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TRANSCRIPT
Leverage- and Cash-Based Tests of Risk and Reward
With Improved Identification
Ivo Welch
Anderson School at UCLA
January 31, 2017
Abstract
Leverage offers not only its own directional implications for both risk and reward,
but also facilitate superior tests of risk-reward theories: Leverage can change with and
without corporate intervention, and even discontinuously so. The evidence suggests
that leverage not only lowers average rates of return (Fama and French (1992)), but
also raises volatility. Changes in leverage work even better. These effects appear in the
large panel of U.S. stock returns, survive progressively better empirical identification,
and even hold in quasi-experimentally identified discontinuity tests using dividend
and equity issues. Unlike many other asset-pricing anomalies, it is difficult to see
how this could be attributed to omitted factors, contamination, information, or corpo-
rate responses. It raises fundamental questions about the perfect-market risk-reward
paradigm.
Keywords: Leverage, Risk, Reward, Quasi-Experiments, Behavioral Finance.
JEL Codes: G12 G31 G32 G35
I thank Malcolm Baker, Mark Garmaise, Lukas Schmid, Richard Thaler, and Jeff Wurgler and seminarparticipants at BYU, Cornell, the FRB, and UCLA for comments. The computer programs were (are) rewrittenindependently to reduce the chance of inadvertent selection issues or programming bugs. The reportedresults were robust to all considered variations.
1
The central paradigm of macro-finance is built around the fact that investors earn more
reward only when they take on more risk. Yet this is remarkably difficult to test. There
is no academic agreement about what the correct risk factors are—although the models
posit that investors are aware of them. Furthermore, unidentified contaminants—such
as new information simultaneously released or counteracting corporate responses—and
simply measurement error can render inference difficult. Nevertheless, the academic faith
in this fundamental risk-reward tradeoff is so strong that academic ignorance has shifted
the burden of proof further in favor of risk-reward models: there are now a wide range of
empirical correlations that may originally have raised doubt but nowadays are no longer
viewed as necessarily inconsistent with the paradigm. Empirical rejections of specific
version of the risk-reward theory are more likely to motivate dismissal of the risk metrics
than dismissal of the risk-reward association.
Nevertheless, there is one near-universal risk implication that should work regardless
of deeper risk factors: leverage. Ceteris paribus, every risky asset should become riskier
with more leverage. This risk prediction should hold for priced and non-priced factors.
It is even more basic than equilibrium factor models. It should apply not only in factor
models, but even if risk-averse investors are unable to diversify. Leverage also offers the
same directional implication (weakly) for expected rates of return. Leverage amplifies
the expected return difference to the risk-free rate of return. Gomes and Schmid (2010)
characterizes the expected return vs. leverage relationship as a fundamental insight of
rational asset pricing:
Increases in financial leverage directly increase the risk of the cash flows to
equity holders and thus raise the required rate of return on equity. This remark-
ably simple idea has proved extremely powerful and has been used by countless
researchers and practitioners to examine returns and measure the cost of capital
across and [sometimes] within firms with varying capital structures.
Paradoxically, Fama and French (1992) had shown that corporate leverage failed to
associate with higher average rates of return in their asset-pricing tests. As Gomes-Schmid
write, “Unfortunately, despite, or perhaps because of, its extreme clarity, this relation
between leverage and returns has met with, at best, mixed empirical success.” Table 2
below will update and confirm the findings in Fama and French (1998). Using various
leverage definitions, controls, and specifications, by-and-large, more levered stocks have
offered similar or lower average rates of return than their less levered counterparts. Since
2
then, leverage has largely been neglected in or omitted from empirical asset-pricing tests,
despite its central theoretical importance.
Fama and French (1998) conclude that there “must be information about profitability
[that] obscures [the] effect of financing decisions,” i.e., one omitted variable contaminating
and invalidating the test. Gomes and Schmid (2010) also propose an omitted variable.
Because leverage is endogenous., riskier firms with more growth options should choose
lower leverage. Thus, riskier firms could end up with both lower leverage and higher
expected returns (due to commensurately higher equity risk). These explanations are not
only conceptually appealing but also make plain sense.
Unfortunately, my own paper shows that information and endogenous leverage choice
cannot put the matter to rest.
First, it offers empirical evidence not only about average rates of return, but also about
risk. The simplest measure of risk is equity volatility. It is interesting not because it should
be priced, but because (net) leverage has sharp, specific, and quantitative implications for
its response. Therefore, it can serve as an indicator either for the basic role of leverage—the
theory that any risky asset should become riskier when levered more—or for distinguishing
between theories in which leverage is exogenous or endogenous—where riskier firms
choose lower leverage. Own volatility is also central to the Gomes-Schmid explanation.
While diversified investors should care more about undiversifiable factor risk (reflected
in expected returns), corporate finance suggests that firms should care more about their
own risk. Focusing on firm’s own variance also has a pragmatic advantage in that it avoids
having to take sides in the controversial academic risk-factor choice and covariance debates.
My paper further shows that controls for many prominent risk factors (those in Fama and
French (2015)) do not invalidate the inference.
Second, it improves on the empirical identification in a number of steps: (1) In the full
panel of U.S. stocks, it investigates not only levels but also changes in leverage. (2) It looks
at changes in leverage that reflect the fact that the same absolute change in leverage means
more for highly-levered firms than it does for less-levered firms. Surprisingly, this turns out
not to matter much. (3) It looks at changes in leverage that are induced by stock returns
before they are (or are not) undone by active corporate responses. (4) It looks at changes
in leverage that occurred jointly with simultaneous same-sign changes in idiosyncratic
volatility; (5) It looks at discrete known-in-advance changes in leverage. The empirical
evidence is clear. Leverage and changes in leverage associate universally positively with
volatility increases and universally negatively with reward. And, paradoxically, average
3
rates of return on equity are even lower after firms have experienced both increases in
leverage and increases in equity volatility.
The settings in which there are discrete known-in-advance change in leverage are
particularly important, because they are not plausibly explainable by an endogenous (or
any other contemporaneous) change in corporate projects and/or by new contaminating
information. Of course, this identification highlights only a small piece of the puzzle, but
one with the advantage that a very clear answer can be found. After briefly exploring
equity issuing activity, my paper focuses on its main discrete known-in-advance leverage
change: the days surrounding discrete cum-to-ex day transitions associated with previ-
ously-announced dividend payments.1 Any systematic news about underlying projects
associated with the dividend new would have already become public at earlier declarations,
which would have been days or weeks before the cum-to-ex date. Conditional on the
past declaration, the cum-to-ex date is no longer endogenous at the firm’s discretion,
and any information would have already been fully conveyed to external investors at the
announcement.
After the declaration but before the cum-to-ex date, the firm’s stockholders in effect own
one low-risk claim on a cash payment plus one higher-risk claim on the remaining equity
components of the projects, both inside the corporate shell. After the payout, investors
still own the same two claims, except that the low-risk asset component has shifted from
inside the corporate shell to the outside. The public stock returns are henceforth only for
the residual riskier project assets. From the owners’ perspective, public equity quotes prior
to the cum-to-ex date are for both claims; quotes after the cum-to-ex date are only for the
more levered claim. The bundle’s net risk and reward would not change—only the part
that is quoted in the stock returns changes.
This is all true regardless of the firm’s underlying investment policy. It is true regardless
of whether the firm already already holds the cash or whether it leaves the dividend-required
resources in risky projects up until the moment of the cum-ex transition: any post-payment
project equity risk would attach to the residual traded firm equity net of the risk-free
dividend payment. The dividend cash was—repurposing an accounting term—de-facto
defeased at the moment of declaration and merely quoted together in the public stock price
as part of a bundle for a few more days.
1Leverage in the divident event study is net leverage, with cash subtracted off obligations, and it can takeon negative values (Acharya, Almeida, and Campello (2007), Pinkowitz, Stulz, and Williamson (2006)). It isnot merely the financial debt structure of the firm.
4
The picture that emerges in all settings is that leverage causally raises total stock
volatility. The effects are well in line with the quantitative predictions of the version
of the leverage theory in which leverage is exogenous. But leverage does not associate
with increases in average rates of return. Neither risk-metric mismeasurement nor new
information nor other contamination can plausibly explain this paradoxical association.
Simply put, investors seem to overprice lower-leverage assets.
This is not “merely” just another empirical anomaly in the zoo of anomalies (Harvey,
Liu, and Zhu (2016)). The purpose of my study is not developing yet another trading
strategy. Instead, it is to investigate leverage as a building block of risk and reward that is
as fundamental and theoretically firmly-predicted as consumption or market betas, but with
the advantage that leverage lends itself to better identification. The leverage risk metric is
known not only to investors (who have to form portfolios to hedge against factor risks),
but also to academics. The leverage risk metric has separable components determined
by financial markets and by corporate managers. The leverage risk metric has discrete
known-in-advance changes. Quasi-experimental identification can also reduce concerns
about measurement error, and information and other potential contamination. The effect
of leverage documented here seems causally suggested by the data and not just by (model)
assumption.
The paper now proceeds as follows: Section I investigates the role of leverage and
leverage changes in the full cross-section of US CRSP and Compustat stocks. Section II
investigates the role of leverage changes in the dividend payment and equity issuing
contexts. Section III speculates on how the findings can be interpreted and offers some
more perspective and relationship to existing research. And Section IV concludes.
