficients of the risk variables, the conclusions remain the same. The small differences relate to the coefficient of BETA: it is positive and significant when we sort firms in 10 size portfolios, yet it loses its statistical significance when we sort them in 100 size portfolios.
23
We also consider a different measure of firm size. The preceding tests employ the natural logarithm of the average market value of equity of the firms in a particular portfolio (in constant 2004 dollars). As an alternative, we measure firm size for each portfolio with values from 1 to 10, as in the univariate analysis. The results are mostly the same. The coefficient of size, however, loses its statistical significance in the specifications of columns (1) and (3). Moreover, the coefficients of the binary variables that flag the largest and the smallest size portfolios are no longer always statistically significant. The coefficient associated with the largest firms is significant only when we distinguish 10 size portfolios, whereas the coefficient that identifies the smallest firms is significant only when we form 100 size portfolios. Finally, we estimate the parameters of equation (1) with the generalized method of moments (GMM). With two exceptions, that estimation approach does not change our main conclusions either. Specifically, we find that risk has a significant coefficient regardless of what proxy we use (that holds also when we add a premium to our reinvestment rate); tiny firms appear to pay too little and very large firms too much cash; and the post-1963 years are associated with lower DIR30s. What changes is that firms with higher dividend yields at the time of portfolio formation do not have higher DIRs when we work with 100 size portfolios—but they still do when we sort firms in 10 size portfolios. Moreover, the coefficient of REPTODIST becomes positive and significant, a rather puzzling result if dividends and share buybacks are substitute methods of disbursing cash. It could be that a market-wide increase in repurchasing activities reflects an increase in overall corporate cash distributions.
24
3.2.4. Summary and conclusions
On the whole, the multivariate analysis offers mixed evidence for our predictions. First, and consistent with Proposition 3, riskier stock investments tend to be associated with higher cash distributions. This holds generally whether we measure risk with return volatility, CAPM-beta, or firm size. The relation can be seen most sharply when sorting firms in 100 size portfolios. Second, however, most specifications suggest that portfolios of firms with higher dividend yields at the time of their formation pay significantly more cash than portfolios of other firms. This contradicts Proposition 6. It seems that dividends convey important pricing information. This might be a reason why firms pay out cash to begin with. Of course, one could also argue that 30 years is too short an investment horizon for non-dividend payers to catch up. Third, portfolios of the smallest firms distribute significantly less cash, and portfolios of the largest firms distribute significantly more. This is a puzzling result. It could be that the cash distributions to these two portfolios are difficult to predict. Very small firms are probably very young and have therefore a very uncertain future. And very large firms could be firms with an exceptional (and hardly sustainable) past performance that makes them equally unpredictable. Figure 2 examines this interpretation. The investment horizon is 30 years. The panel on the lefthand side shows the average cash distributions in constant 2004 dollars by firms in portfolio 1, the largest ones. We report the average as well as the 25th, 50th, and 75th percentiles of those payments. In contrast, the panel on the right-hand side shows the cash distributions by the smallest firms in the sample (portfolio 10). Visual inspection is only partially consistent with our supposition. Whereas the average and the various percentiles of the cash distributions by the smallest firms are indeed fairly volatile, those by the largest firms are comparatively smooth. It
25
might indeed be difficult to price small firms correctly (Fama (1998)), but it is not obvious why the same problem should present itself in the case of large firms.
3.3. Buy-and-participate strategy
The buy-and-hold strategy we have investigated so far ignores share repurchases. Investors could pursue other investment strategies, however. One that is logically consistent with our attempt to measure the actual cash distributions by corporations is a buy-and-participate strategy. It is identical to buy-and-hold except the investor participates in all share repurchases on a prorata basis. Share repurchases surged in the mid-1980s. Whereas in the 1973–1977 and 1978– 1982 periods they averaged 3.37% and 5.12% of aggregate earnings, they rose to 31.42% between 1983 and 1998 (Fama and French (2001)). According to Grullon and Michaely (2002), the reason for the increased popularity is the adoption in 1982 of Rule 10b-18 by the SEC, which protects repurchasing firms from the antimanipulative provisions of the Securities Exchange Act of 1934. If share repurchases have replaced dividends as a means of distributing cash, 10 it is conceivable that a buy-and-participate strategy could yield more cash than buy-and-hold. This section investigates that possibility. Simulating a buy-and-participate strategy faces a few problems and limitations. First, since we use the Compustat tapes, we can measure share repurchases only for industrial firms. Second, data about repurchases do not go back far. Fortunately, repurchases seem to be
10
This possible switch is discussed, among others, in Fama and French (2001), Jagannathan, Stephens, and
Weisbach (2000), Grullon, and Michaely (2002), and Boudoukh, Michaely, Richardson, and Roberts (2006). Allen and Michaely (2003) and DeAngelo, DeAngelo, and Skinner (2004) document the existence, however, of various companies with substantial dividend payments even in the 1980s and 1990s. Moreover, dividends seem to have rebounded in recent years (Brav, Graham, Harvey, and Michaely (2005)).
26
insignificant before 1971, and there are data since then. 11 Third, since actual buyback dates and quantities are often difficult if not impossible to ascertain with much precision, we have to make approximations. Compustat has annual data starting in 1971 and quarterly data starting in 1984. For 1971–1983, our analysis relies on annual data. We switch to quarterly data, however, as soon as they become available. The repurchase price is assumed to equal the average price during the repurchase’s calendar year (quarter). The number of common shares repurchased equals the value of common shares repurchased divided by the average price. And the value of common shares repurchased equals item “Purchase of Common and Preferred Stock” in Compustat’s Statement of Cash Flows minus the decrease in the aggregate value of preferred stock. 12 In our simulation, the proceeds from tendering shares in a share buyback are invested at midyear (midquarter). The fourth limitation of our analysis is the assumption that the hypothetical investor participates on a pro-rata basis in all repurchases we can find with Compustat data, whether they are fixed-price tender offers, Dutch auction repurchases, or open-market repurchases. The problem is that he would not be able to join targeted share repurchases. Fortunately, these
11
With respect to the years prior to the early sixties, for example, DeAngelo and DeAngelo (2006) state that “it
is not surprising that repurchases are mentioned nowhere in MM (1961) since dividends were the only empirically meaningful equity payout at that time, and so the issue of the dividend/repurchase mix was simply not on the profession’s radar screen“ (p. 300). 12
For a discussion of alternative methods of measuring reacquired shares, see Stephens and Weisbach (1998).
Yearly and quarterly purchases of common and preferred stock are measured with Compustat data items #115 and #92, respectively; par value of preferred stock corresponds to the yearly and quarterly data items #130 and #55, respectively. In contrast to Stephens and Weisbach (1998) and Boudoukh, Michaely, Richardson, and Roberts (2006), we use par values instead of redemption values to compute the value of preferred stock repurchased since the latter data are only available on the yearly tapes. The same procedure is adopted by Banyi, Dyl, and Kahle (2005).
27
repurchases do not seem to be very important. Even recently, they were less than 10% of the dollar value of all announced buyback programs (Stephens and Weisbach (1998)). Consistent with what other authors have reported, the importance of share repurchases increases steadily over time—from about 8.5% of all other types of cash distributions in 1971– 1975 to 86.9% in 2001–2004 (not shown). Table 7 reports distribution-to-investment ratios over a 30-year horizon and for risk premiums up to 8%. The DIRs under buy-and-participate are indeed larger than those computed under buy-and-hold (Table 3). It pays to participate in share repurchases. The benefits, however, are numerically only marginal (and statistically never significant). For example, the overall average DIR30 with no risk premium equals 2.575 under buy-and-hold, compared with 2.612 under buy-and-participate. With a 7% risk premium, these numbers are 0.989 under buyand-hold and 1.002 under buy-and-participate. And with an 8% premium, they are 0.888 and 0.899, respectively. Save for these marginal differences, the new data confirm the story we know, namely that: The DIRs grow over time, reach a value of one for risk premiums up to 7%, and then tend to decline; for any given investment horizon, they fall as a function of the imposed risk premiums; they increase monotonically with risk (except for the smallest firms); they are more volatile for higher risk (not shown); and the importance of terminal stock prices falls with the investment horizon (not shown). We also replicated our multivariate regressions under buyand-participate and found coefficients almost identical to those in Table 6 in terms of numerical values and significance.
28
4. Conclusions
We examine whether the cash that corporations distribute to shareholders over the very long run is consistent with the prices they pay. In spite of the popularity of that belief, there is no obvious market mechanism that would help guarantee equality. Arbitrage looks prohibitively expensive and investor learning is very difficult. We are not interested in the cash that investors could receive from selling to each other. Our focus is the cash that firms actually disburse. The main strategy we simulate is buy-and-hold. Our (tax-exempt) investor does not increase his stake in the companies he invests in, does not participate in discretionary share repurchases, ignores stock splits (in the sense that he keeps his shares), does not sell any stock dividends, and holds on to any stock in other firms received during restructurings and mergers. He takes all the cash he collects on his investment, such as ordinary cash dividends, liquidations, cash distributed during mergers and acquisitions, and delisting payments, and reinvests it. We compute the ratio of the aggregate future compounded value of these cash distributions to the future compounded value of the initial investment, and call it distribution-to-investment ratio (DIR). We test whether the DIRs of various size portfolios are consistent with the implications of a DCF model. Overall, we are unable to reject those implications. Over a 30year investment horizon, and ignoring taxes, corporate cash distributions yield returns commensurate with the contemporaneous risk-free rates and the risk premiums reported in the literature for the years in question, on average. Perhaps even more noteworthy, riskier firms tend to distribute more cash. Moreover, the cash distributions of riskier firms are more volatile. And terminal stock prices decline in importance as investment horizons grow longer. These results are robust with respect to different estimation techniques and hold regardless whether we include
29
delisting payments, and whether we restrict the sample to industrial firms or firms listed on the NYSE. However, the picture the data paint has individual patches that seem difficult to reconcile with rationality. Portfolios of firms with higher dividend yields at the time they are put together distribute more cash than portfolios of firms with lower dividend yields. Another apparently anomalous result is that tiny firms seem to return an abnormally small amount of cash, whereas very large firms do the opposite. In the case of tiny firms, the reason could be that their cash distributions are quite uneven time-series, and therefore difficult to predict. It is also possible, however, that a 30-year investment horizon is too short to call these observations anomalies. We find no evidence, however, that, compared with larger firms, tiny firms defer paying out cash for 30 years. We also explore an alternative investment strategy. Our buy-and-participate strategy is identical to buy-and-hold except the investor participates in all buybacks on a pro-rata basis. This strategy enables us to take into account the increased importance of share repurchases in recent decades while maintaining our focus on the cash that firms actually distribute to their shareholders. Overall, buy-and-participate yields slightly higher cash flows than buy-and-hold. More importantly, however, it confirms all the test results we obtain under buy-and-hold. The analysis has ignored taxes. Doing otherwise would have taken us beyond the normal space constraints of a single paper. Still, taxes do not necessarily change our conclusions. Distribution-to-investment ratios are likely to behave the same. To see that we recomputed the numbers in Figure 1 by imposing a 30%-tax rate on both the reinvestment rates and the cash distributions. The predicted regularities are unchanged—they grow to values larger than one for
30
reinvestment rates greater than μ, and they tend asymptotically to a value of one for reinvestment rates equal to μ (Figure 2). In spite of the popularity of DCF models in corporate finance, this seems to be the first paper to take a direct look at actual, comprehensive cash distributions over very long investment horizons. The results suggest that investors are able to predict both the level and the risk of future cash distributions many years ahead correctly, on average. Probably, the reason they can do so in spite of the problems with arbitrage and learning is that firms make predictable (smooth) cash distributions. Besides its relevance to theory, the evidence we find has practical relevance. All management policies with a DCF core, including value-based management approaches, are corroborated by the reported regularities.
31
References
Ackert, Lucy F., and Brian F. Smith, 1993, Stock price volatility, ordinary dividends, and other cash flows to shareholders, Journal of Finance 48, 1147-1160. Allen, Franklin, and Roni Michaely, 2003, Payout policy, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Amihud, Yakov, and Haim Mendelson, 1986, Asset pricing and bid-ask spread, Journal of Financial Economics 17, 223-249.
Amihud, Yakov, 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, 31-56.
Banyi, Monica, Edward A. Dyl, and Kathleen M. Kahle, 2005, Measuring share repurchases, Working paper, Oregon State University. Barberis, Nicholas, and Ming Huang, 2007, Stocks as lotteries: The implications of probability weighting for security prices, Working paper, Yale University. Barberis, Nicholas, and Richard Thaler, 2003, A survey of behavioral finance, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Beck, Nathaniel, 2001, Time-series-cross-section data: What have we learned in the past few years? Annual Review of Political Science 4, 271-293. Beck, Nathaniel, and Jonathan N. Katz, 1995, What to do (and not to do) with time-series crosssection data, American Political Science Review 89, 634-647. Boudoukh, Jacob , Roni Michaely, Matthew Richardson, and Michael Roberts, 2006, On the importance of measuring payout yield: Implications for empirical asset pricing, Journal of Finance 62, 877-916.
Brav, Alon, John R. Graham, Campbell R. Harvey, and Roni Michaely, 2005, Payout policy in the 21st century, Journal of Financial Economics 77, 483-527.
32
Campbell, John Y., and Robert J. Shiller, 1991, Yield spreads and interest rate movements: A bird’s eye view, Review of Economic Studies 58, 495-514. DeAngelo, Harry, Linda DeAngelo, and Douglas J. Skinner, 2004, Are dividends disappearing? Dividend concentration and the consolidation of earnings, Journal of Financial Economics 72, 425-456. DeAngelo, Harry, and Linda DeAngelo, 2006, The irrelevance of the MM dividend irrelevance theorem, Journal of Financial Economics 79, 293-315. De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldman, 1990, Noise trader risk in financial markets, Journal of Political Economy 98, 703-738. Dimson, Elroy, Paul Marsh, and Mike Staunton, 2003, Global evidence on the equity risk premium, Journal of Applied Corporate Finance 15, 8-19. Donaldson, R. Glen, and Mark Kamstra, 1996, A new dividend forecasting procedure that rejects bubbles in asset prices: The case of 1929’s stock crash, Review of Financial Studies 9, 333383. Dwyer, Gerald, and Cora Barnhart, 2002, Are stocks in new industries like lottery tickets? Working Paper, 2002-15, Federal Reserve Bank of Atlanta, Atlanta, GA. Fama, Eugene F., 1970, Efficient capital markets: A review of theory and empirical work, Journal of Finance 25, 383-417.
Fama, Eugene F., 1991, Efficient capital markets: II, Journal of Finance 46, 1575-1617. Fama, Eugene F., 1998, Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics 49, 283-306.
Fama, Eugene F., and Kenneth R. French, 2001, Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics 60, 3-43. Fama, Eugene F., and Kenneth R. French, 2002, The equity premium, Journal of Finance 57, 637-659. Fama, Eugene F., and Merton H. Miller, 1972, The Theory of Finance (Dryden Press, Hinsdale, IL.).