5
I The Full-Panel Relation Between Leverage, Own Risk,
and Reward
We begin with a study of the full panel of US firms. The data are exclusively from CRSP and
Compustat from 1962 to 2015 and therefore immediately and universally replicable. All
Compustat variables are assumed to be dated five months after their applicable fiscal year
end before 2004 and four months after 2004 (Bartov, DeFond, and Konchitchki (2013)).2
Define the following six debt ratios:
bknegcash: The negcash ratio is 1-cash/debt, where cash is preferably (Compustat) CHE,
but CH if not available.
bklev: The leverage ratio is netdebt/(netdebt + equity), where netdebt is debt (itself DLTT
plus DLC) minus cash. The book value of equity is the Compustat book-value (CEQ),
net of the investment tax credit (TXDITC or TXDB) when available, and the value of
preferred stock (PSTK). All ingredients are winsorized at 0.
bkliab: The liability ratio is total liabilities net of cash divided by total assets ((LT–
cash)/AT). It avoids the mistaken omission of (often very large) non-financial li-
abilities in the commonly used measure, financial debt divided by total assets (Welch
(2011)).
mknegcash: This measure replaces the book value of equity (itself inside AT) with the
market value of equity in bknegcash. The market value is preferably from Compustat
(either MKVALT or PRCC_f·CSHO), but from CRSP if a Compustat market-value of
equity is not available. The market-value of equity is always kept contemporaneous
with analogous book values, so the assumed accounting lag is also applied here.
mklev: This measure replaces the book value of equity in bklev with the market value of
equity.
mkliab: This measure replaces the book value of equity in bkliab (itself in AT) with the
market value of equity.
The three basic measures, negcash, lev, and liab ratios can be viewed as in order of measure
breadth. Negcash is the narrowest definition of (negative) leverage, while liab is the
broadest. All debt ratios are winsorized to 0.001 and 0.999.2Not reported, the results strengthen when the lag is shortened.
6
We also define changes in these variables and denote them with prefixes:
schg.ratio: The simple one-year change in the debt ratio.
xchg.ratio: The “extreme change,” defined as 1/(1− ratio). For example, a 5% increase
from 0% to 5% ratio maps into a change in 5.3%; a change from 50% to 55% maps
into a change in 22.2%; and a change from 90% to 95% maps into a change of 1000%.
(This transformation can be shown to appropriately reflect changes in expected rates
of return under further assumptions.)
R.schg.ratio: An imputed change in a debt ratio without knowledge of actual year-end
equity and debt but interim stock returns. Thus, this leverage change can be changed
only by the interim change in stock returns. The end-of-period equity value is
the beginning-of-period equity value times one plus the compound rate of return
on the stock. (It matters little whether the paid dividends are subtracted or not.)
These R.schg variables exclude all managerial capital-structure activity during the
calculation interval. A decomposition of leverage changes into those caused by stock
returns and those caused by managers was investigated in Welch (2004).
Table 1 shows the summary statistics. The panel is dominated by the cross-section, so
the average cross-sectional standard deviation is similar to the overall standard deviation,
typically about 0.25 for the two broader debt-ratio levels, about 0.1 for simple debt-ratio
changes, and about 0.5 for the extreme changes. The narrower negcash leverage measure
spreads are about half that of the two broader leverage measures.
[Insert Table 1 here: Spread of Debt-Ratio Levels and Changes]
My paper also often looks at the performance of stocks sorted into quartiles that maintain
year and asset-size balance. That is, in each year, stocks are first sorted by book-assets
(Compustat AT). Within each set of four contiguous similar-size stocks, the one with the
lowest debt ratio (or change in debt ratio) is assigned to category #1; the one with the
highest debt-ratio is assigned to category #4. Typically, in all rows, the interquartile spread
after asset-size control is a little less than twice the standard deviation of the variables. The
final two rows and columns in Table 1 show that despite year and firm-size control, the
R.schg quartiles maintain a good and meaningful spread in actual leverage debt ratios.
7
A Debt-Ratio Levels and Subsequent Average Rates of Return
[Insert Table 2 here: Corporate Debt-Ratio Levels and Subsequent Rates of Return]
Table 2 shows the panel-wide association between leverage and subsequent average
returns, already mentioned in the introduction. They largely update and confirm the
findings in Fama and French (1998), although financial firms are included in my sample.
Panel A shows the Black-Jensen-Scholes / Fama-French time-series monthly alphas of
portfolios long in the quartile of (asset-size controlled) high-levered stocks and short in the
quartiles of low-levered stocks. As in Fama and French (1992, p.444), when few controls
are included, market liabilities have a positive relation with subsequent rates of return while
book liabilities have a negative relation.3 With all Fama and French (2015) factor controls,
all net-leverage portfolios have negative alphas. Depending on the leverage measure, the
least-levered stock quartiles offered average rates of return of between 0.107 · 12 ≈ 1.5%
(mkliab) and 0.464 · 12 ≈ 5% (mknegcash) per annum more than the most-levered stock
quartiles.
Panel B shows the performance of the quartile portfolios in monthly cross-sectional
Fama-Macbeth regressions. The first coefficient columns (“DT Qrtl”) use simple quartile
indicators (from #1 to #4) in lieu of the debt-ratios (“DT Ratio”). The maximum difference
in quartiles is 3. Depending on specification, the coefficients on this variable suggest that
least-levered quartile stocks outperformed the most-levered quartile per annum by an
insignificant 3 · 0.002 · 12 ≈ 0.7% for mkliab, to 3 · 0.116 · 12 ≈ 4% for mknegcash. The
next sets of columns use the debt ratio measures themselves (rather than their categories),
with their average heterogeneity of about 0.25 for the broader debt ratios. Less levered
stocks offer worse performance, and the quantitative inference remains similar, especially
after controls are included.
Although not all spreads are statistically significant, many are. More importantly, there
is no robust evidence in favor of a positive association, as predicted by a naive theory with
exogenous leverage. This was the motivation of Gomes and Schmid (2010).
3They explain this with book/market effects. The third column shows the positive relationship indeeddisappears after HML is controlled for.
8
B Debt-Ratio Changes, Subsequent Equity Volatility, and Subsequent
Average Rates of Return
[Insert Table 3 here: Changes in Leverage, Annual Daily Return Volatility, and Annual Average Returns
— Controlling for Assets ]
Levels are more easily contaminated by spurious contemporaneous factors than differ-
ences. Nevertheless, I could not locate tests of whether leverage changes affect subsequent
average returns, much less whether they affect subsequent equity volatilities.
For intuition, Table 3 begins with displays of annual statistics for the (year- and asset-
controlled) quartiles. The first column shows that the four quartile portfolios are indeed
well-balanced in terms of firm assets and still maintain good spread in debt-ratio changes.
In the leverage-reducing quartile #1, the average debt-ratio reduction was about 6% for
mknegcash and 9% for mklev and mkliab. In the leverage-increasing quartile #4, the
average increases were about 6% and 10-11%.
To be clear about the timing, denote the leverage at the end of year y as L y (itself
assumed available only a few months after the fiscal year end); the rate of return during
the year as ry−1,y and the daily-volatility during the year sdy−1,y . (The sd is the standard
deviation of daily stock returns during the year, based on≈252 daily stock returns, reported
in annualized terms by multiplying byp
252.) The displayed return statistics (x ∈ {r, sd})are then x y−2,y−1 (lag), x y−1,y (contemporaneous), and x y,y+1 (lead); and the displayed
leverage change is L y − L y−1. A simple diagram is
−1 0 1 2
fyr04 or 5 months
accounting delay
fyr14 or 5 months
accounting delay
fyr2
4 or 5 monthsaccounting delayLvg0 Lvg1
Leverage Change
Lag Return StatisticsCntmp
(usually ignored)
Lead Return Statistics
The middle “Annualized Volatility” columns show each quartile’s total annualized equity
volatilities net of its own benchmark lagged volatility. It is more interesting to discuss equity
volatility changes between lead and lag, sdy,y+1−sdy−2,y−1, ignoring the annualized volatility
in the year of the leverage change measurement. The table shows that annualized volatilities
were similar across quartiles in the year before the leverage change (the “lag”). With the
exception of mknegcash, there are subsequent volatility increases in all leverage ratios (the
9
“lead”). The volatility increases are modest but economically significant.4 Depending on
the measure (and excluding schg.mknegcash), the spreads in volatility changes between
quartiles #1 and #4 are about 6-10% per annum. These volatility increase magnitudes
are also reasonably in line with the form of the theory in which leverage is exogenous and
not endogenous (as in Gomes-Schmid). The differential increase of about 0.2 in leverage
ratios across quartiles maps into predicted volatility increase of about 0.2× 0.5 ≈ 0.1.
Ang et al. (2006) and subsequent research (e.g., Herskovic et al. (2016)) have already
noted that firms with high stock return volatility tend to have low subsequent rates of return.
Thus, one could conjecture that the observed higher equity volatility could result in low
subsequent average returns, too—a hypothesis that could suggest that low average returns
may be due not to Gomes-Schmid, but due (possibly only in part) to the ivol anomaly. One
difference in interpretation is that Ang et al. (2006) consider ivol to be the input, while my
paper considers it to be an output (leverage is the input).
The right “Net Return” columns show that stocks whose leverage increased (positive
schg and xchg) had lower average net returns than stocks whose leverage decreased.
Leverage increasers produced about 2-4% per annum lower average annual rates of return
than leverage decreasers.5
Panels C and G use “extreme” (xchg) change versions rather than simple (schg) change
versions. The xchg sort emphasizes leverage changes for firms with already large leverage
to begin with. Unfortunately, although this is economically a good idea, in practice it is
useless. The results are disappointingly similar to those for the simple changes.
[Insert Table 4 here: Changes in Leverage, Annual Daily Return Volatility, and Annual Average Returns
— Controlling for Lag Returns]
However, the lag net returns in Table 3 had the same ordering across quartiles as the
lead net returns. Thus, increases in leverage predicted not only low subsequent returns,
but also low past returns. (Stocks increase leverage when they perform badly.) This makes
it difficult to judge changes in average rate of returns. In Table 4, we temporarily alter the
sort-control to keep not assets but the lag net return constant. The eighth column in each
panel (“Lag Net Return”) shows that this control is very effective. The tenth column (“Lead
4The large number of firm-years also ensures that they are statistically significant beyond reproach. Thiscan be confirmed by repeated draws that randomize the leverage metric and repeat the calculation of thevolatility statistics.
5The returns are quoted net of value-weighted returns, but the net returns do not sum to zero, because ofcompounding, because of the composition of the value-weighted stock market used here, and because ofJensen’s inequality.
10
Net Return”) can now be interpreted as changes in net returns. It still shows that leverage
decreasers had higher average returns than leverage increasers.
[Insert Table 5 here: Annual Stock Return Characteristics Surrounding Changes in Debt Ratios]
Whereas Table 3 described annual measures in categories, Table 5 describes them with
coefficients from least-square regressions. Each regression explains the lead annual variable
with its own lag annual variable (thus ignoring the interceding contemporaneous annual
leverage-change) plus the contemporaneous measure of the in-between debt-ratio change.
The left-side shows the results of Fama-Macbeth-like regressions. The panel coefficients
are plain OLS, with T-statistics that are double-clustered for serial and time correlation,
with heteroskedasticity-adjustment. The Fama-Macbeth procedure is more useful for stock
returns, where we would expect more severe cross-sectional correlation and less severe
time-series correlation in residuals. Of course, tests on annual returns are less powerful
than on monthly returns, the usual domain of Fama-Macbeth regressions. The regression
coefficients by-and-large back up the inference in Table 3.
Panel A shows how leverage changes predict volatility changes. Again, except for
schg.mknegcash, the coefficients are clearly positive for all other leverage changes. Stocks
that raised leverage experienced increases in volatility. A one-standard change in leverage
of about 0.1 induces an increase of about 0.002 in daily volatility, or about 3% per annum.
Stock return volatility is less noisy and thus easier to measure than average rates
of return. Panel B shows that average rates of return decrease in leverage—except for
schg.mkliab where the coefficients are so insignificant that they are best considered to be
zero.
[Insert Table 6 here: The Effect of Changes in Debt Ratios on Subsequent Monthly Stock Returns, All
Stocks]
The annual return regressions in Table 5 are not state-of-the-art for inference about
average stock returns. Table 6 shows the average stock performance in the familiar Fama-
French and Fama-Macbeth regressions, this time using monthly stock returns, for firms
with different leverage-ratio changes.
Panel A shows that the average quartile spread net portfolio, consisting of long leverage-
increasing stock and short leverage-decreasing stocks, subsequently underperformed in
Fama-French timeseries regressions. In the most stringent control—using six Fama-French
11
factors, including UMD that rolls forward—leverage increases predict lower average rates
of return of between 0.076 ·12 ≈ 1% (schg.mkliab)to about 0.201 ·12 ≈ 2.5% per annum.
The significance is twice this without UMD momentum control. Leverage and momentum
are connected: Stocks that experience high momentum also experience market-based
leverage reductions. However, measures that are not directly influenced by these changes
(mknegcash and the three book measures) continue to compete well. Increases in leverage
predict subsequently low average rates of return.
Panel B shows that the typical change in debt-ratio can explain about a 3 · 0.1 · 12 ≈3.5% spread in the quartile spread portfolios in Fama-MacBeth cross-sectional regressions
(averaged). Firms increasing leverage show subsequently lower average rats of return.
Interestingly, even when we control for lagged volatility (as in the last columns), the
leverage measures continue to come in statistically significant. This suggests that there is
more at work than merely the Ang et al. (2006) idiosyncratic volatility effect. Leverage may
work in decreasing average returns through more than just its increases in own volatility.
In the multivariate specifications, both in Table 5 and Table 6, schg.mkliab seems to
have no reliable influence on subsequent average returns. Other measures of debt increases
are reliable and strong predictors. Stocks that increase their leverage experienced low
average rates of return thereafter.
C Debt-Ratio With Simultaneous Equity Risk Changes
The Gomes-Schmid endogenous-response explanation requires a strong negative leverage-
risk link to overcome the direct positive leverage-average-return association. Leverage
increasers should be accompanied not just by weaker equity volatility increases than what
would obtain if there were no change in underlying projects, but by decreases so strong
that they result in net decreases in equity volatility.
A simple way to investigate the Gomes-Schmid endogeneity explanation is to focus
only on stocks that experience not only leverage increases, but also simultaneous equity
volatility (and, say, market-beta) increases. These stocks are not Gomes-Schmid responders.
There should be few of them, and such stocks should still show both increases in volatility
and increases in average rates of return.
Define one reasonable measure of firm risk:
12
• A positive equity risk change is defined as a volatility increase of at least 0.1% per
day (from the lag year to the contemporaneous year).
• A negative equity risk change is defined as a volatility decrease of at least 0.1% per
day.
(An earlier change required also a simultaneous same-sign change in market-beta, but this
does not influence the results.) The equity risk-change metrics are measured contempora-
neous with the leverage-change metrics, i.e., we examine lead statistics based on L1 − L0
leverage and f y r0 − f y r−1 risk.
[Insert Table 7 here: The Effect of Changes in Market-Based Debt Ratios on Subsequent Monthly Stock
Returns, Cross-Classified Simultaneous Risk (Daily Volatility and Market-Beta) Changes]
Tables 7 show cross-tabulations by leverage quartile and risk change category.
The top row shows that there may be a Gomes-Schmid effect in cash. Firms whose
leverage increased had relatively more observations with equity volatility reductions, com-
pared to firms whose leverage decreased. This is not the case for financial leverage and
total liabilities, where the firms that increased leverage were also the firms that increased
risk.
The middle row shows that subsequent volatility increases in leverage within all risk
classes and all leverage change metrics. There is no evidence that firms that increased
their leverage ended up less risky. On the contrary—equity volatility continues to increase
positively with leverage, just as it should when leverage is exogenous.6
The important evidence of this table appears in the bottom row. The average rate of
return seems to decline with leverage even for firms that experienced equity risk increases.
Paradoxically—contrary not only to formal Gomes-Schmid theory but also to basic leverage
theory and common sense—stocks that suffered from both leverage increases and risk
increases also did not return high but low average rates of return. They were not attractive
investments compared to their opposites.
6However, because (1) volatility is now a sorting variable in itself, and (2) we need to use a past volatilityto benchmark the risk change (i.e., measure the risk change), there are near-mechanical mean-reversionaspects. Firms that experienced a random high equity-risk in year (-1,0) were more likely to experience alower risk not only in year (0,1), leading to categorization as a declining risk stock, but also more likely toexperience a lower risk also in year (1,2), which is the displayed statistic. Our interest is in leverage, not inrisk itself, however. There is no economic interpretation of interest that risk increased from left to right.
13
[Insert Table 8 here: Fama-French Alphas for Quartile Portfolios Spread By Debt-Ratio Changes, Year
and Book-Asset Balanced]
Using the same quartiles, Table 8 reports Fama-French intercepts for a net portfolio of
stocks that increased in leverage, volatility, and market-beta net of a portfolio of stocks that
decreased in leverage, volatility, and market-beta. The evidence suggests that leverage-
and risk-increasers underperformed, although about half of the underperformance can be
explained by the fact that these stocks were also losers in the momentum sense. Again,
momentum and leverage are overlapping phenomena. This is now robust even for the
negcash leverage change measures.
D Stock-Return Instrumented Debt-Ratio Changes
Debt ratios can change based on active corporate intervention or based on experienced
stock returns. Monthly stock returns contain about one order of magnitude more noise
than signal. Returns reflect primarily realizations of stock returns, not reflections of their
expected rates of return.
When shocked with a negative rate of return, and thus an increase in their market-based
leverage and risk, Gomes-Schmid-type managers interested in adjusting their leverage
to fit their risk should undo the stock-return caused change by retiring some debt and
issuing some equity. Yet, Welch (2004) shows that firms did not actively countermand such
stock-return induced changes in leverage. Although debt ratios could have been under a
targeted control, firms (though active) tended not to undo these stock-market changes.
Under the additional assumption that stock returns induce leverage shocks that are
essentially and primarily exogenous, we can test whether these exogenous leverage shocks
result in higher average rates of return even in the absence of managerial intervention.
Before the managerial intervention, average returns should increase in leverage. After the
managerial intervention, they can increase or decrease.
Define as the instrument a change in debt ratio that is based on the start-of-period
debt ratio but using the interim stock return to infer the change. Consequently, a stock
that has had no debt would not be affected by stock returns, while a stock that has had
a lot of debt would experience large changes. The instrument can see changes only for
high-leverage stocks and large stock returns. The instrument is unaffected by managerial
responses during the year. Table 1 shows that the instrument still induces spread in debt
changes, too.