33
Foerster, Stephen, and Stephen Sapp, 2005, The dividend discount model in the long-run: A clinical study, Journal of Applied Finance 15, 55-75. Gordon, Myron J., 1962, The Investment, Financing and Valuation of the Corporation (R. Irwin, Homewood, IL.). Grullon, Gustavo, and Roni Michaely, 2002, Dividends, share repurchases, and the substitution hypothesis, Journal of Finance 62, 1649-1684. Ibbotson Associates, 2000, Stocks, Bonds, Bills and Inflation Yearbook (Ibbotson Associates, Chicago, IL.). Jagannathan, Murali, Clifford P. Stephens, and Michael S. Weisbach, 2000, Financial flexibility and the choice between dividends and stock repurchases, Journal of Financial Economics 57, 355-384. LeRoy, Stephen F., and Richard D. Porter, 1981, The present-value relation: Tests based on implied variance bounds, Econometrica 49, 555-574. Liu, Jun, and Francis A. Longstaff, 2004, Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities, Review of Financial Studies 17, 611-641. Loderer, Claudio, and Lukas Roth, 2005, Discount for limited liquidity: Evidence from the SWX Swiss Exchange and the Nasdaq, Journal of Empirical Finance 12, 239-268. Miller, Merton H., and Franco Modigliani, 1961, Dividend policy, growth, and the valuation of shares, Journal of Business 34, 411-433. Mitchell, Mark, Todd Pulvino, and Erik Stafford, 2002, Limited arbitrage in equity markets, Journal of Finance 57, 551-584.
Mitton, Todd, and Keith Vorkink, 2007, Equilibrium underdiversification and the preference for skewness, Review of Financial Studies 20, 1255-1288. Pástor, Luboš, and Robert F. Stambaugh, 2001, The equity premium and structural breaks, Journal of Finance 56, 1207-1239.
Pástor, Luboš, and Robert F. Stambaugh, Liquidity risk and expected stock returns, Journal of Political Economy 111, 642-685.
34
Schwert, William G., 1991, Review of market volatility by Robert J. Shiller, Journal of Portfolio Management 17, 74-78.
Schwert, William G., 2003, Anomalies and market efficiency, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Shiller, Robert J., 1981, Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review 76, 421-436. Shiller, Robert J., 2002, From efficient market theory to behavioral finance, Journal of Economic Perspectives 17, 83-104.
Shleifer, Andrei, and Lawrence H. Summers, 1990, The noise trader approach to finance, Journal of Economic Perspectives 4, 19-33.
Shleifer, Andrei, and Robert W. Vishny, 1997, The limits of arbitrage, Journal of Finance 52, 35-55. Statman, Meir, 2002, Lottery players/stock traders, Financial Analyst Journal 58, 14-21. Stephens, Clifford P., and Michael S. Weisbach, 1998, Actual share reacquisitions in openmarket repurchase programs, Journal of Finance 53, 313-334. West, Kenneth D., 1988, Dividend innovations and stock price volatility, Econometrica 56, 3761. Williams, John B., 1938, The Theory of Investment Value (Harvard University Press, Cambridge, MA.).
35
Table 1 Aggregate cash distributions under a buy-and-hold strategy The table shows the distributions of our sample firms for the period 1926–2004. These distributions include ordinary and liquidating cash dividends (or the cash value of property), stock and other payouts in connection with exchanges and reorganizations, as well as delisting distributions. The hypothetical investor keeps all distributions of common stock, such as stock splits and stock dividends. We assume a buy-and-hold strategy, and therefore ignore share repurchases. Panel A lists the number of distribution events and the associated dollar amount in constant 2004 dollars by event type. Panel B shows the dollar amount of these distributions by exchange (and for the sample of industrial firms) over time. The data are from CRSP. Panel A: Distribution events by type Event type
Number of events
Ordinary dividends Liquidating dividends Stock delisting Exchanges and reorganizations Total
553,621 4,753 7,451 4,454 570,279
Dollar amount (in billions of constant 2004 dollars) 7,468.45 104.55 250.27 2,118.63 9,939.36
Panel B: Distributions over time. Dollar amounts are in billions of constant 2004 dollars. Period 1926–1930 1931–1935 1936–1940 1941–1945 1946–1950 1951–1955 1956–1960 1961–1965 1966–1970 1971–1975 1976–1980 1981–1985 1986–1990 1991–1995 1996–2000 2001–2004 Total
All sample firms 126.46 100.51 128.96 122.21 157.13 215.66 302.01 410.81 532.88 588.40 822.96 996.89 1,323.19 985.98 1,789.71 1,335.60 9,939.35
NYSE firms 126.46 100.51 128.96 122.21 157.13 215.66 302.01 387.80 494.84 497.61 647.40 842.25 1,108.12 851.29 1,517.34 1,122.01 8,621.60
36
AMEX firms
Nasdaq firms
23.01 38.04 32.84 38.44 37.21 56.89 27.20 36.08 23.87 313.57
57.96 137.13 117.43 158.17 107.49 236.29 189.72 1,004.19
Industrial firms 100.90 80.09 116.08 112.99 144.63 189.82 261.63 348.50 447.51 451.16 619.86 743.97 957.61 640.26 1,162.76 822.44 7,200.20
Table 2 Distribution-to-investment ratios under a buy-and-hold strategy and riskless reinvestment The table lists the distribution-to-investment ratios (DIRs) of investment portfolios a given number of years after creation. DIRs are computed as the ratio of the aggregate payouts (compounded at the risk-free rate) on a stock investment divided by the value of the initial investment (also compounded at the risk-free rate). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Panels A, B, and C report descriptive statistics about distribution-to-investment ratios 15, 20, and 30 years after the initial stock investment. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. Relative size is defined as the average market capitalization of firms in a given portfolio divided by the average market capitalization of firms in portfolio 1 at the time of portfolio formation. Volatility is the equally weighted, average annual standard deviation of return on the stocks in a particular portfolio. It is computed using the 60 monthly stock returns preceding the year of portfolio formation. We require a minimum of 36 monthly data. If the volatility of a particular firm cannot be determined, we ignore it (but we keep the weights of the remaining volatilities in the portfolio the same). Stars (*) indicate the significance of mean comparison tests between the portfolio in question and portfolio 1. Standard errors for the mean-comparison tests are computed with a Newey-West correction for autocorrelation with a number of lags equal to the portfolio holding period. To test the difference of the average DIRs observed for portfolios 1 and 2, for instance, we compute that difference in each sample year, regress it against a constant, and use the Newey-West procedure to estimate the regression standard error. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1926–2004. The data are from CRSP. Panel A: Distribution-to-investment ratios 15 years from inception. The first set of portfolios is formed in 1926 and kept until 1940. There are 65 observations for each size portfolio between 1940 and 2004. Portfolio 1 2 3 4 5 6 7 8 9 10 All
Average 0.909 0.932 0.950 1.020 1.064 1.070 1.104 1.163 1.177 1.135 1.052
* * * * ** ** *
Median 0.929 0.819 0.822 0.886 0.899 0.870 0.937 0.896 0.954 0.878 0.886
First quartile 0.658 0.662 0.669 0.716 0.716 0.669 0.678 0.683 0.672 0.665 0.670
Third quartile 1.097 1.110 1.165 1.194 1.362 1.400 1.391 1.438 1.438 1.360 1.296
37
Min
Max
0.344 0.346 0.283 0.296 0.372 0.352 0.310 0.334 0.272 0.124 0.124
1.586 2.069 2.001 2.412 2.512 2.648 3.518 4.563 3.692 4.772 4.772
Standard deviation 0.293 0.364 0.404 0.463 0.510 0.558 0.643 0.737 0.767 0.822 0.585
Relative size 100.0% 18.57% 8.83% 5.13% 3.29% 2.19% 1.48% 0.96% 0.58% 0.26% –
Volatility 27.9% 32.3% 34.8% 37.2% 38.9% 41.4% 43.1% 46.0% 50.3% 56.8% –
Panel B: Distribution-to-investment ratios 20 years from inception. The first set of portfolios is formed in 1926 and kept until 1945. There are 60 observations for each size portfolio between 1945 and 2004. Portfolio 1 2 3 4 5 6 7 8 9 10 All
Average 1.255 1.310 1.326 1.428 1.523 1.544 1.624 1.680 1.723 1.729 1.514
** ** ** * ** ** *
Median 1.254 1.130 1.184 1.221 1.249 1.261 1.269 1.244 1.400 1.244 1.225
First quartile 0.825 0.878 0.877 0.961 0.977 0.890 0.934 0.932 0.928 0.963 0.918
Third quartile 1.577 1.661 1.661 1.816 2.091 2.030 1.979 2.165 2.073 1.884 1.832
Min
Max
0.470 0.447 0.387 0.390 0.508 0.476 0.481 0.491 0.383 0.201 0.201
2.255 2.885 2.821 3.434 4.075 4.275 4.973 6.301 5.471 8.499 8.499
Standard deviation 0.447 0.553 0.606 0.704 0.792 0.860 1.024 1.122 1.165 1.489 0.937
Relative size 100.0% 19.13% 9.17% 5.36% 3.45% 2.31% 1.56% 1.01% 0.61% 0.28% –
Volatility 27.7% 32.1% 34.5% 36.8% 38.5% 40.8% 42.4% 45.2% 49.4% 55.7% –
Panel C: Distribution-to-investment ratios 30 years from inception. The first set of portfolios is formed in 1926 and kept until 1955. There are 50 observations for each size portfolio between 1955 and 2004. Portfolio
1 2 3 4 5 6 7 8 9 10 All
Average
2.023 2.196 2.202 2.359 2.544 2.694 2.900 2.999 2.942 2.895 2.575
*
** ** ** ** ** ** **
Median
First quartile
Third quartile
Min
Max
1.706 1.867 1.933 1.912 2.124 2.254 2.151 2.205 2.176 1.705 1.936
1.294 1.286 1.182 1.364 1.391 1.310 1.387 1.322 1.411 1.368 1.323
2.687 2.886 2.974 3.327 3.380 3.342 3.403 3.814 3.533 2.905 3.092
0.883 0.748 0.739 0.684 0.703 0.577 0.749 0.557 0.485 0.412 0.412
4.242 5.273 5.295 6.222 8.262 9.173 9.418 10.813 11.009 12.980 12.980
38
Standard deviatio n 0.887 1.151 1.254 1.421 1.637 1.928 2.162 2.379 2.334 2.791 1.903
Relative size
Volatility
100.0% 20.16% 9.81% 5.80% 3.77% 2.54% 1.73% 1.13% 0.69% 0.31% –
27.3% 31.5% 33.9% 36.1% 37.7% 39.7% 41.2% 44.0% 48.0% 54.3% –
Table 3 Distribution-to-investment ratios under a buy-and-hold strategy assuming risk-adjusted reinvestment rates The table lists average distribution-to-investment ratios (DIRs) of investment portfolios 30 years after creation assuming reinvestment rates equal to the risk-free rate plus a constant risk premium. DIRs are computed as the ratio of the aggregate payouts (compounded at a given return) on a stock investment divided by the value of the initial investment (also compounded at the same return). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. Standard errors are reported in parentheses. The sample period is 1926–2004. The data are from CRSP. Portfolio 1 2 3 4 5 6 7 8 9 10 All
0% 2.023
3% 1.289
4% 1.128
Risk premiums 5% 0.994
6% 0.884
7% 0.791
8% 0.712
(-0.125)
(-0.075)
(-0.065)
(-0.056)
(-0.049)
(-0.043)
(-0.038)
2.196
1.398
1.223
1.079
0.958
0.858
0.773
(-0.163)
(-0.096)
(-0.082)
(-0.071)
(-0.061)
(-0.054)
(-0.047)
2.202
1.407
1.233
1.088
0.968
0.867
0.781
(-0.177)
(-0.105)
(-0.090)
(-0.077)
(-0.067)
(-0.059)
(-0.052)
2.359
1.510
1.323
1.168
1.039
0.930
0.839
(-0.201)
(-0.119)
(-0.102)
(-0.088)
(-0.076)
(-0.067)
(-0.059)
2.544
1.622
1.419
1.250
1.110
0.993
0.893
(-0.232)
(-0.136)
(-0.116)
(-0.099)
(-0.086)
(-0.075)
(-0.066)
2.694
1.702
1.485
1.305
1.155
1.030
0.925
(-0.273)
(-0.158)
(-0.134)
(-0.114)
(-0.098)
(-0.085)
(-0.074)
2.900
1.815
1.578
1.382
1.220
1.085
0.971
(-0.306)
(-0.177)
(-0.149)
(-0.127)
(-0.110)
(-0.095)
(-0.083)
2.999
1.878
1.633
1.430
1.262
1.121
1.003
(-0.336)
(-0.196)
(-0.167)
(-0.142)
(-0.122)
(-0.106)
(-0.093)
2.942
1.858
1.619
1.422
1.257
1.119
1.003
(-0.330)
(-0.194)
(-0.165)
(-0.141)
(-0.122)
(-0.106)
(-0.093)
2.895
1.828
1.593
1.398
1.235
1.099
0.985
(-0.395)
(-0.236)
(-0.201)
(-0.173)
(-0.150)
(-0.131)
(-0.115)
2.575
1.631
1.423
1.252
1.109
0.989
0.888
(-0.085)
(-0.050)
(-0.043)
(-0.037)
(-0.032)
(-0.027)
(-0.024)
39
Table 4 Distribution-to-investment ratios under a buy-and-hold strategy, with and without terminal stock prices The table lists the average distribution-to-investment ratios (DIRs) with and without terminal stock prices computed over a 15-year and 30-year investment horizon, respectively. DIRs are computed as the ratio of the aggregate payouts (compounded at the risk-free rate plus a constant risk-premium of 7%) on a stock investment divided by the value of the initial investment (also compounded at the risk-free rate plus a constant risk-premium of 7%). DIRs are formally defined in equation (3) of the text. We show DIRs with and without the stock prices observed at the end of the holding period. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. The sample period is 1926–2004. The data are from CRSP. Portfolio
1 2 3 4 5 6 7 8 9 10 All
15 years after portfolio inception Average DIR Average of terminal stock price divided Without With by value of cash terminal terminal distribution stock stock prices prices (1) (2) (3) 0.562 1.057 83% 0.579 1.096 83% 0.590 1.109 82% 0.629 1.141 75% 0.653 1.197 76% 0.656 1.192 75% 0.671 1.244 79% 0.699 1.286 77% 0.706 1.314 83% 0.692 1.385 96% 0.644 1.202 81%
40
30 years after portfolio inception Average DIR Average of terminal stock price divided Without With by value of cash terminal terminal distribution stock stock prices prices (4) (5) (6) 0.791 1.061 31% 0.858 1.110 27% 0.867 1.111 27% 0.930 1.161 23% 0.993 1.236 22% 1.030 1.297 22% 1.085 1.352 22% 1.121 1.393 20% 1.119 1.416 22% 1.099 1.430 25% 0.989 1.257 24%
Table 5 Descriptive statistics of regression variables (buy-and-hold strategy) The table shows descriptive statistics of variables in regression equation (10) of the text. The sample period is 1926–2004. For each size portfolio, we estimate average return standard deviation and CAPM-beta using data from the 60 monthly observations preceding portfolio formation. Thus, the first ten size portfolios with the necessary information are those we create at the beginning of 1931. The first distribution-to-investment ratios are observed 30 years later, in 1960. Panel A reports descriptive statistics, and Panel B shows variable definitions. The data are from CRSP. Panel A: Descriptive statistics Variable DIR30 VOLA BETA LNSIZE DY REPTODIST
Average
Median
2.730 0.116 1.128 12.053 0.042 0.081
2.141 0.105 1.106 12.024 0.039 0.000
First quartile 1.434 0.079 0.989 10.752 0.027 0.000
Third quartile 3.337 0.140 1.249 13.311 0.055 0.110
Min
Max
0.487 0.050 0.596 7.397 0.000 0.000
12.651 0.320 1.776 16.114 0.210 0.511
Standard deviation 1.914 0.049 0.200 1.849 0.023 0.148
Panel B: Variable definitions Variable
DIR30
Definition
Expected sign of coefficient Distribution-to-investment ratio, defined as the ratio of the aggregate payouts on N/A an investment in a portfolio of equities of given market capitalization (compounded at the risk-free rate) divided by the value of the initial investment (also compounded at the risk-free rate). The holding period is 30 years. Distribution-to-investment ratios are formally defined in equation (3) of the text;
RISK
Risk, defined alternatively as return volatility (VOLA), CAPM-beta (BETA), and natural logarithm of firm size (LNSIZE);
+
VOLA
Average standard deviation of return (volatility) of the firms in a given size portfolio in a particular year. Stock return volatility is computed using data from the 60 months preceding the year in question (we require a minimum of 36 observations);
+
BETA
Average CAPM-beta of the firms in a given size portfolio in a particular year. CAPM-beta is computed with a market model using data from the 60 months preceding the year in question (we require a minimum of 36 observations); the market index is the value-weighted CRSP index;
+
LNSIZE
Natural logarithm of firm size (in constant 2004 dollars), defined as the average market value of equity of the firms in a given size portfolio in the year the portfolio is formed;
–
DY
Average dividend yield of the firms in a given size portfolio the year the portfolio
0
41
was created. Dividend yield is defined as cash dividends paid during the year divided by stock price at year end; REPTODIST
Ratio of the aggregate value of share repurchases divided by the aggregate value of total cash distributions by industrial firms on both the CRSP and the Compustat tapes in a given year. Data on share repurchases for industrial firms are available only from 1971 on. As argued in the text, buybacks seem to have been insignificant before 1971. Before that date, this variable is therefore set to zero;
–
D-LARGE-10%
Binary variable equal to 1 for the largest-size portfolio, and equal to 0 otherwise;
0
D-SMALL-10%
Binary variable equal to 1 for the smallest-size portfolio, and equal to 0 otherwise;
0
D-1963
Binary variable equal to 1 if the portfolio is started at the beginning of 1963 or later, and equal to 0 otherwise.