14
[Insert Table 9 here: The Effect of Changes in Stock-Implied Not-Firm-Managed Changes in Debt
Ratios on Subsequent Monthly Stock Returns]
Table 9 shows that stocks whose leverage increased due to a decline in their equity price,
even in the absence of managerial intervention, did not offer higher but lower average
rates of return. Explanations that require active managerial responses are thus unlikely to
explain the high-leverage-low-reward association.7
II Discrete Managerially-Induced Leverage Changes
The full panel study has shown that the paradoxical negative association between leverage
and reward requires an explanation that is also consistent with a positive association
between leverage and risk. The negative association between leverage and reward cannot
stem from a negative association between leverage and risk.8 Moreover, it should be
consistent with a scenario in which stocks that increase in the both leverage and equity
volatility.
The full CRSP-Compustat panel shows a positive association between leverage and equity
volatility. Although it has improved on the identification of the effects of leverage—using
changes, instrumented changes, and risk-and-leverage changes, and effects not only on
average returns but also on volatility—it is not inconceivable that omitted factors could still
explain these associations. There could be an unmeasured systematic risk factors—different
from those already controlled for (like XMKT, SMB, HML, RMW, CMA, and UMD, as in
Fama and French (2015))—which decreased so greatly that they could overcome the direct
leverage effect and thereby explain the reduction in average rates of return. Investors
would learn that the equity of firms increasing their leverage would be becoming safer—
better hedges against some academically unknown risk factor—so that their subsequent
average rates would be lower, though somehow leaving their equity volatility higher. This
is not impossible but also not a priori expected. If the theory is based on managerial
capital-structure optimization and financial distress, it would have to explain how and why
managers reduce this mysterious risk-factor exposure and not their own equity risk.
7The effect does not appear when momentum is included. This is not surprising, because the instrument isitself very similar to momentum. Unreported, momentum has more influence on highly-levered stocks thanlow-levered stocks. The former have about 80bp/mo momentum, while the latter have 60bp/mo momentum.But leverage changes cannot explain momentum in itself.
8It may well be that leverage reflects higher unlevered asset risk, but it is the equity risk that is relevant inexplaining equity average returns.
15
Therefore, the paper now turns to event-study settings, in which omitted factor expla-
nations are even less plausible: (1) equity issuing, and (2) dividend issuing activity. These
issuing activities are not in themselves the primary object of inquiry. They merely serve
as discontinuity instruments for leverage changes.9 To exclude information concerns, we
investigate the rates of return only after the public declaration. The comparison is between
the lag return statistics (just before the actual known-in-advance execution) vs. the lead
return statistics (just after, excluding the event itself), ignoring the contemporaneous return
statistics. A timeline helps to illustrate the relevant event windows:
PublicDeclaration
−w −w + 1 −2 −1 1 2 w − 1 w−1
(←Cum)Pre
0
(Ex→)Post
before⇒ after-dummy=0
after⇒ after-dummy=1
omitted(after-dummy=NA)
ignored(after-dummy=NA)
The short-term nature of the returns makes it unlikely that there is a non-leverage related
factor-exposure change. Both risk and reward should decrease after equity issues and
increase after dividend payments. These effects rely on the same restructuring arguments
as Modigliani-Miller.
Compare to the full panel studies in Section I, event-studies are less prone to contami-
nation from the corporate supply side. After the action has been publicly announced, over
spans as short as 5-10 days, corporate changes should not be surprises on average. More
likely, if there are return effects, they are more likely from the investor demand side.
A Seasoned Equity-Issuing Executions
In an equity issue, cash moves from owner-investors through the corporate wall into the
firm, with predictions of subsequently lower leverage, volatility, and average returns for
the corporate equity. The change is discrete, but, unlike for dividend issues in Subsection B,
there can be some uncertainty that is resolved in the days before the completion. Equity
9Kaplan, Moskowitz, and Sensoy (2013) provided perhaps the most prominent exception and a “gold-standard” study—a real experiment in U.S. financial markets on the effect of short-sales constraints. Althoughevent studies have been quasi-experimental in design and have been in use for decades, more recent eventstudies have not sought to test basic asset-pricing implications other than stock market efficiency at theannouncement. Moreover, it is not even clear how one would test factor asset pricing with an event study.What would pre-identified exogenous shocks to equity factor betas in isolation of other changes be?
16
issues can and have been cancelled. Their success is not just dependent on corporate
actions, but also on investor participation. The successful equity-issue completion could
still reveal information, despite earlier public announcements. A second contaminating
aspect is that firms often issue debt together with equity and new equity has effects that
depend on the firm’s prior capital structure (Welch (2004)). Therefore, we will cover equity
issuing activity in less detail than dividend issuing activity.
All stock return data in this eventstudy is from CRSP. The event dates are from the
Thomson SDC global issue database. In early 2016, it listed 1,131,497 offerings, of which
130,349 were corporate equity offerings. Removing IPOs yielded 97,440 offerings, of which
20,010 occurred in the United States, 17,862 were not privately placed, and 16,995 were
identified as the issue containing the entire filing amount. The need for a stock ticker,
CUSIP, a filing date, an issue date, complete filing amount, specific issue filing amount,
primary shares sold, at least 10 days between filing and offering date, and a merge with
CRSP by CUSIP, left 9,569 corporate equity offerings.10 The WRDS event-study program
yielded 7,859 offerings that had complete or near-complete stock return histories from
seven days before the offering to seven days after the offering, with about 7,600–7,800
stock return days per event day. Note again that all equity issues used in this study were
already publicly announced on the first day on which we look at stock returns.
[Insert Table 10 here: Explaining Market-Adjusted Stock Returns Around Actual Equity-Issue
Execution Dates, Given Previous Declaration]
Table 10 shows that every daily equity volatility before the issue execution is higher
than every daily equity volatility after. The average absolute rate of return from event
day –6 to –3 is 4.63%, while the average absolute rate of return from event day +3 to +6
is 3.46%. This is as it should be. Yet again, the average rate of return is not lower but
higher. In the days before the issue, the average rate of return is –0.041%/day. In the
days after, it is 0.078%/day. Together, these relations are in line with the full panel results
from Section I. Again, the risk decreases, which is expected; but the reward increases,
which is paradoxical. The panel regressions confirm the descriptive evidence and show
that the result is statistically significant. Investors receive higher average rates of return for
the less volatile equity after firms have issued equity. The chosen window from –6 to –3
versus +3 to +6 is conservative, in that pulling it one day closer to the issue date would
10Some hand-checking revealed that the CRSP data are not a good data source for the number of sharesoutstanding. CRSP is more (but not greatly) reliable at picking up reasonable number-of-shares estimates atmonth-ends than mid-months. This is also why we did not attempt to measure the dilution.
17
further increase the difference. However, this is a very short interval. Over longer intervals,
presumably as firms use the funds to execute investment plans and ordinary return noise
reasserts itself, the difference in average returns declines.
Unfortunately, there are no further large issuing or repurchasing capital structure
experiments that easily lend themselves to similar tests.11 Equity repurchases are not
suitable, because they tend to be spread over long time windows. Equity shelf-offerings are
not suitable for lack of clear event dates.12 Debt issues and repurchases do not have a clear
directional predictions for corporate net leverage.
B Dividend Payments
Dividend payments are of a smaller-magnitude than equity offerings, but also very common,
important in their aggregate effects over time, and a cleaner experiment. Again, we are
considering not announcements but dates around actual dividends payments13 of dividends
after the public declaration. We compare the behavior of stock returns just before to just
after the cum-ex transition (1) while restricting (conditioning) the sample to days on which
the declaration had already been made public many days earlier, and (2) excluding the
cum-to-ex and surrounding days themselves. This is especially important because of known
dividend-tax cum-ex drops.14
The actual dividend payments are small shocks that increase net leverage. For under-
standing the intuition that any investment actions of the firm between announcement
and payment no longer have relevance, consider two extreme examples for a firm whose
business is holding the underlying stock market index (so that it has a market-beta of 1).
In one extreme case, the firm immediately sells some index shares and puts the funds into
stock, in effect defeasing the dividend at the moment of the announcement. It is now a
bundle of stocks and bonds up to the cum date and stocks only after the ex date. Clearly,
the risk and reward should go up at the cum-ex transition. In the other extreme case, the
11One other unexploited event may be relatively rare call-forced conversions. Again, the emphasis wouldbe on the execution date, not the announcement date.
12This is also why exchange offers, as in Korteweg (2004), are not suitable for this experiment. An exchangeoffer is usually not executed on one sharp day, but over multiple weeks.
13For convenience and intuitive clarity, this study often refers to the ex-day day as the payment day. Thestudy always ignores the actual payment day on which the checks are mailed out.
14Including them would only further strengthen the results. Similarly, all reported results are robust toreasonably different event windows.
18
firm remains fully invested in the stock market up to the final moment.15 It then sells index
shares to satisfy the payment promise. At the moment of the declaration, the firm becomes
a composite of one risk-free claim worth DV and one levered claim worth 100%−DV . If the
stock-market has a rate of return of rM between the announcement and the payment, then
the risk-free claim will pay DV and the residual firm will be worth 100% · (1+ rM)− DV .
The entire risk is on the residual claim, which is riskier than 100% · (1+ rM). In net terms,[see also table with numerical
example in the appendix]
the cum-dividend stock returns are always less levered than the ex-dividend stock returns.