–
42
Table 6 Multivariate analysis of distribution-to-investment ratios under a buy-and-hold strategy We examine the relation between the distribution-to-investment ratios 30 years after portfolio formation and possible determinants. LNDIR30 is the natural logarithms of DIR30, under riskless compounding. Distribution-toinvestment ratios are defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given firm-size portfolio. Once created, these portfolios are maintained over time. However, we form new portfolios every year. The analysis is based on a Prais-Winsten panel regression approach with panel corrected standard errors. We allow for heteroskedastic disturbances across panels (size portfolios). Moreover we assume that the disturbances are contemporaneously correlated across panels, and that the disturbances of any one panel are serially correlated of order one. Descriptive statistics and definition of the variables are in Table 5. Numbers in parentheses are robust tstatistics. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1926–2004. The data are from CRSP. Independent variables
VOLA
Dependent variable: LNDIR30 10 firm-size portfolios 100 firm-size portfolios (1) (2) (3) (4) 4.028*** 3.658*** (3.267)
(3.671)
BETA
0.195**
0.061 (0.265)
–0.269*** (–6.263)
(–9.248)
(–5.451)
(–7.358)
DY
6.742***
4.078***
1.724***
1.286***
(6.398)
(4.319)
(4.137)
(3.114)
D-LARGE-10%
0.870***
1.364***
0.463***
0.680***
(6.885)
(8.290)
(5.332)
(6.119)
D-SMALL-10% REPTODIST D-1963 Constant Number of observations Number of years Number of portfolios per year R-squared Wald χ-squared
–0.659
–0.463***
(1.974)
LNSIZE
***
–1.090
***
–0.176***
–0.446
***
–0.266***
–0.523***
(–4.871)
(–6.282)
(–7.021)
(–6.853)
–0.524
–0.542
–0.267
–0.359
(–0.492)
(–0.522)
(–0.211)
(–0.268)
–0.228**
–0.144
–0.473***
–0.494***
(–1.978)
(–1.136)
(–3.943)
(–3.799)
3.353
***
6.181
***
2.594
***
3.884***
(5.482)
(8.558)
(5.626)
(8.267)
450 45 10 0.626 165.3***
450 45 10 0.577 139.8***
4,500 45 100 0.379 146.3***
4,500 45 100 0.319 118.8***
43
Table 7 Distribution-to-investment ratios for industrials under a buy-and-participate strategy assuming risk-adjusted reinvestment rates The table reports average distribution-to-investment ratios (DIRs) 30 years after the initial stock investment for the full sample period and for different risk premiums. Unlike in the preceding tables, investors participate on a prorata basis in all share repurchases by the firm. DIRs are computed as the ratio of the aggregate payouts (compounded at a given return) on a stock investment divided by the value of the initial investment (compounded at the same return). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, delisting distributions, as well as the proceeds from stock repurchases. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The investor keeps all distributions of common stock such as stock splits and stock dividends. Standard errors are reported in parentheses. The sample period is 1926–2004. The data are from CRSP. Portfolio 1 2 3 4 5 6 7 8 9 10 All
0% 2.065
3% 1.314
4% 1.149
Risk premiums 5% 1.012
6% 0.899
7% 0.804
8% 0.724
(-0.123)
(-0.074)
(-0.063)
(-0.055)
(-0.048)
(-0.042)
(-0.037)
2.235
1.420
1.242
1.094
0.972
0.869
0.783
(-0.161)
(-0.095)
(-0.081)
(-0.070)
(-0.061)
(-0.053)
(-0.047)
2.230
1.424
1.247
1.100
0.978
0.876
0.790
(-0.176)
(-0.104)
(-0.089)
(-0.077)
(-0.067)
(-0.058)
(-0.051)
2.384
1.526
1.336
1.180
1.049
0.940
0.847
(-0.200)
(-0.119)
(-0.102)
(-0.088)
(-0.076)
(-0.067)
(-0.059)
2.568
1.637
1.432
1.262
1.121
1.002
0.902
(-0.231)
(-0.136)
(-0.115)
(-0.099)
(-0.086)
(-0.075)
(-0.065)
2.727
1.722
1.502
1.320
1.168
1.042
0.935
(-0.272)
(-0.158)
(-0.134)
(-0.114)
(-0.098)
(-0.085)
(-0.074)
2.944
1.841
1.600
1.402
1.237
1.100
0.984
(-0.304)
(-0.175)
(-0.149)
(-0.127)
(-0.109)
(-0.094)
(-0.082)
3.038
1.902
1.653
1.448
1.278
1.135
1.015
(-0.335)
(-0.196)
(-0.166)
(-0.142)
(-0.122)
(-0.106)
(-0.092)
2.978
1.880
1.638
1.438
1.271
1.131
1.014
(-0.331)
(-0.194)
(-0.165)
(-0.141)
(-0.122)
(-0.106)
(-0.093)
2.948
1.860
1.620
1.421
1.256
1.117
1.001
(-0.392)
(-0.235)
(-0.201)
(-0.173)
(-0.150)
(-0.131)
(-0.115)
2.612
1.653
1.442
1.268
1.123
1.002
0.899
(-0.085)
(-0.050)
(-0.042)
(-0.036)
(-0.031)
(-0.027)
(-0.024)
44
2.0
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
70
Years DIR(RF=5%)
DIR(k=6%)
DIR(k=7%)
DIR(k=9%)
DIR(k=10%)
DIR(k=11%)
DIR(k=8%)
Figure 1. Simulated distribution-to-investment ratios (DIR) as a function of different reinvestment returns. The figure computes distribution-to-investment ratios for an initial investment of $100 and a constant annual perpetuity of $10 as a function of different reinvestment returns. The risk-free interest rate is 5% and the required rate of return is 10%.
45
2.0
DIR
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
70
Years
DIR(k=5%, before-tax) DIR(k=10%, before-tax)
DIR(k=5%, after-tax) DIR(k=10%, after-tax)
Figure 2. Simulated distribution-to-investment ratios (DIR) before and after taxes as a function of different reinvestment returns. The figure computes distribution-to-investment ratios before and after taxes for an initial investment of $100 and a constant pre-tax annual perpetuity of $10 as a function of different reinvestment returns. We assume a pre-tax risk-free interest rate of 5%, a pre-tax required rate of return of 10%, and a tax rate of 30%.
46
Portfolio 1
Portfolio 10 14
Cash distributions (in constant 2004 dollars)
Cash distributions (in constant 2004 dollars)
14 12 10
75th percentile
8
Mean
6
Median
4
25th percentile
2 0
75th percentile
12 10 8
Mean
6 4
Median
2
25th percentile
0 1
5
10
15
20
25
30
Years (relative to the year of portfolio inception)
1
5
10
15
20
25
30
Years (relative to the year of portfolio inception)
Figure 2. Annual cash distributions under a buy-and-hold strategy over a 30-year time horizon. The figure shows annual cash distributions in constant 2004 dollars on the largest- (portfolio 1) and smallest-size portfolios (portfolio 10) in the sample. Portfolios are formed with all CRSP firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Once created, these portfolios are maintained over time. The sample years are 1926–2004. The investment horizon is 30 years. New portfolios are formed every year, the last one in 1975. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends.
47
Appendix Proof of Proposition 1. Let’s focus on one share of stock and use the DCF model to express
the stock price, P0 , as the present value of the stream of future cash distributions the investment is expected to make:
P0 =
c3 c1 c2 + + + ... , 2 (1 + μ) (1 + μ) (1 + μ)3
(A1)
where μ (the required rate of return) is assumed constant for purposes of exposition, and c t is the cash distribution investors expect to receive in year t conditional on public information available at time 0. With riskless discounting, the stock price, P0F , equals:
P0F =
c3 c1 c2 + + + ... , 1 2 (1 + R F ) (1 + R F ) (1 + R F )3
(A2)
where R F is also assumed constant for simplicity. Clearly, P0 < P0F . We can use these two equations to assess how the value of the stock’s cash distributions compares with the initial stock price. To find out, let us rearrange equation (A2) and compound everything at the risk-free rate over an investment horizon of T years (we will consider the case of other rates k > R F later):
c3 c1 c2 × (1 + R F )T + × (1 + R F )T + × (1 + R F )T + ... 1 2 (1 + R F ) (1 + R F ) (1 + R F )3 (A3) = P0F × (1 + R F )T > P0 × (1 + R F )T ,
48
where the inequality follows from the fact that P0F > P0 . In words, the reinvested value of the stock’s cash distributions between time 0 and time T plus the value of the distributions expected thereafter equals the value of the original stock price in a risk-free world ( P0F ) compounded for a number of periods T. The value of those distributions, however, is larger than the future value of the original stock price ( P0 ) compounded at the risk-free rate. If we now deduct the cash distributions beyond time T from the left-hand side of equation (A3) and rearrange, we obtain: c1 × (1 + R F )(T −1) + c2 × (1 + R F )(T − 2) + c3 × (1 + R F )(T −3) + ... + cT (A4) ≤ P0F × (1 + R F )T > P0 × (1 + R F )T . Because of equation (A3), as we extend the investment horizon T, the cumulative compounded value of the stock’s cash distributions approaches the value P0F × (1 + R F )T from below and eventually exceeds the future value of the initial stock price compounded at the risk-free rate, P0 × (1 + R F )T . A similar argument shows that this prediction holds for all reinvestment rates k such that RF ≤ k < μ. In other words, the cumulative value of the cash distributions reinvested at a return k eventually surpasses the value of the original investment compounded at the same return k. In the limit, however, when k = μ, the value of those distributions will converge toward the value of P0 × (1 + μ)T from below. In terms of our distribution-to-investment ratios (DIR), these predictions imply that the DIR of a given stock grows with the investment horizon and eventually exceeds one for reinvestment returns RF ≤ k < μ.
49
Claudio Loderer and Lukas Roth * November 4, 2007
* Claudio Loderer is at the Universität Bern, Switzerland; Lukas Roth is at the Pennsylvania State University. We wish to thank Nancy Macmillan for the great editorial help. We have benefited from the helpful comments of Ingolf Dittmann, Jean Helwege, Petra Joerg, John Long, John McConnell, Urs Peyer, Cesare Robotti, Kurt Schmidheiny, Tim Simin, and John Wald. We would also like to thank the seminar participants at Pennsylvania State University, and the participants of the 2007 EWGFM Conference in Rotterdam, the CRSP Forum 2006 in Chicago, the 2006 European Finance Association Meetings in Zürich, the 2006 Eastern Finance Association Meetings in Philadelphia, the 2005 European Financial Management Association Meetings in Milan, the 2005 Financial Management Meetings in Chicago, and the 10th Symposium on Finance, Banking, and Insurance at the Universität Karlsruhe. Special thanks go to Philippe Mueller and Urs Waelchli for their substantial help in the early stages of the paper.
Abstract We ask whether corporations pay out the cash that shareholders anticipate and find consistent evidence. We study the firms traded on the NYSE, the AMEX, and the Nasdaq in 1926–2004. Over 30-year investment horizons, and ignoring taxes, corporate cash distributions yield returns commensurate with the contemporaneous risk-free rates and the risk premiums assessed in the literature, on average. Riskier stocks pay out more cash, although with greater volatility. Moreover, terminal stock prices decline in importance as the investment horizon grows longer. Relative to their prices, however, large firms appear to pay too much cash, and tiny firms too little.
Keywords: Market efficiency, equity risk premium, cash distributions, dividends JEL classification: G12, G14, G35
“Properly formulated, the dividend approach defines the current worth of a share as the discounted value of the stream of dividends to be paid on the share in perpetuity.” Miller and Modigliani (1961, p. 419) Much of finance theory rests on the assumption that stock prices are the present value of the future cash flows which shareholders expect to receive. That claim goes back to at least Williams (1938) and Gordon (1962). However, the vast majority of the tests of this proposition have focused on short-term dividends and subsequent resale prices. This paper inquires whether corporations themselves distribute enough cash over time to justify the investment that shareholders make. We take into account all forms of cash distribution, not just ordinary dividends. Stock market efficiency is a hotly debated subject with formidable advocates on either side of the issue. Whereas Fama (1970, 1991, 1998) claims the evidence favors efficient markets (see also Schwert, 2002, and the literature cited therein), other academics, especially behavioral finance specialists, think otherwise. According to Barberis and Thaler (2003), deviations from information efficiency occur because of limits to arbitrage and deviations from full investor rationality. Most studies concentrate on stock returns and their time-series and cross-sectional properties and are therefore concerned, as we said, with dividend yields and capital gains. A notable exception are Donaldson and Kamstra (1996), who compare the discounted value of dividend forecasts with the stock prices observed in the 1920s. 1 Another exception is the strand of literature, which, starting with LeRoy and Porter (1981) and Shiller (1981), has focused on
1
Foerster and Sapp (2005) examine the dividend discount model in a clinical study.
1
contrasting the volatility of stock price changes with that of future dividends. 2 These latter studies, however, do not make direct comparisons of cash distributions and stock prices— presumably to avoid the thorny issue of assessing the correct risk-adjusted discount rates. This paper conducts that experiment and asks whether the future value of the cash distributions yielded by an initial investment in equities matches the compounded value of that investment over the very long run. We are unable to avoid the problem of the appropriate risk-adjusted discount rates completely, but the propositions we test do not require a quantitative answer. Our approach is more intuitive than one that relies on present values because it reproduces possible investment strategies. We take into account all forms of cash payout and ignore the proceeds shareholders receive from selling to each other. We test various implications of a discounted-cash-flow (DCF) model of stock prices and find mostly consistent evidence. Ignoring taxes, the aggregate cash that firms distribute over investment horizons of 30 years yields internal rates of return equal to the contemporaneous riskfree rates plus the average equity risk premium reported in the recent literature for the years in question. Perhaps more impressive, riskier stocks at the time of the original investment yield more volatile yet larger cash distributions. There are also observations apparently inconsistent with a DCF model. The market seems to erroneously price firms with low dividend yields. Investors seem to be too optimistic about
2
Many studies report evidence of excess volatility. These tests have been questioned, however, because they
make various stationarity assumptions (at least the early ones; for tests that get around the stationarity problems, see West (1988), and Campbell and Shiller (1991)), assume constant discount rates (see the criticism, among others, of Fama (1991), and Schwert (1991)), or ignore non-dividend forms of cash distributions (see the criticism of Ackert and Smith (1993)). Yet according to the critics of the efficient market hypothesis, those reservations cannot account fully for the evidence (see, for example, Shiller (2002)).
2
these firms. Moreover, compared to the prices they trade for, tiny firms seem to pay too little cash and very large firms disburse too much. Our experiment is similar in spirit to Fama and French (2002). They are interested in assessing the expected stock return on the basis of fundamentals, and in contrasting those estimates with the actual average stock return. We are interested in assessing whether the future value of the cash disbursed by firms is consistent with the prices investors pay. Since both papers ultimately rely on a DCF model, they share similarities. We have, however, a different perspective, and we take into account all forms of cash distribution. More important, we are interested in the cross-sectional aspects of those distributions, such as whether higher risk means more sizable and volatile cash distributions. In addition, we examine more than the S&P 500 index, namely all firms traded on the NYSE, the AMEX, and the Nasdaq. The issue we explore is not trivial. Even though there is a strong presumption that stock prices equal the current value of future cash distributions, equality is not automatic. The market needs an equilibrating mechanism when stock prices wander off the fundamental values. Arbitrage would seem to be such a mechanism. However, its effectiveness is compromised for the very reasons pointed out by Barberis and Thaler (2003). Arbitrage requires money and is risky. 3 Suppose in fact that stock prices were smaller than the present value of the expected future cash distributions. Arbitrageurs could then borrow to buy stocks and use the cash distributions to cover the interest on their liabilities. Eventually, they would make a profit. However, the cash distributions might not always be sufficient to cover the interest on the loans. Moreover, lenders might decide to call the loans prematurely and arbitrageurs’ expectations
3
might be wrong (Mitchell, Pulvino, and Stafford (2002)). Arbitrage is arguably an ineffective equilibrating mechanism in this case. Alternatively, investors could learn from their mistakes and adjust the prices they are willing to pay. They would have to wait a long time to recognize mistakes, however. Learning under those circumstances would be difficult if not impossible. The paper is organized as follows. The next section presents the experiment in more detail and derives testable implications. Section 2 discusses the data and their source. Section 3 presents the results. Our initial focus is on a buy-and-hold strategy. Thereafter, we replicate our analysis under a buy-and-participate strategy, where the hypothetical investor participates in all share buybacks. Section 4 draws the conclusions.
1. Test design Most of our analysis involves a hypothetical investor who buys and holds shares without ever selling (buy-and-hold strategy). For better understanding, let us illustrate the strategy formally. We begin with an initial investment of I0 at time 0 and invest it in one stock. We assume that all cash distributions are made at year-end and ignore personal taxes. For simplicity, we also ignore stock splits, stock dividends, liquidations, mergers, and delistings that would only complicate the exposition. We address these issues in the empirical section. n years after the initial investment, the value of the cash flows generated by our strategy, reinvested at a rate of return k, equals:
3
That is typically the case of real-world arbitrage. See De Long, Shleifer, Summers, and Waldman (1990),
Shleifer and Summers (1990), Shleifer and Vishny (1997), Mitchell, Pulvino, and Stafford (2002), and Liu and Longstaff (2004).
4
VnS =
I0 ⎡ n (n − j) ⎤ × ⎢ ∑ c j × (1 + k ) ⎥, P0 ⎣ j=1 ⎦
(1)
where
I0 P0 P0
cj
= number of shares purchased with the initial investment I0 at time 0; = stock price at time 0;
= annual cash per share distributed by the firm at the end of year j.
The amount of money we will have after n years equals the number of shares originally bought (I0/P0) times the sum of the reinvested annual cash distributions per share. To find out whether the firm’s cash distributions justify the initial investment, we compare the value of our buy-and-hold strategy with the value of the initial I0, if we invest and roll it over at a rate of return k every year. After n years, the resulting value, VnF , will equal: VnF = I 0 × (1 + k ) . n
(2)
To measure how quickly, if at all, the total cash distributions made by the firm to its shareholders exceed the initial investment, we compute the ratio of VnS and VnF and call it the distribution-toinvestment ratio (DIR):
I0 ⎡ n n− j ⎤ c 1 k × × + ( ) ⎢ ∑ ⎥ j VnS P0 ⎣ j=1 ⎦. DIR n = F = n Vn I0 × (1 + k )
(
)
Equations (1) to (3) assume we invest in one stock only. We made this simplification for purposes of illustration. In the empirical analysis, we invest in portfolios of stocks. Section 3.1.1. will explain our investment strategy in that context.
5
(3)
The strategy we just described is one of buy and hold. Other investment strategies are conceivable, including one that participates in all share repurchases. If firms switch from paying dividends to repurchasing shares (Fama and French (2001), Grullon and Michaely (2002)), tendering in share repurchases could be more beneficial than simply buying and holding. The empirical section therefore also investigates the alternative of buying and participating in share repurchases on a pro-rata basis (buy-and-participate strategy). Whatever strategy investors follow, the hypothesis that corporate cash distributions justify the prices that shareholders pay implies the following six testable propositions. Proposition 1. Over time, the reinvested value of the cash distributions grows and exceeds
the compounded value of the initial investment at rates of return (k) between the risk-free rate ( R F ) and the required rate of return (μ). Put differently, the distribution-to-investment ratio (DIR) should grow and eventually exceed one for R F ≤ k < μ as the investment horizon grows. When the reinvestment return is μ, DIR asymptotically approaches the value of one from below. The proof is in the Appendix. Since we are unable to assess the required rate of return (μ) correctly, we test whether the predicted regularity between DIR and k holds as k grows farther from the risk-free rate. Figure 1 illustrates this proposition by plotting various DIRs as a function of different reinvestment rates of return. For simplicity, we assume an initial investment of $100 and a constant annual perpetuity of $10. For all reinvestment rates of return smaller than the required rate of return of 10%, the DIRs grow with the investment horizon and eventually exceed one. They all asymptotically approach a given value above one. For example, for k = 8%, the DIR reaches the value of one after 21 years and then asymptotically approaches the value of 1.25.
6
When k = 10%, the DIR asymptotically moves toward the value of one from below, and when k = 11%, it tends to 0.91 without ever reaching the value of one. Proposition 2. The preceding logic also implies that the greater k, the smaller the DIR for a
given investment horizon T. Figure 1 illustrates this phenomenon. For any investment horizon, the highest DIR is that computed when the reinvestment return equals the risk-free rate (5%), and the lowest DIR is that associated with a reinvestment return of 10%. Proposition 3. Riskier stocks should eventually make higher cash distributions than stocks
that are less risky. If we invest the same amount of money in two different stocks, the investment with higher risk will eventually have to make higher cash distributions—larger cash flows are needed to offset higher discount rates. It follows that, as we extend the investment horizon T, the DIRs of riskier stocks should eventually be higher (keeping the reinvestment rate of return the same). This is probably the most restrictive test of market rationality we perform, since it requires that investors predict both future cash distributions and risk over long time horizons. Since companies change capital structure, products, and markets over time, predicting risk would seem like a daunting task. Proposition 4. Riskier stocks at the time of the investment should subsequently yield more
volatile cash distributions. Proposition 5. Terminal stock prices should decline in importance over time (Fama and
Miller (1972)). To illustrate this implication, we restate the DCF model using the stock price at time T, PT, and write:
7
T
P0 = ∑ t =1
ct PT + t (1 + μ) (1 + μ)T
(4)
P0 should converge to a finite limit as T approaches infinity. But this requires that the value of PT as a proportion of the compounded future value of the cash distributions decline with T, on average. Proposition 6. Stocks with the same risk should have the same distribution-to-investment
ratios in the long run regardless whether they distribute cash from the beginning or initiate payouts only later. This follows from equation (3) above with the appropriate rearrangements.
2. Data
We study the NYSE, the AMEX, and the Nasdaq. The sample period covers the years 1926 to 2004 and the data are from CRSP. We compile all cash distributions that firms make to their shareholders ignoring for the moment share buybacks (Section 3.3. drops that restriction when investigating the buy-and-participate strategy). This involves the cash (or the cash value of property) paid out as ordinary and liquidating dividends, and all cash paid out as part of exchanges and reorganizations. Ordinary dividends are annual, semiannual, quarterly, and monthly cash dividends, year-end and special cash dividends, interim and nonrecurring cash dividends, and cash dividends with unknown frequency. We keep all distributions of common stock, such as stock splits and stock dividends, and add them to our initial shares. 4 Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash
4
We do, however, sell preemptive rights. We have no simple alternative, since CRSP does not report a price-
adjustment factor for rights issues. Selling preemptive rights is in principle inconsistent with our plan of focusing
8
generated by these stock distributions is added to the proceeds from investing in the original stock. One complication we have to deal with is delisting events. When a stock is delisted, it is dropped from CRSP. That happens, in particular, when a company goes private, when it switches to an exchange other than NYSE, AMEX, and Nasdaq, and when the company ceases to comply with stock exchange regulations or SEC rules. In those cases, we include the CRSP delisting amount as a final distribution. That amount is either an off-exchange price or pricequote, or the sum of cash distributions. All other delisting cases, including mergers and liquidations, are treated as any other form of cash or stock distribution. Strictly taken, delisting amounts are not necessarily cash distributions by the firm. The results do not change, however, when we ignore these payments. Table 1 provides descriptive statistics about the frequency of cash distributions as well as their value over time and by exchange. As one can see from Panel A, there are 570,279 distribution events, 553,621 of which are ordinary dividends, 4,753 are liquidating dividends, 7,451 are delisting distributions, and 4,454 are exchanges and reorganizations. The aggregate dollar amount in question is 9,939 billion constant 2004 dollars; roughly 75% of this amount is ordinary dividends, 4% reflects liquidating dividends and delisting distributions, and 21% comprises exchanges and reorganizations (keep in mind we are ignoring share buybacks for the moment). For 967 dividend payments, no payment date is specified on the CRSP tapes. In these cases, we use the ex-dividend dates as proxies. According to Panel B, NYSE firms make up roughly 87% of the total corporate cash disbursement, compared with 3% for AMEX, and 10%
on the cash distributed by firms and ignoring the cash received from other investors. Fortunately, rights issues are fairly rare—they represent only 0.1% of the value of all distributions by CRSP firms in the 1926–2004 period.
9
by Nasdaq firms. Industrial firms are responsible for about 72% of the aggregate sum; utilities and financials pay out the rest.
3. Results
We begin with an analysis of distribution-to-investment ratios for different firm-size portfolios under buy-and-hold. We use these data to test our six propositions. We start with a univariate analysis and then reexamine our conclusions in a multivariate context. Finally, we replicate the analysis under a buy-and-participate strategy.
3.1. Buy-and-hold: Univariate analysis 3.1.1. Portfolio formation and characteristics
We compute distribution-to-investment ratios for investments in equity portfolios. To form these portfolios, we rank firms on the CRSP tapes on any given month by market capitalization and assign them to ten buckets in descending order. Portfolios are then established by spreading an initial $100 equally across all the firms available in each bucket. Portfolio 1 combines the largest firms, portfolio 10 the smallest ones. We form the first portfolios in January of 1926. For each of the ten portfolios, we compute the cash payouts each individual stock in the portfolio yields during the following years. Portfolio composition remains the same until 2004. Stocks of firms that are taken over for cash or liquidated make a last payment and drop out of the portfolio. For exchanges of stock, we take the new stock and add it to the portfolio. In the first part of our analysis, we reinvest all cash distributions we receive at the risk-free rate observed at the end of a particular month. The proxy
10
for the risk-free rate is the one-month T-bill rate from the CRSP Fama Risk Free Rate Files. Later, we replicate our analysis by reinvesting at risk-adjusted rates of return. Alternatively, we put the same initial $100 in one-month T-bills in 1926 and renew that investment every month. That computation yields the value of our original investment under risk-free compounding over time. At given points in time, namely 15, 20, and 30 years after 1926, we then compute distribution-to-investment ratios (DIR) by dividing the aggregate compounded value of the cash distributions to a given portfolio by the compounded value of our original investment. We compute these ratios for each size portfolio. In January of 1927, we start a new round of investments. We rank firms by market capitalization and assign them again to ten buckets in descending order. We then invest in the various firms in each size bucket (and, alternatively, in the risk-free asset). Again, for each equally weighted stock portfolio, we compute DIRs 15, 20, and 30 years thereafter. In January of 1928, we start yet another round of investments. We repeat this procedure until the end of the sample period in 2004. To identify DIRs by the time elapsed since the underlying portfolios were formed, we add the corresponding numeral—DIR15, for instance, denotes DIRs 15 years after portfolio formation. The last DIRs observed in 2004 refer to portfolios established in 1990 (DIR15), 1985 (DIR20), and 1975 (DIR30), respectively. Because we start new portfolios every year, and because the CRSP firm population and firm value change over time, the composition of our newly created size portfolios generally changes from one year to the next as well. For example, the portfolio 1 we start in 1955 does not necessarily include the same firms as the portfolio 1 we start in 1956. The composition of existing portfolios, however, remains the same (unless firms are delisted).
11
Since we form new portfolios every year, their DIRs cover overlapping periods. For example, the portfolios we form in 1927 cover the same years as the portfolios we form in 1926 (except for 1926). Consequently, even if the composition of our portfolios is not necessarily the same from one year to the next, the distribution-to-investment ratios will tend to be serially correlated. The DIR15s, for example, are highly correlated, although they do not seem to necessarily follow the same stochastic process (not shown). To deal with the overlapping data, the significance tests involving the distribution-toinvestment ratios rely on a Newey-West autocorrelation consistent covariance estimator approach. In the multivariate analysis, we address the serial correlation problem with a PraisWinsten approach that has the merit of also allowing for panel-corrected standard errors.