The cash-flow split is determined at the moment of declaration, not at the moment of
payment.16
Because the approach is quasi-experimental, the model itself can be simple. In the
exogenous leverage-risk-reward paradigm framework,
Equitypre = EquityEquity-Other + (EquityRisk-free = Dividend) ,
R̃pre = (1−δ) · R̃Equity-Other + δ · RRisk-free ,
Equitypost = EquityEquity-Other ,
R̃post = R̃Equity-Other ,
where δ is the single-event dividend yield paid at the event date. Therefore, the expected
rate of return on equity should increase by the dividend-yield scaled expected rate of return
on the prepayment equity above the risk-free rate,
E(R̃post) =�
11−δ
�
· E(R̃pre) −�
δ
1−δ
�
· RRisk-free ,
which is strictly greater than E(R̃pre) if E(R̃pre) > RRisk-free. For small δ and risk-free rates,
E(R̃)post − E(R̃pre) ≈ δ · E(R̃pre). For daily stock returns, this is a tiny but strictly positive
increase. If expected rates of return are similar, then the increase is quantitatively pinned
15Realistically, it is likely that liquidation of ordinary risky projects into cash would occur more than 5-10days before the payment, and dividend payments would be paid out of cash and short-term investments.Over time, firms would then replenish cash, either through cash flow or external financing. Farre-Mensa,Michaely, and Schmalz (2014) show that about a third of the dividends were externally financed. However,these were long-term finance patterns, and not likely to occur exactly at the dividend payment date. And,again, even if such managerial choices had had any influences on the average rate of return patterns, it isdifficult to see how such an explanation could explain both averages and volatilities.
16To have a different impact on leverage would require that firms do more than just cover the dividendpayment at the day of the dividend payment. For example, if they also sell further assets cum-day for cash,then the project leverage and risk could decline. There is no reason to believe that this should happensystematically.
19
down by the model. An empirical change larger or smaller than the prediction rejects the
exogenous-leverage paradigm.17
Because risk-free dividends have zero variability, the equivalent implications on second
moments require no caveat about the risk-free rate:18
σ(R̃post) =�
11−δ
�
·σ(R̃pre) .
For ordinary firms, the exogenous-leverage model predicts that equity volatilities should
increase roughly one-to-one in accordance with the increase in dividend yields. For small
δ, 1/(1−δ) ≈ (1+δ).
The leverage-risk and leverage-reward predictions are again separate. This means that
each test can stand on itself, and the equity volatility risk measure need not be priced in
terms of expected return.
B.1 Measure Sufficiency and Quantitative Prediction
The firm’s leverage and cash ratios are themselves not inputs into the predicted risk and
reward changes. This is because the pre-payment equity characteristics are sufficient
statistics for all changes caused by dividend payouts. Of course, high-cash zero-leverage
firms are expected to experience small increases when paying dividends, while low-cash
high-leverage firms are expected to experience larger increases. But this is captured by the
multiplicative factor on the ex-ante return attributes. There is neither a need nor a desire
to include leverage or cash measures (e.g., as control). This is an important test advantage:
under the exogenous-leverage paradigm, the calculations are agnostic with respect to how
leverage is measured and whether leverage measures are for operational or financial lever-
age. Attempts to use financial statements to tease out pre-existing leverage are theoretically
neither necessary nor helpful within the paradigm even for the quantitative predictions.
(Nevertheless, in Table 14, we show that existing leverage is of no consequence.)
17The test is a joint test that the (average) stock has a positive expected rate of return and that the expectedrate of return increases. Stocks with negative expected rates of return (e.g., due to extremely negativemarket-betas in the CAPM) would have opposite predictions. In equilibrium, this should be a rare case. Notealso that if we had a good proxy for E(R̃pre), we could improve the test. Stocks with higher cum expectedrates of return should experience higher increases. Alas, the test would require a reciprocal of the expectedreturn, and our measurement techniques are not accurate enough to facilitate such.
18Similarly, for any exposure to any factor, βpost = (1/(1−δ)) · βpre.
20
The predictions of the theory are quantitative: ceteris paribus, twice the dividend
payment should have twice the effect. Because both the volatility and the means tests are
scaled by the strictly positive dividend yield, they both have strictly positive predictions.
However, the volatility predictions are quantitatively larger. This is because the factor
multiplies the initial value, and the average daily volatility is about 1%, while the average
daily mean is two orders of magnitude lower—positive but near zero. The average return
prediction is near zero.
B.2 Data and Methods
All data are from CRSP, including the dividend announcement and cum-ex payment dates.
Therefore, this study is immediately and universally replicable. Except for Table 13, the
event-study uses only ordinary cash dividends, CRSP distribution code 1232. We define
the (one-event-payment) dividend yield as the dividend payment divided by the market
price of the stock at the start of the event window (either 5 or 9 days before the payment);
and winsorize it at 50%.19 The signal-to-noise ratio for detecting the effects of dividend
payments on stock returns is necessarily very small. Stock returns are very volatile on a daily
basis (1-3% per day) relative to their means (1-3 bp per day). The dividend-payment yields
are typically under 1%.20 Consequently, dividend payments predict only extremely small
changes in stock return averages and modest changes in volatility. Fortunately, there are
many observations. Unfortunately, dividends from before 1962 had to be excluded because
CRSP does not report their declaration dates. This leaves 494,643 ordinary cash-dividend
distributions from 1962 to 2015.
[Insert Table 11 here: Dividend Event-Study Descriptive Statistics]
Panel A of Table 11 shows the distribution of days between the declaration and the
cum-ex transition. CRSP reports no cases in which a firm has already declared a dividend
but fails to pay it as promised, nor are any cases familiar to me. (For further discussion of
selection biases and their possible effects, see Section III.)
The primary data restriction is the requirement of a specific number of days between
the dividend declaration and the dividend (cum-to-ex) payment date. This is because
19Winsorization affects about 300 dividend events. The results are similar if yields are winsorized at 10%,20%, or if such observations are completely removed. (This is valid, because the declaration has alreadyoccurred and therefore this criterion is based on an ex-ante known characteristic.)
20They are on the order of 1% of equity per payment in an unweighted portfolio and 1.5% of equity in thedividend-weighted portfolio. The inference is the same, regardless of weighting.
21
the maintained assumption in the experiment is that any information about the leverage
change, projects, or dividends must have already been released and thus is already known.
The event window never begins earlier than three trading days after the declaration. Events
in which the payment occurs more closely to the declaration dates are excluded. The
imposition of the requirement of availability of rate of return data from two days after the
declaration through the payment date is not a concern, because the declaration-to-ex-day
timespan is a known ex-ante (pre-event) criterion. (It does affect the kind of dividend
events from and to which the findings obtain—only distributions that would occur no
sooner than in 7 or 11 days.) Stocks that disappeared from the CRSP data set before the
dividend announcement dates are not included in CRSP. Thus they cannot affect the study,
either. However, the window choice could have raised another potential complication.
Availability of certain stocks’ returns in the window could change the composition of stocks.
In other words, some (but not other) stocks with shorter declaration notices may not mix
in the averages on different days. Permitting composition changes could cause spurious
differences in stock return moments. However, the results are robust to the treatment of
this complication in this study. It just so happened to be unimportant here. (Figure 1 and 2
will provide some support for this claim.) The paper’s main specifications are based on
stocks with 5-day and 9-day windows that have full data throughout their entire event pre-
and post-windows. The imposition of the same-firm-set requirement could have introduced
a bias if large attrition had occurred just after the payment date. This again turns out not
to be a concern. Out of 434,923 distribution events with a stock return at the payment
date, 433,375 had a stock return five days after the payment date. The reduction is just
the normal background attrition of stock returns on CRSP. Robustness checks indicate that
the results remain very robust when all stock returns on any available dates are used, which
means (for example) including stocks that were delisted during the window and even
mixing different stocks into different days.
The event study itself requires little sophistication. The event dates are not (greatly)
clustered (and we considered various [unreported] time regularity dummies), and the 1-2
week time intervals are relatively short. Moreover, the most common return adjustment
method used in this paper subtracts off the contemporaneous equal-weighted stock market
rate of return to reduce first-factor noise. The averages and standard errors can be presumed
to have been (nearly) independent draws. The results are not different if the standard errors
are calculated from the event time-series or if raw returns are used. Heteroskedasticity could
have been an issue, and thus the paper often reports both plain and White heteroskedasticity-
adjusted standard errors. Again, it matters little.
22
The study only makes sense for a few days around the dividend payment. Indeed,
when firms pay dividends every quarter, after 6 weeks, the post-payment period from the
previous payment becomes the pre-payment period for the next payment. (The pattern
already evens out after a shorter time-frame.) This design is simply not amenable to testing
long-term average return patterns.
Panel B of Table 11 shows background statistics on dividend payments and stock returns.
In the 5-day and 9-day event windows around dividend dates, stock returns have average
rates of return of 5-6 bp above the prevailing 30-day Treasury bill and 1-2 bp below
the equal-weighted stock market. In our most common specification, stock returns are
winsorized at –20% and +20%. The volatility of stock returns is about 2% per day. Dividend
yields are about 0.75% per event (i.e., about 3% per annum).
B.3 Dividend-Payment Leverage-Risk Associations
As in Section I, this section first investigates risk and then reward.
[Insert Table 12 here: Risk and Reward Changes Around Dividend Cum-Ex Transitions]
Panel A in Table 12 provides tests for a difference in the volatility of stock returns
before vs. after the dividend cum-ex transition. Each row shows the coefficients of one
panel regression. The inference is through the coefficient on an “after-payment” dummy
that takes a value of 0 before the payment and 1 after. (It can be considered NA during
the three cum-ex transition days, as well as outside the measurement interval) An earlier
draft considered many variations in the specifications of the event-window, the abnormal
return adjustment, the volatility metric, the choice of fixed effects, etc. The results were
always not just similar but nearly identical, so the table shows only some representative
variations. The coefficients on the “after-payment” dummy in A.1 through A.3 suggest
that equity volatility increases after the payment by about 1-2 bp/day, accumulating to
about 10-20 basis points over the 5-10 day event windows. The large sample ensures that
statistical accuracy is never an issue. With an average dividend payment yield of about
0.9% (see Table 11) on a base daily volatility of about 1.5%/day, the 1-2 bp/day magnitude
of the volatility increase is almost perfectly in line with the prediction of the exogenous
leverage-risk paradigm.