3.1.2. Distribution-to-investment ratios: Testing Propositions 1, 3, and 4
The various panels of Table 2 provide descriptive statistics for the distribution-to-investment ratios of different size portfolios and over different investment horizons. All ratios are computed assuming reinvestment at the risk-free rate. For ease of interpretation, the next-to-last column in each panel reports the relative size of each portfolio, computed by dividing the average market capitalization of firms in that portfolio by the average market capitalization of the largest firms (portfolio 1). Note that the smallest firms have an average size that is only 0.3% of the average size of the largest firms. The last column reports the average standard deviation of return on each size portfolio. Panel A refers to distribution-to-investment ratios fifteen years after portfolio creation. Because we form the first portfolios at the beginning of 1926, we observe the first DIR15s at the end of 1940. From then until 2004, there are 64 additional DIR15 values we observe for each
12
portfolio. Across all portfolios, the average DIR15 is greater than one. Hence, it takes 15 years for an investment in stocks to generate sufficient cash to justify the initial outlay under riskless compounding (remember, however, that we ignore the possible liquidation proceeds). The individual portfolios’ average DIR15s are between 0.909 (for portfolio 1) and 1.177 (for portfolio 9). With the exception of portfolio 1, we cannot reject the hypothesis that these DIR15s equal one at customary levels of significance (not shown). We also see that DIR and firm size are inversely correlated. The smaller firm size, the higher the distribution-to-investment ratio. Portfolio 10, however, does not have the highest DIR. This seems to contradict Proposition 3, since riskier portfolios should distribute more cash over time. We assume that risk is inversely related to market capitalization—and the volatility figures in the last column of the panel support that assumption. It could be that the smallest size portfolio includes young firms that originally pay little cash and have therefore fallen behind in their payouts compared with other firms. As predicted by Proposition 4, the dispersion of distribution-to-investment ratios within each portfolio is inversely correlated with firm size. That is true for both the spread between the minimum and the maximum values and the standard deviation. Portfolio 1, for example, has a minimum DIR15 of 0.344 and a maximum of 1.586 with a standard deviation of 0.293. In comparison, portfolio 10 has a minimum of 0.124 and a maximum of 4.772 with a standard deviation of 0.822. Panel B shows the distribution-to-investment ratios 20 years after portfolio formation. As predicted by Proposition 1, all DIR20s have increased from what they were five years before and are larger than one. Moreover, the inverse relation between firm size and DIR predicted by
13
Proposition 3 is monotonic. And so is the relation between firm size and the DIR dispersion measures, which confirms Proposition 4. The same comments apply to the distribution characteristics of DIR30 in Panel C. Average and median DIRs have increased uniformly from the level they had ten years before. All average DIRs have increased by at least 50% compared with the DIR20 values. The first quartiles of the distributions of DIR30 are larger than one, and all third quartiles are close to or exceed three (portfolios 1 and 2 are the exceptions). The dispersion of DIR values within each portfolio has also increased substantially, and it is still a monotonic function of risk. The standard deviation, for example, has about doubled in all size portfolios. The only observation not fully in line with our predictions is the impact of risk on DIR value. Contrary to Proposition 3, the inverse relation between firm size and DIR is not monotonic over the full domain. Portfolio 10 has a smaller DIR than the preceding three size portfolios. Overall, Table 2 therefore supports almost all our predictions. The DIRs grow to values larger than one over time. The relation between risk and DIR dispersion is uniformly positive. And risk and the distribution-to-investment ratios are positively correlated. However, the smallest firms do not have the highest DIRs, whether we look at short or long horizons. The same conclusion follows if we measure risk by return variance or CAPM-beta rather than firm value (not shown). The smallest firms seem to pay too little cash. All these results are confirmed when we replicate the analysis by dropping all AMEX and Nasdaq firms or when we focus only on industrial firms. Consequently, the regularities we observe, including that the smallest firms do not have the highest DIRs, are not driven by the presence of AMEX and Nasdaq firms—nor by that of financials and utilities.
14
3.1.3. Distribution-to-investment ratios with risk-adjusted reinvestment rates: Testing Propositions 2 and 3
Table 3 repeats the analysis with reinvestment returns higher than the risk-free rate. To choose a meaningful equity risk premium, we invoke the literature. For 1900 to 2002, Dimson, Marsh, and Staunton (2003) measure a real premium relative to bills of 7.2% (arithmetic mean); Fama and French (2002) report a 5.57% premium relative to commercial paper for 1872 to 2000; 5 Pastor and Stambaugh (2001) offer estimates “based on reasonable priors” that fluctuate between 3.9% and 6.0% since 1834; and the data in Ibbotson Associates (2000) imply a premium of 7.5% between 1926 and 1999 ???. We therefore investigate the value of distribution-toinvestment ratios over a 30-year investment horizon with nominal premiums between 0% and 8%. We do not claim to have the correct risk-adjusted discount rates. All we want to do is test the predicted regularities 2 and 3 for reinvestment rates reasonably close to their correct values. The evidence is generally consistent with the propositions in question. In agreement with Proposition 2, the cross-sectional average DIR30 drops with the risk premium we impose—it equals 2.575 for a risk premium of 0%, and 0.888 for one of 8%. The same results hold for the individual size portfolios. More importantly, the average DIR30 exceeds one for risk premiums up to 6%, equals one (statistically) for a 7% premium, and falls below one for an 8% premium. Since 7% is in the ballpark range of the premium estimates reported in the literature for the years in question, this evidence fails to reject the claim that firms disburse payments commensurate with the prices that shareholders pay, on average.
5
For the same period, Fama and French (2002) also compute an equity premium using dividend growth rates of
3.54%. Since that figure is imputed from dividend data, and since we use dividend data ourselves, relying on that estimate would involve a circular argument.
15
The numbers are mostly supportive also of the hypothesis that, for a given investment horizon, the distribution-to-investment ratios go up with risk (Proposition 3). A look at the table shows that the DIR30 for each portfolio increases almost monotonically with the risk premium— the exceptions are Portfolios 9 and 10. Note that, if one is willing to assume market efficiency, one can follow a logic similar to that in Fama and French (2002) to assess the risk premiums appropriate for the various size portfolios. As implied by Proposition 1, distribution-to-investment ratios reach one asymptotically for reinvestment rates equal to the required rate of return. The table tells us roughly where that is the case for each individual portfolio. The implied risk premiums go from 5% (Portfolio 1) to 8% (Portfolios 6–10). We shaded the corresponding values in the table.
3.1.4. The importance of the terminal stock price: Testing Proposition 5
In our computation, we have omitted the liquidation proceeds at the end of the investment horizon. In computing DIR15, for instance, we disregard the money investors would receive if they sold their portfolios after 15 years. The rationale is that we want to measure only the cash that firms actually disburse to shareholders rather than the cash that shareholders receive from selling to each other. What follows explores the importance of that omission and tests whether, as predicted by Proposition 5, the relevance of the terminal stock price falls with the investment horizon. Table 4 examines the importance of terminal stock prices for investment horizons of 15 and 30 years. The reinvestment return equals the risk-free interest plus a 7%-risk premium. Column (1) lists the average DIR15s without liquidation proceeds (these DIR15s are those reported in Table 2); in contrast, column (2) documents what value the DIR15s would have, on average, if
16
we liquidated the investment after 15 years and added the liquidation proceeds to the cash distributions. The inclusion of terminal stock prices about doubles the overall average DIR15 (from 0.644 to 1.202). The average terminal stock price itself is between 75% and 96% of the reinvested cash distributions in the individual size portfolios, with an overall average value of 81% (column 3). The right-hand side of the table replicates the analysis for a 30-year investment horizon and confirms Proposition 5. Doubling the horizon cuts the terminal stock price’s importance from 81% to 24%. For the individual size portfolios, their value is now between 20% and 31% of the cash distributions. Even after 30 years, the liquidation proceeds remain fairly sizable. A spreadsheet calculation shows that ignoring them does not significantly affect our conclusions, however. Given the initial $100-investment, a nominal discount rate of 11%, 6 and the observed 24%-ratio of terminal stock price to accumulated cash distributions, omitting the liquidation proceeds affects the implied-yield-to-maturity by a mere 80 basis points. Table 4 also helps us understand the small-firm puzzle a bit better. As we have seen, the smallest size portfolio seems to pay too little cash. The table shows that this is not because tiny firms postpone their distributions. In fact, if we look at the table’s last column, we see that the ratio of terminal stock price to aggregate distributions for the top three portfolios is at least 27%; for the smallest firms, it is 25%. If investors truly believed that tiny firms deliberately defer their cash distributions for more than 30 years, their ratio would be higher rather than lower than 27%.
6
For the years in question, Ibbotson Associates (2000) report an annualized return on equities of 11.3 percent.
17
3.1.5. The importance of the delisting amounts
The preceding analysis treats the delisting amounts reported on the CRSP tapes as corporate cash distributions. In some cases, however, these “distributions” are simply off-exchange prices or price-quotes. We therefore retrace the steps of our analysis and investigate what happens when we ignore these fictitious corporate payments (not shown). The results are qualitatively the same. The only difference is that, without delisting amounts, the DIRs are lower, especially for the smallest firms, since they are the ones most likely to delist. With a 5%-risk premium, for example, the smallest size portfolio has a DIR30 of 1.398 when we include the delisting amounts and one of 1.093 when we don’t.
3.1.6. Summary and conclusions
Overall, the evidence uncovered so far supports the prediction that distribution-toinvestment ratios grow with the investment horizon and eventually exceed one for reinvestment returns smaller than the firm’s required rate of return (Proposition 1); moreover, they are inversely related to the magnitude of the reinvestment return (Proposition 2). Also, the evidence confirms that riskier portfolios (as measured by size) have more volatile cash distributions (Proposition 4) and that the importance of terminal stock prices falls with the investment horizon (Proposition 5). Perhaps most importantly, we document that, using a common reinvestment rate of return, the distribution-to-investment ratios are a positive and monotone function of risk (Proposition 3). The exception is the smallest firms. This finding, however, is the result of a univariate analysis and therefore potentially misleading, since risk (firm value, in our analysis) might be correlated with other variables. We therefore reexamine Proposition 3 in a multivariate context.
18
3.2. Buy-and-hold: Multivariate analysis 3.2.1. General considerations
The purpose of our multivariate analysis is to test the propositions that average distributionto-investment ratios: a)
Increase with risk (Proposition 3). Remember, we compute our DIRs assuming a common reinvestment rate of return. Consequently, the higher portfolio risk the higher its DIR. We measure risk alternatively as CAPM-beta, standard deviation of return, and firm size. We should point out that we have to assess risk at the time of portfolio formation, just as investors have to. Firm size could also be a proxy for market liquidity. According to the evidence, the two are directly related (see, among others, Amihud and Mendelson (1986), Amihud (2002), Pástor and Stambaugh (2003), and Loderer and Roth (2005)). If so, illiquid firms would have to yield higher DIRs on average. The logic is similar to that used to justify the relation between DIRs and risk;
b)
Correlate with the dividend payout at the time we assemble our portfolios. All else being equal, higher current dividend yields should not imply higher distribution-to-investment ratios (Proposition 6);
c)
Are abnormal for either very large or very small firms. The preceding tables suggest that tiny firms differ from the rest. The null hypothesis is that there is no difference;
d)
Change over time. Time effects could occur because of different sample composition after 1962 and 1972, the years in which CRSP adds AMEX and Nasdaq companies, respectively,
19
to its tapes. Alternatively, time effects could capture changes in risk premiums (Fama and French (2002)). If so, our DIRs should be lower after 1962.
We focus on distribution-to-investment ratios computed over 30 years. We assume reinvestment returns equal the risk-free interest (we relax this assumption when examining the robustness of our results). Since valuable information might be lost by aggregating firms into large portfolios, we repeat the calculations by sorting firms not in 10 but rather in 100 portfolios in descending order of firm size. With either sample, we estimate the following regression:
LNDIR30i,t = α 0 + α1RISK i,t + α 2 LNSIZEi,t + α 3DYi,t + α 4 D-LARGE-10%i,t
(5)
+ α 5 D-SMALL-10%i,t + α 6 REPTODISTi,t +α 7 D-1963i,t + ε i,t , where the subscript i refers to a given size portfolio, the subscript t is the year in which we observe the DIR in question, and εi,t is an error term. LNDIR30 is the natural logarithm of DIR30. The results remain the same without the logarithmic transformation. ‹D-› in front of a variable labels it as a binary variable equal to one if a certain condition applies, and equal to zero otherwise. Variable definitions, descriptive statistics, and expected sign of their coefficients are shown in Table 5. The variable REPTODIST is added for control purposes. REPTODIST assesses the relative market-wide importance of share repurchases as a form of cash distribution in a given calendar year. If firms replace dividend payments with share repurchases, its coefficient should be negative, since the cash distributions under our buy-and-hold investment policy omit all share repurchases.
20
The regression is a pooled cross-section time-series regression. We estimate it with a PraisWinsten approach with panel-corrected standard errors (PCSE), as specified in the Stata software. 7 In implementing this approach, we allow for disturbances with different standard deviations across panels (heteroskedasticity across panels). Also, we permit contemporaneous correlation in disturbances across panels, and autocorrelation of order one in the disturbances within panels. Unless otherwise specified, statistical significance is with confidence 0.95 in a two-sided test.
3.2.2. Estimation results
The results are reported in Table 6. Columns (1) and (2) sort firms in 10 size portfolios, and columns (3) and (4) in 100 size portfolios. Column (1) refers to the regression specification in equation (6) using return volatility (VOLA) as the measure of investment risk. With 63%, this regression specification has fairly large explanatory power. The coefficient on VOLA is positive and statistically significant with confidence better than 0.99. Similarly, the coefficient associated with firm size (LNSIZE) has a negative and highly significant coefficient. Both observations are consistent, in principle, with Proposition 3, according to which higher risk leads to higher DIRs. Firm size, however, could also capture the effect of market liquidity. We also find that the variable DY, which gauges the importance of ordinary cash dividends, has a positive and significant coefficient. Hence, the cash distributions of firms with a lower ordinary dividend yield at the time the portfolio is created do not catch up with the payoffs of firms that
7
StataCorp. 2007. Stata Statistical Software: Release 9.2. College Station, TX: Stata Corporation. The method
of panel corrected standard errors was developed by Beck and Katz (1995). See also Beck (2001).
21
pay a higher ordinary dividend from the start. Taken at face value, this is inconsistent with Proposition 6. The coefficient of the binary variable D-LARGE-10% is positive and significant; that of the binary variable D-SMALL-10% is negative and significant. These two findings are also difficult to explain. Very large firms seem to distribute abnormally more cash, whereas tiny firms appear to do the opposite. Thus, very large firms would seem to be under- and tiny firms overpriced. One possible explanation for the result involving the very small firms is that investors may look upon them as gambles. 8 Given their high return volatility (see Table 2), 9 investors might regard these equities as unique chances to strike it rich, even if the probability of doing so is small. Investors might therefore be willing to pay more than these firms are worth. That leaves us with the puzzle, however, of why very large firms appear to be underpriced. The variable REPTODIST has a negative and statistically insignificant coefficient, apparently inconsistent with the claim that share repurchases are a partial substitute for cash dividends in the firm’s payout policy. Finally, the negative and significant coefficient of the binary variable D-1963 suggests that portfolios of firms created during the last four decades of the sample period yield distribution-toinvestment ratios that are lower than those of previous periods. As mentioned above, this could reflect the secular decline in equity risk premiums postulated by Fama and French (2002). Column (2) of the table repeats the estimation by replacing return volatility with CAPMbeta. This new risk proxy has a coefficient that is insignificantly different from zero at
8
For papers that discuss this notion, see, among others, Dwyer and Barnhart (2002), Statman (2002), Barberis
and Huang (2007), and Mitton and Vorkink (2007). 9
The smallest firms have an average standard deviation of return that is twice as large as that of the largest firms
(Table 2).
22
conventional levels of confidence. The remaining results are in line with what we observe under the preceding specification. The explanatory power of the regression is almost unchanged, too. Columns (3) and (4) perform the same analysis by splitting firms into 100 rather than 10 size portfolios. All variables have significant coefficients with the sign observed in the first two columns. The coefficient of BETA, in particular, becomes positive and significant. The explanatory power of these regressions is generally lower. Going from 10 to 100 portfolios therefore seems to add a significant amount of noise to our experiment, but it confirms our conclusions.
3.2.3. Robustness checks
To assess the robustness of our findings we replicate the analysis with alternative variable definitions and estimation approaches (not shown in separate tables). First, we ignore all delisting amounts. The results are identical. Second, we examine a shorter time horizon of 15 years. We observe essentially the same results. The main difference is that, except for firm size, our risk measures have statistically insignificant coefficients, regardless whether we form 10 or 100 size portfolios. One possible explanation is that 15 years is too short a time period for the cash distributions of riskier firms to catch up. The analysis in Table 6 assumes reinvestment at the risk-free rate. To probe the importance of that assumption, we repeat the computations under the assumption of different risk premiums. With minor changes in the coefficients of the risk variables, the conclusions remain the same. The small differences relate to the coefficient of BETA: it is positive and significant when we sort firms in 10 size portfolios, yet it loses its statistical significance when we sort them in 100 size portfolios.
23
We also consider a different measure of firm size. The preceding tests employ the natural logarithm of the average market value of equity of the firms in a particular portfolio (in constant 2004 dollars). As an alternative, we measure firm size for each portfolio with values from 1 to 10, as in the univariate analysis. The results are mostly the same. The coefficient of size, however, loses its statistical significance in the specifications of columns (1) and (3). Moreover, the coefficients of the binary variables that flag the largest and the smallest size portfolios are no longer always statistically significant. The coefficient associated with the largest firms is significant only when we distinguish 10 size portfolios, whereas the coefficient that identifies the smallest firms is significant only when we form 100 size portfolios. Finally, we estimate the parameters of equation (1) with the generalized method of moments (GMM). With two exceptions, that estimation approach does not change our main conclusions either. Specifically, we find that risk has a significant coefficient regardless of what proxy we use (that holds also when we add a premium to our reinvestment rate); tiny firms appear to pay too little and very large firms too much cash; and the post-1963 years are associated with lower DIR30s. What changes is that firms with higher dividend yields at the time of portfolio formation do not have higher DIRs when we work with 100 size portfolios—but they still do when we sort firms in 10 size portfolios. Moreover, the coefficient of REPTODIST becomes positive and significant, a rather puzzling result if dividends and share buybacks are substitute methods of disbursing cash. It could be that a market-wide increase in repurchasing activities reflects an increase in overall corporate cash distributions.
24
3.2.4. Summary and conclusions
On the whole, the multivariate analysis offers mixed evidence for our predictions. First, and consistent with Proposition 3, riskier stock investments tend to be associated with higher cash distributions. This holds generally whether we measure risk with return volatility, CAPM-beta, or firm size. The relation can be seen most sharply when sorting firms in 100 size portfolios. Second, however, most specifications suggest that portfolios of firms with higher dividend yields at the time of their formation pay significantly more cash than portfolios of other firms. This contradicts Proposition 6. It seems that dividends convey important pricing information. This might be a reason why firms pay out cash to begin with. Of course, one could also argue that 30 years is too short an investment horizon for non-dividend payers to catch up. Third, portfolios of the smallest firms distribute significantly less cash, and portfolios of the largest firms distribute significantly more. This is a puzzling result. It could be that the cash distributions to these two portfolios are difficult to predict. Very small firms are probably very young and have therefore a very uncertain future. And very large firms could be firms with an exceptional (and hardly sustainable) past performance that makes them equally unpredictable. Figure 2 examines this interpretation. The investment horizon is 30 years. The panel on the lefthand side shows the average cash distributions in constant 2004 dollars by firms in portfolio 1, the largest ones. We report the average as well as the 25th, 50th, and 75th percentiles of those payments. In contrast, the panel on the right-hand side shows the cash distributions by the smallest firms in the sample (portfolio 10). Visual inspection is only partially consistent with our supposition. Whereas the average and the various percentiles of the cash distributions by the smallest firms are indeed fairly volatile, those by the largest firms are comparatively smooth. It
25
might indeed be difficult to price small firms correctly (Fama (1998)), but it is not obvious why the same problem should present itself in the case of large firms.
3.3. Buy-and-participate strategy
The buy-and-hold strategy we have investigated so far ignores share repurchases. Investors could pursue other investment strategies, however. One that is logically consistent with our attempt to measure the actual cash distributions by corporations is a buy-and-participate strategy. It is identical to buy-and-hold except the investor participates in all share repurchases on a prorata basis. Share repurchases surged in the mid-1980s. Whereas in the 1973–1977 and 1978– 1982 periods they averaged 3.37% and 5.12% of aggregate earnings, they rose to 31.42% between 1983 and 1998 (Fama and French (2001)). According to Grullon and Michaely (2002), the reason for the increased popularity is the adoption in 1982 of Rule 10b-18 by the SEC, which protects repurchasing firms from the antimanipulative provisions of the Securities Exchange Act of 1934. If share repurchases have replaced dividends as a means of distributing cash, 10 it is conceivable that a buy-and-participate strategy could yield more cash than buy-and-hold. This section investigates that possibility. Simulating a buy-and-participate strategy faces a few problems and limitations. First, since we use the Compustat tapes, we can measure share repurchases only for industrial firms. Second, data about repurchases do not go back far. Fortunately, repurchases seem to be
10
This possible switch is discussed, among others, in Fama and French (2001), Jagannathan, Stephens, and
Weisbach (2000), Grullon, and Michaely (2002), and Boudoukh, Michaely, Richardson, and Roberts (2006). Allen and Michaely (2003) and DeAngelo, DeAngelo, and Skinner (2004) document the existence, however, of various companies with substantial dividend payments even in the 1980s and 1990s. Moreover, dividends seem to have rebounded in recent years (Brav, Graham, Harvey, and Michaely (2005)).
26
insignificant before 1971, and there are data since then. 11 Third, since actual buyback dates and quantities are often difficult if not impossible to ascertain with much precision, we have to make approximations. Compustat has annual data starting in 1971 and quarterly data starting in 1984. For 1971–1983, our analysis relies on annual data. We switch to quarterly data, however, as soon as they become available. The repurchase price is assumed to equal the average price during the repurchase’s calendar year (quarter). The number of common shares repurchased equals the value of common shares repurchased divided by the average price. And the value of common shares repurchased equals item “Purchase of Common and Preferred Stock” in Compustat’s Statement of Cash Flows minus the decrease in the aggregate value of preferred stock. 12 In our simulation, the proceeds from tendering shares in a share buyback are invested at midyear (midquarter). The fourth limitation of our analysis is the assumption that the hypothetical investor participates on a pro-rata basis in all repurchases we can find with Compustat data, whether they are fixed-price tender offers, Dutch auction repurchases, or open-market repurchases. The problem is that he would not be able to join targeted share repurchases. Fortunately, these
11
With respect to the years prior to the early sixties, for example, DeAngelo and DeAngelo (2006) state that “it
is not surprising that repurchases are mentioned nowhere in MM (1961) since dividends were the only empirically meaningful equity payout at that time, and so the issue of the dividend/repurchase mix was simply not on the profession’s radar screen“ (p. 300). 12
For a discussion of alternative methods of measuring reacquired shares, see Stephens and Weisbach (1998).
Yearly and quarterly purchases of common and preferred stock are measured with Compustat data items #115 and #92, respectively; par value of preferred stock corresponds to the yearly and quarterly data items #130 and #55, respectively. In contrast to Stephens and Weisbach (1998) and Boudoukh, Michaely, Richardson, and Roberts (2006), we use par values instead of redemption values to compute the value of preferred stock repurchased since the latter data are only available on the yearly tapes. The same procedure is adopted by Banyi, Dyl, and Kahle (2005).
27
repurchases do not seem to be very important. Even recently, they were less than 10% of the dollar value of all announced buyback programs (Stephens and Weisbach (1998)). Consistent with what other authors have reported, the importance of share repurchases increases steadily over time—from about 8.5% of all other types of cash distributions in 1971– 1975 to 86.9% in 2001–2004 (not shown). Table 7 reports distribution-to-investment ratios over a 30-year horizon and for risk premiums up to 8%. The DIRs under buy-and-participate are indeed larger than those computed under buy-and-hold (Table 3). It pays to participate in share repurchases. The benefits, however, are numerically only marginal (and statistically never significant). For example, the overall average DIR30 with no risk premium equals 2.575 under buy-and-hold, compared with 2.612 under buy-and-participate. With a 7% risk premium, these numbers are 0.989 under buyand-hold and 1.002 under buy-and-participate. And with an 8% premium, they are 0.888 and 0.899, respectively. Save for these marginal differences, the new data confirm the story we know, namely that: The DIRs grow over time, reach a value of one for risk premiums up to 7%, and then tend to decline; for any given investment horizon, they fall as a function of the imposed risk premiums; they increase monotonically with risk (except for the smallest firms); they are more volatile for higher risk (not shown); and the importance of terminal stock prices falls with the investment horizon (not shown). We also replicated our multivariate regressions under buyand-participate and found coefficients almost identical to those in Table 6 in terms of numerical values and significance.
28
4. Conclusions
We examine whether the cash that corporations distribute to shareholders over the very long run is consistent with the prices they pay. In spite of the popularity of that belief, there is no obvious market mechanism that would help guarantee equality. Arbitrage looks prohibitively expensive and investor learning is very difficult. We are not interested in the cash that investors could receive from selling to each other. Our focus is the cash that firms actually disburse. The main strategy we simulate is buy-and-hold. Our (tax-exempt) investor does not increase his stake in the companies he invests in, does not participate in discretionary share repurchases, ignores stock splits (in the sense that he keeps his shares), does not sell any stock dividends, and holds on to any stock in other firms received during restructurings and mergers. He takes all the cash he collects on his investment, such as ordinary cash dividends, liquidations, cash distributed during mergers and acquisitions, and delisting payments, and reinvests it. We compute the ratio of the aggregate future compounded value of these cash distributions to the future compounded value of the initial investment, and call it distribution-to-investment ratio (DIR). We test whether the DIRs of various size portfolios are consistent with the implications of a DCF model. Overall, we are unable to reject those implications. Over a 30year investment horizon, and ignoring taxes, corporate cash distributions yield returns commensurate with the contemporaneous risk-free rates and the risk premiums reported in the literature for the years in question, on average. Perhaps even more noteworthy, riskier firms tend to distribute more cash. Moreover, the cash distributions of riskier firms are more volatile. And terminal stock prices decline in importance as investment horizons grow longer. These results are robust with respect to different estimation techniques and hold regardless whether we include
29
delisting payments, and whether we restrict the sample to industrial firms or firms listed on the NYSE. However, the picture the data paint has individual patches that seem difficult to reconcile with rationality. Portfolios of firms with higher dividend yields at the time they are put together distribute more cash than portfolios of firms with lower dividend yields. Another apparently anomalous result is that tiny firms seem to return an abnormally small amount of cash, whereas very large firms do the opposite. In the case of tiny firms, the reason could be that their cash distributions are quite uneven time-series, and therefore difficult to predict. It is also possible, however, that a 30-year investment horizon is too short to call these observations anomalies. We find no evidence, however, that, compared with larger firms, tiny firms defer paying out cash for 30 years. We also explore an alternative investment strategy. Our buy-and-participate strategy is identical to buy-and-hold except the investor participates in all buybacks on a pro-rata basis. This strategy enables us to take into account the increased importance of share repurchases in recent decades while maintaining our focus on the cash that firms actually distribute to their shareholders. Overall, buy-and-participate yields slightly higher cash flows than buy-and-hold. More importantly, however, it confirms all the test results we obtain under buy-and-hold. The analysis has ignored taxes. Doing otherwise would have taken us beyond the normal space constraints of a single paper. Still, taxes do not necessarily change our conclusions. Distribution-to-investment ratios are likely to behave the same. To see that we recomputed the numbers in Figure 1 by imposing a 30%-tax rate on both the reinvestment rates and the cash distributions. The predicted regularities are unchanged—they grow to values larger than one for
30
reinvestment rates greater than μ, and they tend asymptotically to a value of one for reinvestment rates equal to μ (Figure 2). In spite of the popularity of DCF models in corporate finance, this seems to be the first paper to take a direct look at actual, comprehensive cash distributions over very long investment horizons. The results suggest that investors are able to predict both the level and the risk of future cash distributions many years ahead correctly, on average. Probably, the reason they can do so in spite of the problems with arbitrage and learning is that firms make predictable (smooth) cash distributions. Besides its relevance to theory, the evidence we find has practical relevance. All management policies with a DCF core, including value-based management approaches, are corroborated by the reported regularities.
31
References
Ackert, Lucy F., and Brian F. Smith, 1993, Stock price volatility, ordinary dividends, and other cash flows to shareholders, Journal of Finance 48, 1147-1160. Allen, Franklin, and Roni Michaely, 2003, Payout policy, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Amihud, Yakov, and Haim Mendelson, 1986, Asset pricing and bid-ask spread, Journal of Financial Economics 17, 223-249.
Amihud, Yakov, 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, 31-56.
Banyi, Monica, Edward A. Dyl, and Kathleen M. Kahle, 2005, Measuring share repurchases, Working paper, Oregon State University. Barberis, Nicholas, and Ming Huang, 2007, Stocks as lotteries: The implications of probability weighting for security prices, Working paper, Yale University. Barberis, Nicholas, and Richard Thaler, 2003, A survey of behavioral finance, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Beck, Nathaniel, 2001, Time-series-cross-section data: What have we learned in the past few years? Annual Review of Political Science 4, 271-293. Beck, Nathaniel, and Jonathan N. Katz, 1995, What to do (and not to do) with time-series crosssection data, American Political Science Review 89, 634-647. Boudoukh, Jacob , Roni Michaely, Matthew Richardson, and Michael Roberts, 2006, On the importance of measuring payout yield: Implications for empirical asset pricing, Journal of Finance 62, 877-916.
Brav, Alon, John R. Graham, Campbell R. Harvey, and Roni Michaely, 2005, Payout policy in the 21st century, Journal of Financial Economics 77, 483-527.