Lines A.4 and A.5 show coefficients of similar panel regressions that also include the
dividend yield itself plus a cross-variable on the dividend-yield before versus after the
23
event. Stocks paying higher dividends should experience greater increases. The leverage-
theory prediction fits the exogenous leverage paradigm nearly perfectly. The cross-variable
subsumes almost the entire intercept—only the higher-dividend payment events show
marked increases in volatility, and the intercept becomes insignificant. The volatility
evidence is exactly in line with (the quantitative predictions of) the leverage-risk theory
and consistent with the evidence in Section I.
B.4 Dividend-Payment Leverage-Reward Associations
Panel B provides analogous tests for the difference in average rates of returns before vs. after
the dividend cum-ex transition. The “after-payment dummy” coefficients in B.1 through
B.3 show that the average return decreases by about 3-6 bp per day. Over a window of 10
days, the estimate implies a cumulative rate of return of 30 bp less after that the payment
date. This 30 bp is high enough to be economically meaningful, but not high enough
to attract more (risky) arbitrage to eliminate it. Hartzmark and Solomon (2012) find a
similar average-return decline around dividend cum-ex transitions in their Section 4.3,
although their investigation originated from a set of related but different monthly dividend
anomalies. The positive average-rate-of-return effect is the opposite of that predicted by
the leverage-reward paradigm, but in line with the full CRSP panel evidence in Section I
and the equity issuing activity in Subsection A.
Lines B.4 and B.5 show results of similar panel regressions as A.4 and A.5 that also
include the dividend yield itself plus a cross-variable on the dividend-yield before versus
after the event. The leverage-risk-reward paradigm again predicts the opposite of what the
empirical evidence shows; and the cross-variable again largely subsumes the after-dividend
dummy: Only the higher-dividend yield stock events show the marked decrease in average
returns.21
B.5 Extended and Graphical Perspective
21Not reported, there was moderate year observation clustering, but the reported results are not drivenby the year of payment. They were similarly not driven by day-of-week effects or day-of-month effects.Including individual time-regularity dummies to control for such effects did not change the reported meansand standard deviations to the level of accuracies reported in the paper.
24
[Insert Figure 1 here: Effects of Pre-Announced Dividend Payments on Absolute Rates of Return]
[Insert Figure 2 here: Effects of Pre-Announced Dividend Payments on Average Rates of Return]
Figure 1 and 2 plot observed equity volatility and average return changes, respectively,
for different pre-announced dividend payment yields for 22 trading days surrounding the
payment. Each plotted point is one simple cross-sectional mean over all absolute or simple
rates of returns (net of the equal-weighted market) on the given event day. In clockwise
order, the payments are below 1%, between 1% and 2%, above 2%;22 and indiscriminate.
The dividend-yield implied change in volatility is noted in the middle of the graphs. The
previously mentioned concern is the changing mix of firms imposed by selection constraints.
Thus, each graph plots the effects of imposing a 5-day, 10-day, 15-day, and 20-day constraint,
as well as the effect of mixing in returns from different stocks, ignoring changes in the
composition.
For small dividend payments, there are almost no volatility and average return changes;
for medium payments, there are modest changes; and for large payments, there are
pronounced changes from about 2 weeks before to 2 weeks after the payment. Dividend
payments associate with approximately linear increases in stock return volatility and
approximately linear decreases in average returns. (The scale changes in the y-axis visually
understates the even better alignment of the averages.) For the high payments, for about 2
weeks before and after the payment, every single pre-event average rate of return is higher
than every single post-event average rate of return. The average return reverted modestly
for each day left and right of the payment event.23
An investor who is long for 3 weeks before large payments therefore earns about 5 basis
points times 15 trading days relative to the equal-weighted average (and/or the preceding
average returns), or about 75 basis points. An investor who is short for 3 week after the
large payments earns about another 75 basis points. the total effect is about half of the
dividend payment itself. Note that this does not suggest an arbitrage strategy, because
there is a time-offset (first long holdings, then short holdings).
The reversion here is as it must be: Over longer intervals, the change-in-leverage
average effect must become less pronounced. If the figure was extended right, the quarterly
22The number of dividend distributions per year ranged from (the absolute low of) 390 in 1962 to 644 in2015, with local maxima of around 1,800-2,500 from 1973 to 1982, and above 1,000 in 1990, 1991, and2008. Thus, even though the cutoff was in nominal terms rather than in quantile terms, the results are robust.
23Data selection effects in Figure 2 are (even) less important here than they were in Figure 1. The effectsare also similar if the stock returns are adjusted just for the risk-free rate of instead of the equal-weightedmarket rate of return.
25
dividend payment returns would reappear on the left.24 Firms also earn more and replenish
their cash, which should induce lower risk and reward.
Although the tests stand independently, we can also decompose the observed volatility
change (each calculated as a 4-day absolute deviation from its own mean) into one part
attributable to the dividend yield (Predicted Dividend-Related Volatility Change, PDRV∆)
and one part not attributable (Residual Dividend-Unrelated Volatility Change, URDUV∆). If
the financial mean effect is related to the same dividend-yield effect as the volatility increase,
then the PDRV coefficient should be negative. (The URDUV coefficient measures potentially
contaminating aspects.) The change in the average return from the four cum-days to the
four ex-days (Mean Return Change, MR∆) is then
MR∆ = −0.0 − 4.62× PDRV∆ + 0.23×URDUV∆
with standardized coefficients of –0.006 and +0.19, both highly statistically significant.25
Most volatility and mean returns are just dividend-unrelated correlations across stocks.
However, the increases in volatility that are attributable to the dividend-yield are different
from the more generic noise-mean associations. The effect is small, but it again suggests
that it is the exogenous volatility increase (that is due to the exogenous dividend-induced
net leverage change) that associates negatively with the average rate of return. Stocks
with more dividend-induced volatility increases showed greater declines in average returns.
This is robust to specification changes.
In sum, the increase in volatility in response to dividend payments, exactly quantitatively
in line with the prediction of the leverage-risk link, is prima-facie evidence that the financial
markets are aware of and respond appropriately to the increases in leverage caused by
dividend payments. (No alternative hypothesis seems to offer this prediction naturally.)
The leverage-risk relation is positive, but the leverage-reward relation is negative. Instead
of tiny increases in average returns, the known-in-advance payments of dividends associate
with strong decreases in average returns. The stock price increases “too much” before and
through the dividend payment, thus reducing post-payment average rates of returns relative
to prepayment average rates of return.
24Moreover, over time, cash from operations should flow back into the firm and reduce leverage. Notealso that the effect documented in the paper is a reduction in average returns, unlike the effects documentedin studies of post-announcement or dividend payments, which generally show increases in average returns.This is not inconsistent. The study designs are simply quite different.
25Stock return means are difficult to explain, and in this cross-sectional specification, each event is only oneobservation. A two-step panel regression approach yields higher T-statistics, but is more difficult to interpret.
26
Dividend payments are the most cleanly identified test of mean and volatility changes
around leverage changes. Therefore, we now look at some remaining pragmatic concerns
that deserve further empirical investigation, related to dividend taxes, the types of dividend
paid, the year-to-year changes, the surprises investors experience, the firms’ leverage
positions (despite the theoretical irrelevance), and liquidity and trading considerations.
B.6 Concerns About Dividend Taxes
The dividend experiment is not about corporate capital structure or dividend payout policy.
Answering different questions, this paper does not share event periods with earlier corporate
finance work. That is, unlike earlier dividend literature (explored and reviewed in, e.g.,
Michaely, Thaler, and Womack (1995) or Allen and Michaely (2003)), my paper explores
the stock returns around neither the dividend announcement dates nor the dividend cum-ex
dates.
There is theory and evidence that show that personal dividend taxes play an important
role on the (single) cum-ex day rate of return (e.g., Michaely (1991), Poterba (2004),
Chetty and Saez (2005), Chetty, Rosenberg, and Saez (2007)). There is no coherent theory
for a “slow tax effect.” Investor clientele trading effects could blunt even the cum-ex tax
effect, but the empirical evidence suggests that clientele trading, even if present, is not
of first-order importance to the stock return process. There seems to be a full response
on the single cum-to-ex day, indicating an effect in line with prevailing dividend tax rates.
To be a coherent explanation, somehow, many low-tax investors would have to buy into
dividend-paying stocks sooner than necessary, selling investors would have to be scarcer
than buying investors, there would still have to be enough buyers to have a price impact,
and the prices themselves would have to fail to adjust instantly (i.e., before the event
window) despite full advance common knowledge in the market. Moreover, somehow,
there would have to be an impact on volatility opposite to the impact on average returns.
Nevertheless, we can examine whether there is an empirical link between the surrounding
stock returns documented in my paper and dividend taxes.
[Insert Figure 3 here: Year-by-Year Coefficients Explaining Stock Return Moments after Payment and
highest Individual Dividend Income Tax Rates]
Because non-anonymous stock holding and trading data is not available, my tests cannot
investigate tax-exempt holdings directly. I can investigate whether the effects were stronger
when dividend taxes were more important. Figure 3 shows that the highest Federal income
27
dividend tax rates were fairly steady from 1962 to 1982 (around 65-70%), declined all
the way down to 15% from 1982 to 2013, and finally increased again to 20% and then
24%. In 1986 and 2003, there were particularly sharp declines in tax rates. The two lower
panels plot the most interesting OLS coefficients (on the bivariate-only post-ex dummy and
on the multivariate cross-variables) when run year by year. The plots show that although
a tax-related phenomenon may have contributed a little to the coefficients, the relation
between the dividend-tax rates and the before-after dummy is weak. The dummy and
the cross-coefficients show no clear or pronounced trends corresponding to large changes
in prevailing dividend tax rates.26 There is no time association between years in which
dividend taxes are high or low and the 5-day effects documented in the paper. Volatility
always increases with dividend payments, average returns always decrease.
[Insert Table 13 here: Different Types of Dividends]
Not all dividends are taxable. About 1 in 50 dividend payments are treated as a return
of capital and not taxed. In these cases, tax imperfections can be excluded as potential
explanations. Table 13 shows that non-taxable dividend distribution suffer almost identical
declines in average rates of return as taxable dividend distributions.
[Insert Table 14 here: Cum-To-Ex Association?]
Finally, it is an interesting question whether the effect documented in my paper is related
to the cum-ex drop. This could be the case, e.g., if the cum-to-ex return drop itself is a
noisy proxy for tax or perhaps other unspecified effects, and the same effects influences the
expected returns and volatilites around the event. In the sample, the cum-to-ex average rate
of return was about 25bp—implying an average effective tax rate of about 25/90 ≈ 28%—
with a standard deviation of 212bp. The regressions Table 14 control for the cum-to-ex
drop. Firms with higher cum-to-ex rates of return also have lower post-event mean returns.
However, controlling for the cum-ex stock return has no effect on the inference about the
difference between pre-cum and post-ex rates of return (the dummy). The cum-to-ex return
drop phenomenon is unrelated to the further changes in average rates of return around
dividends that are documented in my paper.
All evidence suggests that tax effects do not play an important role in the two weeks
left and right of but excluding the cum-ex date.26Unreported regressions explaining the volatility of year-by-year “after the event dummy” coefficients
(and cross-coefficients) with dividend taxes have adjusted R2s that are negative. Regressions explaining theaverage return year-by-year “after the event dummy” coefficients (and cross-coefficients) with dividend taxeshave adjusted R2’s of 3-5%.
28
B.7 Other Plausible Concerns
Pre-Existing Leverage: Though similarly atheoretical, we can investigate whether more
levered firms experience more of an effect. Panel B in Table 13 divided stocks into three
groups based on their Compustat total liabilities (LT) net of cash, divided by total assets
(AT), at the end of the previous fiscal year. The empirical evidence is not clear. Higher-
liability firms seem seem to have a lesser mean drop than low- and medium-liability firms,
but the cross-coefficient is about the same. Pre-existing leverage does not seem to be a
promising direction for further investigation.
Surprises, Endogeneity, Selection, Survivorship: The design of this experiment is
resistant to project endogeneity concerns. By the day that stock returns are beginning
to be included in the stock return calculations, the impending dividend-leverage change
has already been determined and announced. Publicly-traded company are not known to
retract dividends after they have been declared. It is implausible that investors increase
in belief that payments would occur in the days before the payment date. Even if the
dividend payment were not paid but instead completely dissipated, in order to explain the
documented lower average returns, non-payments would have to occur about 1-in-100
times, with hundreds of companies failing to pay declared dividends every year.27
Nevertheless, we can push the endogeneity consideration even further backwards. We
can separate the sample into dividends payments that are regular and long-standing (i.e.,
where investors could commonly assess that a dividend would be paid months in advance)
versus payments that are new and special. The evidence in Table 13 shows there is no
difference. (The coefficient for special dividends is about four times higher because the
yield typically paid out in special dividends is about four times higher.) Regularity of
payments does not seem to be a promising direction for further investigation.
[Insert Figure 4 here: Explaining Average Trading Liquidity Patterns around Previously Declared
Payment Dates]
Liquidity and Trading: Although prices can change in the absence of trading, to the
extent that investors in the aggregate had time-varying preferences, they could leave an
imprint on trading activity. For example, some investors could trade into dividend-paying
27The leverage-reward finding could be consistent with firms moving large amounts of risky stock-marketholdings into cash the day after the payment, thus becoming safer. However, beside the fact that such behavioris not known, it is also inconsistent with the leverage-risk findings.
29
stocks before the payment and then trade out again. This could but need not be rational
(e.g., tax trading). Table 4 plots the day-by-day average log number of trades and log
dollar volume (also obtained from CRSP). There is the tiniest of up-blips in liquidity on
days –1 and 0, but there are no increasing or decreasing trends either before or after the
payment. In the event windows used for calculating volatilities and average returns, there
is no increasing buying pressure before the payment or decreasing selling pressure after
the payment. Not shown, in unreported regressions, the after-payment dummy regression
coefficients in panel regressions explaining either liquidity variable is insignificant. It is
a fair characterization that prices seemed to move without unusual extra trading volume
patterns. Although the sophistication of the trading tests could be enhanced, liquidity and
trading does not seem to be a promising direction for further investigation.
B.8 Less Plausible Concerns
Timing and Managerial Response: Even if corporate managers had the forecasting ability
to time their dividend payments to occur on days when average stock returns would then be
lower (which is implausible), naive versions of this hypothesis would require that investors
would not recognize this already at the moment of announcement. Dividend catering, as
in Baker and Wurgler (2004), should similarly be reflected on the announcement date and
not occur around the payment date, either. Managerial response misspecification concerns
seem implausible.
Underlying Investment Activities: Although it is the defeasance of the dividend that
should matter and not the actual underlying risky investment patterns, correlated changes
in risk patterns—other than those directly due to the leverage change—seem unlikely. And
again, even an explanation based on the firm aggressively buying stock futures before the
dividend payment and liquidating them afterwards cannot explain both mean decreases
and volatility increases.28 Growth options, as in Gomes and Schmid (2010), are unlikely to
explain simultaneous increases in variance and decreases in means. While plausible and
consistent in their context, it seems implausible in this context.
Intrinsic Leverage or Volatility Preferences: Investors may like the increases in id-
iosyncratic volatility so much that they bid up the price, leaving lower average rates of
return after the payment-induced risk-increase. In unreported regressions, if the rate of re-
turn is explained with the absolute rate of return and the cross-effect post-payment dummy,
28Besides, if firms could follow strategies with higher average returns and lower risk, why would they stopdoing so after the dividend payment?
30
it appears that it is the stocks with the higher post-event volatilities that experienced lower
average returns after the payments.29 This suggests again that investors earned lower
average rates of return when volatility increased because of the payment, and perhaps
specifically because the payment increased volatility (Goyal and Santa-Clara (2003)). Al-
though such a theory would also suggest that managers could increase shareholder value by
gambling more aggressively, the problem remains that the option-induced higher expected
rates of return should have been reflected at the dividend declaration itself. This seems
implausible.
III Speculative Discussion
This paper has already repeatedly mentioned the primary perfect-market explanation—a
mysterious risk-factor that not only declines in leverage, but declines systematically and
so much after the leverage increase that it can reverse the direct positive average rate of
return implication. The risk-factor exposure decline in leverage would somehow further
increase simultaneously with firm volatility, although the latter happens to be quantitatively
exactly in line with the leverage-change prediction. The observed risk change constellation
would also be puzzling from the perspective of most corporate finance theories, in which
managers typically want to reduce not their systematic factor exposures but their own
volatilities (in order to reduce financial distress costs). And on a pragmatic basis, even
if managers (unlike academics) understand this mysterious risk factor, it is unclear howmanagers would mechanically adjust their leverage to reflect both the decreasing factor
risk and increasing own risk effects simultaneously.
The leverage anomaly here seems related to the idiosyncratic volatility anomaly in Ang
et al. (2006). Higher risk seems to be associated with lower average returns. However,
the basic primitive in my paper is different, and there is some evidence that the effects are
different. Leverage is important even when risk is controlled for.
The alternatives to the perfect-market explanation are imperfect-market explanations, in
which investors bid up the prices of stocks increasing leverage and thereby drive down sub-
sequent average rates of return. These changes would be as puzzling as “non-arbitrageble.”
There are two potential market imperfection that come to mind.
29When the mean is not-zero, then there is an association between returns and absolute returns. It should,however, be weak.
31
Investor Preferences: The first reason is behavioral. Investors become infatuated with
low leverage. When there are dividend payments, they bid up the price a little too
much before the dividend. Investors behaved as if they had wanted to be present just
in time to receive the dividends. The historical average rates of return were thus not
reflective of investors’ true expected rates of return, because investors were naive
and non-anticipatory. Put differently, the return patterns could have been caused by
a financial market which was non-blissfully ignorant of risks and outlooks, with more
levered companies having been exposed to more post-payment risk (and malaise)
more frequently. Thus, higher-leverage dividend-paying stocks could have had lower
post-payment average rates of return, with financial market prices not taking this
added risk appropriately into account.
Investor Agency: The second reason is agency-related. This is particularly prominent in
Harris, Hartzmark, and Solomon (2016), which finds that mutual funds may have
had preferences for dividends, because dividends to mutual-fund investors labeled
as such are required to come from dividends in the underlying stock holdings.30
Mutual funds report twice as much in quarterly dividends as their quarterly reported
holdings would justify. Harris-Hartzmark-Solomon show that this “juicing” harms
fund investors. (Incidentally, it is the opposite of rational tax trading, where it is the
tax-exempt that should gravitate towards dividend payments.) They also note that
this agency hypothesis pushes mutual funds into the dividend-preference direction
because their retail investors seem, in turn, to be irrationally attached to receiving
payments labeled dividends. The two hypotheses blend.31
These preferences explanation are ad-hoc, but they are not entirely implausible—Lamont
and Thaler (2003) document even stranger law-of-one-price violations probably also due
to investor-demand effects. Their evidence appears in a small number of isolated stocks
with close-to-indisputable value evidence (and, of course, absence of easy arbitrage). It is
sometimes discounted as mere “aberrations” when investors were particularly irrational.
In contrast, the effects documented in my paper are more pervasive. Although Baker,
30Mutual funds can still pay out funds, but they would not carry the dividend label. Quoting Harris-Hartzmark-Solomon, “while distributing cash to the fund’s shareholders is easy, such distributions only canbe labeled as ‘dividends’ if they correspond to dividends received by the fund on its underlying securities.This constraint arises because funds must satisfy a ‘pass-through rule’ that requires that they distribute allgains and losses each year to avoid paying corporate income taxes.”
31Hartzmark and Solomon (2012) compares expected dividend with non-dividend payers and focuses onan extended dividend anomaly that is also unlikely to be explained by risk. However, as already mentioned,in Section 4.1, it does show evidence related to the mean effect around dividend payments.
32
Hoeyer, and Wurgler (2016) explore Gomes-Schmid-like long-run performance and have
overlapping implications (e.g., riskier firms choosing lower leverage), Baker-Hoeyer-Wurgler
interpret the evidence as suggestive of risk-leverage mispricing. They then consider both
the perspective and optimal behavior of the corporation.32
A Other and Simultaneous Explanations
The imperfect-market behavioral investor preference evidence here and elsewhere should
not be viewed as mutually exclusive with the perfect-market hypotheses in Fama and French
(1992) or Gomes and Schmid (2010). More than likely, the economic forces all play roles
in the association of leverage with risk and reward, possibly differently at different times
or for different firms. Economic theories often hold in some contexts, but not others. Like
all economic tests, the empirical findings are context specific, and the measured effects are
only “net.”
There is however one shortcoming in the earlier “asset supply side” arguments in Fama
and French (1992) and Gomes and Schmid (2010) worth mentioning. They embraced
the perfect-market rational paradigm with too little skepticism. They failed to allow for
and/or to embed less appealing “investor demand side” alternatives that can play roles,
too. What if financial markets are imperfect and it is not risk but other characteristics
that investors prize? What if financial markets simply did not respond (appropriately) to
financial leverage? What if investors or their investment agents “liked” some (aspects of)
firms too much?
The evidence in my paper suggests that more skepticism is appropriate when interpreting
previous long-run empirical evidence. Before concluding that the associations between
leverage and returns are solely or primarily due to information revelation or corporate
responses to growth options based on book-to-market moments, it seems appropriate not
to make asset supply effects the entire working hypothesis. One should not ignore investor
demand effects, including non-arbitrageable, collectivist, imperfect-market (tax, agency)
and/or behavioral investor preferences.
32The findings are also not inconsistent with the views expressed in Hoberg and Prabhala (2009) that thevolatility increases in Campbell et al. (2001) could have had direct corporate finance implications—thoughperhaps in the opposite direction.
33
Future tests of the Gomes and Schmid (2010) option-growth theory could also benefit
(1) from tests that measure growth options and leverage responses more directly33 and (2)
break out other possible investor demand-based forces. Supply and demand effects can lead
to interestingly similar and different conclusions. Similar critiques can be offered for other
reflexive perfect-market interpretations. Could the Fama and French (1992) value factor
be similar to low leverage, offering high average rates of return without commensurate
declines in risk? Unfortunately, in the absence of discrete shocks to value (as there are to
leverage), this is difficult to determine.
B Odds and Ends
• The methods and results proposed in my paper are relevant not only in the (not so
narrow) leverage test context. Consider any other deep risk factor (e.g., a consump-
tion hedge or HML) that is supposed to explain reward. It should be amplified by
leverage. Thus, variation in leverage can be used as an instrument to improve tests. If
either the mean or factor loading is not appropriately disturbed by leverage changes,
it is implausible that this factor should be viewed as a valid priced equilibrium risk
factor. Future research could thus not only test factor responses, but design factor
tests that identify off of leverage changes or instrument factor tests.
• The leverage-risk-reward relation is not just important in the asset-pricing realm.
Leverage is also a fundamental building block in corporate finance. If increases in
leverage do not induce increases in required reward, it would change capital-structure
tradeoffs, too. Ceteris paribus, firms should then issue even more debt, as equity
would no longer suffer commensurate risk externalities.
• My paper relates loosely to a strand of literature about the CAPM and the security-
market line. However, these papers are primarily concerned about the underper-
formance of high-beta vs. low-beta stocks, observed as early as Black, Jensen, and
Scholes (1972). Based on the Black (1972), Black (1993, p.76) proposes leverage
aversion of borrowing-constrained investors as one possible explanation for the better
performance of low-beta stocks.34 Asness, Frazzini, and Pedersen (2012) improve
33Growth options in this context are typically not inferred from supply-side aspects in the firm, but fromindirect inference measures such as book-to-market ratios. Although this is plausible, demand forces couldalso impact market prices and thus effect book-to-market ratios.
34Black also briefly discusses the reaction of stocks to leverage offerings on the announcement date itself asevidence for a preference of investors in favor of debt financing. However, this is usually attributed primarilyto news about the firm.
34
on Black’s early work and also call the underperformance of stocks relative to bonds
“leverage aversion.” However, at their broad asset-class level, the Sharpe-ratio differ-
ential of 0.47 vs 0.35 seems more in line with the tax differential between capital
gains and interest payments than with leverage aversion. Frazzini and Pedersen
(2014) present more convincing evidence that higher beta stocks have pervasively
lower alphas in many different markets and also within equally-taxed asset classes.
Importantly, these papers mostly mean investor leverage when they discuss leverage
aversion and leverage constraints, and not corporate leverage. Consequently, unlike
my own paper, they are not looking at the same evidence about the stocks’ corporate
leverage, much less do they investigate average return and idiosyncratic risk patterns
associated with changes in corporate leverage. However, both their and my findings
could be related to an intrinsic like or dislike of risk and leverage.35
IV Conclusion
Consumption asset-pricing tests are theoretically well identified, but their empirical failures
to explain the cross-section of stock returns can be blamed on ignorance of the relevant risk
metrics. This makes them difficult to reject. Empirical factor models (such as Fama and
French (2015)) can explain large average stock return differentials, but their theoretical
bases remain controversial. In both cases, misidentification of risk factors is a first-order
concern. If risk proxies (say, beta, momentum, or value) fail to explain average returns, then
it “only” raises skepticism about whether the proxies were good, and not about whether
the perfect-market theory is wrong. The risk proxies are themselves largely endogenous
and continuous. There are no academic papers that have investigated quasi-exogenous
discrete shocks to these proxies.
Leverage as a risk proxy has important advantages over deeper risk factors and thus
risk-reward tests. It is solidly identified. Its is more resistant to measurement concerns
and problems stemming from academic ignorance. It works regardless of the deeper factor
structure. It offers empirical identification strategies that stem from active and discrete
managerial interventions. Some of these tests offer discrete changes. And empiricists
can choose among tests with different degrees of coverage, endogeneity, information
contamination, and corporate response concerns.
35Another loose relation is to a new literature that uses information to time strategies (e.g., Daniel andMoskowitz (2016)). A prominent timer is the aggregate time-series volatility, as in Moreira and Muir (2016).
35
The leverage-risk-reward paradigm predictions are also not deep. They require no hyper-
sophistication and knowledge by investors (itself exceeding that of the most sophisticated
financial economists). They are simply that investors should suffer more risk when firms
lever up and thus earn higher average returns. Yet the evidence in my paper rejects this. It
is not a matter of ignorance or test power: The effect of leverage always appears clearly in
firm’s own equity volatility. But average stock returns paradoxically decrease in leverage. A
simple restatement of the puzzle is that investors recognize the increase in risk but like the
higher leverage so much that they bid up stock prices too much—the opposite of leverage
aversion. The question for which no one has an answer is: Why?
This throws down the gauntlet for a theory capable of tying together the basic building
blocks of asset pricing—corporate leverage, risk, and reward. The theory needs to explain
the following:
• Average return decreases in leverage levels, after (many) controls.
• Equity volatility increases in corporate leverage.
• Average return decreases in leverage changes.
• Average return is also lower when leverage increases together with equity volatility
(and market-beta).
• The effects appear even when leverage changes cannot be due to managerial actions
but can only be due to stock price changes (most of which are primarily value shocks
and not primarily reflections of expected returns).
• The effects appear even when leverage changes are sharp and discrete, on time-
horizons as short as a few days (where underlying corporate changes [from the
supply side] should be be less important than investor preferences [from the demand
side]).
• And they appear even when it cannot possibly be due to contaminating new informa-
tion.
After this theory has identified this mysterious factor that can explain these effects—i.e.,
a factor that would (co-)decrease so strongly with leverage that it could explain lower
average returns as leverage increases—we would of course still want to know why this
factor would decrease in leverage to begin with.
36
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Table 1: Spread of Debt-Ratio Levels and Changes
tbl:panel-descriptives in v4-xsect/panel-descriptives.tex, January 31, 2017
Panel Standard Deviations Quartile MeansMean All