32
Campbell, John Y., and Robert J. Shiller, 1991, Yield spreads and interest rate movements: A bird’s eye view, Review of Economic Studies 58, 495-514. DeAngelo, Harry, Linda DeAngelo, and Douglas J. Skinner, 2004, Are dividends disappearing? Dividend concentration and the consolidation of earnings, Journal of Financial Economics 72, 425-456. DeAngelo, Harry, and Linda DeAngelo, 2006, The irrelevance of the MM dividend irrelevance theorem, Journal of Financial Economics 79, 293-315. De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldman, 1990, Noise trader risk in financial markets, Journal of Political Economy 98, 703-738. Dimson, Elroy, Paul Marsh, and Mike Staunton, 2003, Global evidence on the equity risk premium, Journal of Applied Corporate Finance 15, 8-19. Donaldson, R. Glen, and Mark Kamstra, 1996, A new dividend forecasting procedure that rejects bubbles in asset prices: The case of 1929’s stock crash, Review of Financial Studies 9, 333383. Dwyer, Gerald, and Cora Barnhart, 2002, Are stocks in new industries like lottery tickets? Working Paper, 2002-15, Federal Reserve Bank of Atlanta, Atlanta, GA. Fama, Eugene F., 1970, Efficient capital markets: A review of theory and empirical work, Journal of Finance 25, 383-417.
Fama, Eugene F., 1991, Efficient capital markets: II, Journal of Finance 46, 1575-1617. Fama, Eugene F., 1998, Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics 49, 283-306.
Fama, Eugene F., and Kenneth R. French, 2001, Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics 60, 3-43. Fama, Eugene F., and Kenneth R. French, 2002, The equity premium, Journal of Finance 57, 637-659. Fama, Eugene F., and Merton H. Miller, 1972, The Theory of Finance (Dryden Press, Hinsdale, IL.).
33
Foerster, Stephen, and Stephen Sapp, 2005, The dividend discount model in the long-run: A clinical study, Journal of Applied Finance 15, 55-75. Gordon, Myron J., 1962, The Investment, Financing and Valuation of the Corporation (R. Irwin, Homewood, IL.). Grullon, Gustavo, and Roni Michaely, 2002, Dividends, share repurchases, and the substitution hypothesis, Journal of Finance 62, 1649-1684. Ibbotson Associates, 2000, Stocks, Bonds, Bills and Inflation Yearbook (Ibbotson Associates, Chicago, IL.). Jagannathan, Murali, Clifford P. Stephens, and Michael S. Weisbach, 2000, Financial flexibility and the choice between dividends and stock repurchases, Journal of Financial Economics 57, 355-384. LeRoy, Stephen F., and Richard D. Porter, 1981, The present-value relation: Tests based on implied variance bounds, Econometrica 49, 555-574. Liu, Jun, and Francis A. Longstaff, 2004, Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities, Review of Financial Studies 17, 611-641. Loderer, Claudio, and Lukas Roth, 2005, Discount for limited liquidity: Evidence from the SWX Swiss Exchange and the Nasdaq, Journal of Empirical Finance 12, 239-268. Miller, Merton H., and Franco Modigliani, 1961, Dividend policy, growth, and the valuation of shares, Journal of Business 34, 411-433. Mitchell, Mark, Todd Pulvino, and Erik Stafford, 2002, Limited arbitrage in equity markets, Journal of Finance 57, 551-584.
Mitton, Todd, and Keith Vorkink, 2007, Equilibrium underdiversification and the preference for skewness, Review of Financial Studies 20, 1255-1288. Pástor, Luboš, and Robert F. Stambaugh, 2001, The equity premium and structural breaks, Journal of Finance 56, 1207-1239.
Pástor, Luboš, and Robert F. Stambaugh, Liquidity risk and expected stock returns, Journal of Political Economy 111, 642-685.
34
Schwert, William G., 1991, Review of market volatility by Robert J. Shiller, Journal of Portfolio Management 17, 74-78.
Schwert, William G., 2003, Anomalies and market efficiency, in George M. Constantinides, Milton Harris, and R. Stulz, eds.: Handbook of the Economics of Finance (North-Holland, Amsterdam). Shiller, Robert J., 1981, Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review 76, 421-436. Shiller, Robert J., 2002, From efficient market theory to behavioral finance, Journal of Economic Perspectives 17, 83-104.
Shleifer, Andrei, and Lawrence H. Summers, 1990, The noise trader approach to finance, Journal of Economic Perspectives 4, 19-33.
Shleifer, Andrei, and Robert W. Vishny, 1997, The limits of arbitrage, Journal of Finance 52, 35-55. Statman, Meir, 2002, Lottery players/stock traders, Financial Analyst Journal 58, 14-21. Stephens, Clifford P., and Michael S. Weisbach, 1998, Actual share reacquisitions in openmarket repurchase programs, Journal of Finance 53, 313-334. West, Kenneth D., 1988, Dividend innovations and stock price volatility, Econometrica 56, 3761. Williams, John B., 1938, The Theory of Investment Value (Harvard University Press, Cambridge, MA.).
35
Table 1 Aggregate cash distributions under a buy-and-hold strategy The table shows the distributions of our sample firms for the period 1926–2004. These distributions include ordinary and liquidating cash dividends (or the cash value of property), stock and other payouts in connection with exchanges and reorganizations, as well as delisting distributions. The hypothetical investor keeps all distributions of common stock, such as stock splits and stock dividends. We assume a buy-and-hold strategy, and therefore ignore share repurchases. Panel A lists the number of distribution events and the associated dollar amount in constant 2004 dollars by event type. Panel B shows the dollar amount of these distributions by exchange (and for the sample of industrial firms) over time. The data are from CRSP. Panel A: Distribution events by type Event type
Number of events
Ordinary dividends Liquidating dividends Stock delisting Exchanges and reorganizations Total
553,621 4,753 7,451 4,454 570,279
Dollar amount (in billions of constant 2004 dollars) 7,468.45 104.55 250.27 2,118.63 9,939.36
Panel B: Distributions over time. Dollar amounts are in billions of constant 2004 dollars. Period 1926–1930 1931–1935 1936–1940 1941–1945 1946–1950 1951–1955 1956–1960 1961–1965 1966–1970 1971–1975 1976–1980 1981–1985 1986–1990 1991–1995 1996–2000 2001–2004 Total
All sample firms 126.46 100.51 128.96 122.21 157.13 215.66 302.01 410.81 532.88 588.40 822.96 996.89 1,323.19 985.98 1,789.71 1,335.60 9,939.35
NYSE firms 126.46 100.51 128.96 122.21 157.13 215.66 302.01 387.80 494.84 497.61 647.40 842.25 1,108.12 851.29 1,517.34 1,122.01 8,621.60
36
AMEX firms
Nasdaq firms
23.01 38.04 32.84 38.44 37.21 56.89 27.20 36.08 23.87 313.57
57.96 137.13 117.43 158.17 107.49 236.29 189.72 1,004.19
Industrial firms 100.90 80.09 116.08 112.99 144.63 189.82 261.63 348.50 447.51 451.16 619.86 743.97 957.61 640.26 1,162.76 822.44 7,200.20
Table 2 Distribution-to-investment ratios under a buy-and-hold strategy and riskless reinvestment The table lists the distribution-to-investment ratios (DIRs) of investment portfolios a given number of years after creation. DIRs are computed as the ratio of the aggregate payouts (compounded at the risk-free rate) on a stock investment divided by the value of the initial investment (also compounded at the risk-free rate). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Panels A, B, and C report descriptive statistics about distribution-to-investment ratios 15, 20, and 30 years after the initial stock investment. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. Relative size is defined as the average market capitalization of firms in a given portfolio divided by the average market capitalization of firms in portfolio 1 at the time of portfolio formation. Volatility is the equally weighted, average annual standard deviation of return on the stocks in a particular portfolio. It is computed using the 60 monthly stock returns preceding the year of portfolio formation. We require a minimum of 36 monthly data. If the volatility of a particular firm cannot be determined, we ignore it (but we keep the weights of the remaining volatilities in the portfolio the same). Stars (*) indicate the significance of mean comparison tests between the portfolio in question and portfolio 1. Standard errors for the mean-comparison tests are computed with a Newey-West correction for autocorrelation with a number of lags equal to the portfolio holding period. To test the difference of the average DIRs observed for portfolios 1 and 2, for instance, we compute that difference in each sample year, regress it against a constant, and use the Newey-West procedure to estimate the regression standard error. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1926–2004. The data are from CRSP. Panel A: Distribution-to-investment ratios 15 years from inception. The first set of portfolios is formed in 1926 and kept until 1940. There are 65 observations for each size portfolio between 1940 and 2004. Portfolio 1 2 3 4 5 6 7 8 9 10 All
Average 0.909 0.932 0.950 1.020 1.064 1.070 1.104 1.163 1.177 1.135 1.052
* * * * ** ** *
Median 0.929 0.819 0.822 0.886 0.899 0.870 0.937 0.896 0.954 0.878 0.886
First quartile 0.658 0.662 0.669 0.716 0.716 0.669 0.678 0.683 0.672 0.665 0.670
Third quartile 1.097 1.110 1.165 1.194 1.362 1.400 1.391 1.438 1.438 1.360 1.296
37
Min
Max
0.344 0.346 0.283 0.296 0.372 0.352 0.310 0.334 0.272 0.124 0.124
1.586 2.069 2.001 2.412 2.512 2.648 3.518 4.563 3.692 4.772 4.772
Standard deviation 0.293 0.364 0.404 0.463 0.510 0.558 0.643 0.737 0.767 0.822 0.585
Relative size 100.0% 18.57% 8.83% 5.13% 3.29% 2.19% 1.48% 0.96% 0.58% 0.26% –
Volatility 27.9% 32.3% 34.8% 37.2% 38.9% 41.4% 43.1% 46.0% 50.3% 56.8% –
Panel B: Distribution-to-investment ratios 20 years from inception. The first set of portfolios is formed in 1926 and kept until 1945. There are 60 observations for each size portfolio between 1945 and 2004. Portfolio 1 2 3 4 5 6 7 8 9 10 All
Average 1.255 1.310 1.326 1.428 1.523 1.544 1.624 1.680 1.723 1.729 1.514
** ** ** * ** ** *
Median 1.254 1.130 1.184 1.221 1.249 1.261 1.269 1.244 1.400 1.244 1.225
First quartile 0.825 0.878 0.877 0.961 0.977 0.890 0.934 0.932 0.928 0.963 0.918
Third quartile 1.577 1.661 1.661 1.816 2.091 2.030 1.979 2.165 2.073 1.884 1.832
Min
Max
0.470 0.447 0.387 0.390 0.508 0.476 0.481 0.491 0.383 0.201 0.201
2.255 2.885 2.821 3.434 4.075 4.275 4.973 6.301 5.471 8.499 8.499
Standard deviation 0.447 0.553 0.606 0.704 0.792 0.860 1.024 1.122 1.165 1.489 0.937
Relative size 100.0% 19.13% 9.17% 5.36% 3.45% 2.31% 1.56% 1.01% 0.61% 0.28% –
Volatility 27.7% 32.1% 34.5% 36.8% 38.5% 40.8% 42.4% 45.2% 49.4% 55.7% –
Panel C: Distribution-to-investment ratios 30 years from inception. The first set of portfolios is formed in 1926 and kept until 1955. There are 50 observations for each size portfolio between 1955 and 2004. Portfolio
1 2 3 4 5 6 7 8 9 10 All
Average
2.023 2.196 2.202 2.359 2.544 2.694 2.900 2.999 2.942 2.895 2.575
*
** ** ** ** ** ** **
Median
First quartile
Third quartile
Min
Max
1.706 1.867 1.933 1.912 2.124 2.254 2.151 2.205 2.176 1.705 1.936
1.294 1.286 1.182 1.364 1.391 1.310 1.387 1.322 1.411 1.368 1.323
2.687 2.886 2.974 3.327 3.380 3.342 3.403 3.814 3.533 2.905 3.092
0.883 0.748 0.739 0.684 0.703 0.577 0.749 0.557 0.485 0.412 0.412
4.242 5.273 5.295 6.222 8.262 9.173 9.418 10.813 11.009 12.980 12.980
38
Standard deviatio n 0.887 1.151 1.254 1.421 1.637 1.928 2.162 2.379 2.334 2.791 1.903
Relative size
Volatility
100.0% 20.16% 9.81% 5.80% 3.77% 2.54% 1.73% 1.13% 0.69% 0.31% –
27.3% 31.5% 33.9% 36.1% 37.7% 39.7% 41.2% 44.0% 48.0% 54.3% –
Table 3 Distribution-to-investment ratios under a buy-and-hold strategy assuming risk-adjusted reinvestment rates The table lists average distribution-to-investment ratios (DIRs) of investment portfolios 30 years after creation assuming reinvestment rates equal to the risk-free rate plus a constant risk premium. DIRs are computed as the ratio of the aggregate payouts (compounded at a given return) on a stock investment divided by the value of the initial investment (also compounded at the same return). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. Standard errors are reported in parentheses. The sample period is 1926–2004. The data are from CRSP. Portfolio 1 2 3 4 5 6 7 8 9 10 All
0% 2.023
3% 1.289
4% 1.128
Risk premiums 5% 0.994
6% 0.884
7% 0.791
8% 0.712
(-0.125)
(-0.075)
(-0.065)
(-0.056)
(-0.049)
(-0.043)
(-0.038)
2.196
1.398
1.223
1.079
0.958
0.858
0.773
(-0.163)
(-0.096)
(-0.082)
(-0.071)
(-0.061)
(-0.054)
(-0.047)
2.202
1.407
1.233
1.088
0.968
0.867
0.781
(-0.177)
(-0.105)
(-0.090)
(-0.077)
(-0.067)
(-0.059)
(-0.052)
2.359
1.510
1.323
1.168
1.039
0.930
0.839
(-0.201)
(-0.119)
(-0.102)
(-0.088)
(-0.076)
(-0.067)
(-0.059)
2.544
1.622
1.419
1.250
1.110
0.993
0.893
(-0.232)
(-0.136)
(-0.116)
(-0.099)
(-0.086)
(-0.075)
(-0.066)
2.694
1.702
1.485
1.305
1.155
1.030
0.925
(-0.273)
(-0.158)
(-0.134)
(-0.114)
(-0.098)
(-0.085)
(-0.074)
2.900
1.815
1.578
1.382
1.220
1.085
0.971
(-0.306)
(-0.177)
(-0.149)
(-0.127)
(-0.110)
(-0.095)
(-0.083)
2.999
1.878
1.633
1.430
1.262
1.121
1.003
(-0.336)
(-0.196)
(-0.167)
(-0.142)
(-0.122)
(-0.106)
(-0.093)
2.942
1.858
1.619
1.422
1.257
1.119
1.003
(-0.330)
(-0.194)
(-0.165)
(-0.141)
(-0.122)
(-0.106)
(-0.093)
2.895
1.828
1.593
1.398
1.235
1.099
0.985
(-0.395)
(-0.236)
(-0.201)
(-0.173)
(-0.150)
(-0.131)
(-0.115)
2.575
1.631
1.423
1.252
1.109
0.989
0.888
(-0.085)
(-0.050)
(-0.043)
(-0.037)
(-0.032)
(-0.027)
(-0.024)
39
Table 4 Distribution-to-investment ratios under a buy-and-hold strategy, with and without terminal stock prices The table lists the average distribution-to-investment ratios (DIRs) with and without terminal stock prices computed over a 15-year and 30-year investment horizon, respectively. DIRs are computed as the ratio of the aggregate payouts (compounded at the risk-free rate plus a constant risk-premium of 7%) on a stock investment divided by the value of the initial investment (also compounded at the risk-free rate plus a constant risk-premium of 7%). DIRs are formally defined in equation (3) of the text. We show DIRs with and without the stock prices observed at the end of the holding period. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends. The sample period is 1926–2004. The data are from CRSP. Portfolio
1 2 3 4 5 6 7 8 9 10 All
15 years after portfolio inception Average DIR Average of terminal stock price divided Without With by value of cash terminal terminal distribution stock stock prices prices (1) (2) (3) 0.562 1.057 83% 0.579 1.096 83% 0.590 1.109 82% 0.629 1.141 75% 0.653 1.197 76% 0.656 1.192 75% 0.671 1.244 79% 0.699 1.286 77% 0.706 1.314 83% 0.692 1.385 96% 0.644 1.202 81%
40
30 years after portfolio inception Average DIR Average of terminal stock price divided Without With by value of cash terminal terminal distribution stock stock prices prices (4) (5) (6) 0.791 1.061 31% 0.858 1.110 27% 0.867 1.111 27% 0.930 1.161 23% 0.993 1.236 22% 1.030 1.297 22% 1.085 1.352 22% 1.121 1.393 20% 1.119 1.416 22% 1.099 1.430 25% 0.989 1.257 24%
Table 5 Descriptive statistics of regression variables (buy-and-hold strategy) The table shows descriptive statistics of variables in regression equation (10) of the text. The sample period is 1926–2004. For each size portfolio, we estimate average return standard deviation and CAPM-beta using data from the 60 monthly observations preceding portfolio formation. Thus, the first ten size portfolios with the necessary information are those we create at the beginning of 1931. The first distribution-to-investment ratios are observed 30 years later, in 1960. Panel A reports descriptive statistics, and Panel B shows variable definitions. The data are from CRSP. Panel A: Descriptive statistics Variable DIR30 VOLA BETA LNSIZE DY REPTODIST
Average
Median
2.730 0.116 1.128 12.053 0.042 0.081
2.141 0.105 1.106 12.024 0.039 0.000
First quartile 1.434 0.079 0.989 10.752 0.027 0.000
Third quartile 3.337 0.140 1.249 13.311 0.055 0.110
Min
Max
0.487 0.050 0.596 7.397 0.000 0.000
12.651 0.320 1.776 16.114 0.210 0.511
Standard deviation 1.914 0.049 0.200 1.849 0.023 0.148
Panel B: Variable definitions Variable
DIR30
Definition
Expected sign of coefficient Distribution-to-investment ratio, defined as the ratio of the aggregate payouts on N/A an investment in a portfolio of equities of given market capitalization (compounded at the risk-free rate) divided by the value of the initial investment (also compounded at the risk-free rate). The holding period is 30 years. Distribution-to-investment ratios are formally defined in equation (3) of the text;
RISK
Risk, defined alternatively as return volatility (VOLA), CAPM-beta (BETA), and natural logarithm of firm size (LNSIZE);
+
VOLA
Average standard deviation of return (volatility) of the firms in a given size portfolio in a particular year. Stock return volatility is computed using data from the 60 months preceding the year in question (we require a minimum of 36 observations);
+
BETA
Average CAPM-beta of the firms in a given size portfolio in a particular year. CAPM-beta is computed with a market model using data from the 60 months preceding the year in question (we require a minimum of 36 observations); the market index is the value-weighted CRSP index;
+
LNSIZE
Natural logarithm of firm size (in constant 2004 dollars), defined as the average market value of equity of the firms in a given size portfolio in the year the portfolio is formed;
–
DY
Average dividend yield of the firms in a given size portfolio the year the portfolio
0
41
was created. Dividend yield is defined as cash dividends paid during the year divided by stock price at year end; REPTODIST
Ratio of the aggregate value of share repurchases divided by the aggregate value of total cash distributions by industrial firms on both the CRSP and the Compustat tapes in a given year. Data on share repurchases for industrial firms are available only from 1971 on. As argued in the text, buybacks seem to have been insignificant before 1971. Before that date, this variable is therefore set to zero;
–
D-LARGE-10%
Binary variable equal to 1 for the largest-size portfolio, and equal to 0 otherwise;
0
D-SMALL-10%
Binary variable equal to 1 for the smallest-size portfolio, and equal to 0 otherwise;
0
D-1963
Binary variable equal to 1 if the portfolio is started at the beginning of 1963 or later, and equal to 0 otherwise.
–
42
Table 6 Multivariate analysis of distribution-to-investment ratios under a buy-and-hold strategy We examine the relation between the distribution-to-investment ratios 30 years after portfolio formation and possible determinants. LNDIR30 is the natural logarithms of DIR30, under riskless compounding. Distribution-toinvestment ratios are defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given firm-size portfolio. Once created, these portfolios are maintained over time. However, we form new portfolios every year. The analysis is based on a Prais-Winsten panel regression approach with panel corrected standard errors. We allow for heteroskedastic disturbances across panels (size portfolios). Moreover we assume that the disturbances are contemporaneously correlated across panels, and that the disturbances of any one panel are serially correlated of order one. Descriptive statistics and definition of the variables are in Table 5. Numbers in parentheses are robust tstatistics. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1926–2004. The data are from CRSP. Independent variables
VOLA
Dependent variable: LNDIR30 10 firm-size portfolios 100 firm-size portfolios (1) (2) (3) (4) 4.028*** 3.658*** (3.267)
(3.671)
BETA
0.195**
0.061 (0.265)
–0.269*** (–6.263)
(–9.248)
(–5.451)
(–7.358)
DY
6.742***
4.078***
1.724***
1.286***
(6.398)
(4.319)
(4.137)
(3.114)
D-LARGE-10%
0.870***
1.364***
0.463***
0.680***
(6.885)
(8.290)
(5.332)
(6.119)
D-SMALL-10% REPTODIST D-1963 Constant Number of observations Number of years Number of portfolios per year R-squared Wald χ-squared
–0.659
–0.463***
(1.974)
LNSIZE
***
–1.090
***
–0.176***
–0.446
***
–0.266***
–0.523***
(–4.871)
(–6.282)
(–7.021)
(–6.853)
–0.524
–0.542
–0.267
–0.359
(–0.492)
(–0.522)
(–0.211)
(–0.268)
–0.228**
–0.144
–0.473***
–0.494***
(–1.978)
(–1.136)
(–3.943)
(–3.799)
3.353
***
6.181
***
2.594
***
3.884***
(5.482)
(8.558)
(5.626)
(8.267)
450 45 10 0.626 165.3***
450 45 10 0.577 139.8***
4,500 45 100 0.379 146.3***
4,500 45 100 0.319 118.8***
43
Table 7 Distribution-to-investment ratios for industrials under a buy-and-participate strategy assuming risk-adjusted reinvestment rates The table reports average distribution-to-investment ratios (DIRs) 30 years after the initial stock investment for the full sample period and for different risk premiums. Unlike in the preceding tables, investors participate on a prorata basis in all share repurchases by the firm. DIRs are computed as the ratio of the aggregate payouts (compounded at a given return) on a stock investment divided by the value of the initial investment (compounded at the same return). DIRs are formally defined in equation (3) of the text. Portfolios are formed with firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Once created, these portfolios are maintained over time. However, we form new portfolios every year. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, delisting distributions, as well as the proceeds from stock repurchases. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The investor keeps all distributions of common stock such as stock splits and stock dividends. Standard errors are reported in parentheses. The sample period is 1926–2004. The data are from CRSP. Portfolio 1 2 3 4 5 6 7 8 9 10 All
0% 2.065
3% 1.314
4% 1.149
Risk premiums 5% 1.012
6% 0.899
7% 0.804
8% 0.724
(-0.123)
(-0.074)
(-0.063)
(-0.055)
(-0.048)
(-0.042)
(-0.037)
2.235
1.420
1.242
1.094
0.972
0.869
0.783
(-0.161)
(-0.095)
(-0.081)
(-0.070)
(-0.061)
(-0.053)
(-0.047)
2.230
1.424
1.247
1.100
0.978
0.876
0.790
(-0.176)
(-0.104)
(-0.089)
(-0.077)
(-0.067)
(-0.058)
(-0.051)
2.384
1.526
1.336
1.180
1.049
0.940
0.847
(-0.200)
(-0.119)
(-0.102)
(-0.088)
(-0.076)
(-0.067)
(-0.059)
2.568
1.637
1.432
1.262
1.121
1.002
0.902
(-0.231)
(-0.136)
(-0.115)
(-0.099)
(-0.086)
(-0.075)
(-0.065)
2.727
1.722
1.502
1.320
1.168
1.042
0.935
(-0.272)
(-0.158)
(-0.134)
(-0.114)
(-0.098)
(-0.085)
(-0.074)
2.944
1.841
1.600
1.402
1.237
1.100
0.984
(-0.304)
(-0.175)
(-0.149)
(-0.127)
(-0.109)
(-0.094)
(-0.082)
3.038
1.902
1.653
1.448
1.278
1.135
1.015
(-0.335)
(-0.196)
(-0.166)
(-0.142)
(-0.122)
(-0.106)
(-0.092)
2.978
1.880
1.638
1.438
1.271
1.131
1.014
(-0.331)
(-0.194)
(-0.165)
(-0.141)
(-0.122)
(-0.106)
(-0.093)
2.948
1.860
1.620
1.421
1.256
1.117
1.001
(-0.392)
(-0.235)
(-0.201)
(-0.173)
(-0.150)
(-0.131)
(-0.115)
2.612
1.653
1.442
1.268
1.123
1.002
0.899
(-0.085)
(-0.050)
(-0.042)
(-0.036)
(-0.031)
(-0.027)
(-0.024)
44
2.0
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
70
Years DIR(RF=5%)
DIR(k=6%)
DIR(k=7%)
DIR(k=9%)
DIR(k=10%)
DIR(k=11%)
DIR(k=8%)
Figure 1. Simulated distribution-to-investment ratios (DIR) as a function of different reinvestment returns. The figure computes distribution-to-investment ratios for an initial investment of $100 and a constant annual perpetuity of $10 as a function of different reinvestment returns. The risk-free interest rate is 5% and the required rate of return is 10%.
45
2.0
DIR
1.5
1.0
0.5
0.0 0
10
20
30
40
50
60
70
Years
DIR(k=5%, before-tax) DIR(k=10%, before-tax)
DIR(k=5%, after-tax) DIR(k=10%, after-tax)
Figure 2. Simulated distribution-to-investment ratios (DIR) before and after taxes as a function of different reinvestment returns. The figure computes distribution-to-investment ratios before and after taxes for an initial investment of $100 and a constant pre-tax annual perpetuity of $10 as a function of different reinvestment returns. We assume a pre-tax risk-free interest rate of 5%, a pre-tax required rate of return of 10%, and a tax rate of 30%.
46
Portfolio 1
Portfolio 10 14
Cash distributions (in constant 2004 dollars)
Cash distributions (in constant 2004 dollars)
14 12 10
75th percentile
8
Mean
6
Median
4
25th percentile
2 0
75th percentile
12 10 8
Mean
6 4
Median
2
25th percentile
0 1
5
10
15
20
25
30
Years (relative to the year of portfolio inception)
1
5
10
15
20
25
30
Years (relative to the year of portfolio inception)
Figure 2. Annual cash distributions under a buy-and-hold strategy over a 30-year time horizon. The figure shows annual cash distributions in constant 2004 dollars on the largest- (portfolio 1) and smallest-size portfolios (portfolio 10) in the sample. Portfolios are formed with all CRSP firms sorted in descending order of market capitalization by spreading a hypothetical $100 over the stocks available in a given decile of firm value. Portfolio 1 includes the largest firms on the CRSP monthly tapes, portfolio 10 the smallest ones. Once created, these portfolios are maintained over time. The sample years are 1926–2004. The investment horizon is 30 years. New portfolios are formed every year, the last one in 1975. Cash distributions consist of ordinary and liquidating cash dividends, cash distributed in connection with exchanges and reorganizations, the value of any distributed property, as well as delisting distributions. Distributions of other firms’ stock are added to the initial stock investment and held; any subsequent cash or property distributions on these stock distributions are added to the proceeds from investing in the original stock. The hypothetical investor follows a buy-and-hold strategy, and therefore ignores share repurchases. He also keeps all distributions of common stock, such as stock splits and stock dividends.
47
Appendix Proof of Proposition 1. Let’s focus on one share of stock and use the DCF model to express
the stock price, P0 , as the present value of the stream of future cash distributions the investment is expected to make:
P0 =
c3 c1 c2 + + + ... , 2 (1 + μ) (1 + μ) (1 + μ)3
(A1)
where μ (the required rate of return) is assumed constant for purposes of exposition, and c t is the cash distribution investors expect to receive in year t conditional on public information available at time 0. With riskless discounting, the stock price, P0F , equals:
P0F =
c3 c1 c2 + + + ... , 1 2 (1 + R F ) (1 + R F ) (1 + R F )3
(A2)
where R F is also assumed constant for simplicity. Clearly, P0 < P0F . We can use these two equations to assess how the value of the stock’s cash distributions compares with the initial stock price. To find out, let us rearrange equation (A2) and compound everything at the risk-free rate over an investment horizon of T years (we will consider the case of other rates k > R F later):
c3 c1 c2 × (1 + R F )T + × (1 + R F )T + × (1 + R F )T + ... 1 2 (1 + R F ) (1 + R F ) (1 + R F )3 (A3) = P0F × (1 + R F )T > P0 × (1 + R F )T ,
48
where the inequality follows from the fact that P0F > P0 . In words, the reinvested value of the stock’s cash distributions between time 0 and time T plus the value of the distributions expected thereafter equals the value of the original stock price in a risk-free world ( P0F ) compounded for a number of periods T. The value of those distributions, however, is larger than the future value of the original stock price ( P0 ) compounded at the risk-free rate. If we now deduct the cash distributions beyond time T from the left-hand side of equation (A3) and rearrange, we obtain: c1 × (1 + R F )(T −1) + c2 × (1 + R F )(T − 2) + c3 × (1 + R F )(T −3) + ... + cT (A4) ≤ P0F × (1 + R F )T > P0 × (1 + R F )T . Because of equation (A3), as we extend the investment horizon T, the cumulative compounded value of the stock’s cash distributions approaches the value P0F × (1 + R F )T from below and eventually exceeds the future value of the initial stock price compounded at the risk-free rate, P0 × (1 + R F )T . A similar argument shows that this prediction holds for all reinvestment rates k such that RF ≤ k < μ. In other words, the cumulative value of the cash distributions reinvested at a return k eventually surpasses the value of the original investment compounded at the same return k. In the limit, however, when k = μ, the value of those distributions will converge toward the value of P0 × (1 + μ)T from below. In terms of our distribution-to-investment ratios (DIR), these predictions imply that the DIR of a given stock grows with the investment horizon and eventually exceeds one for reinvestment returns RF ≤ k < μ.
49
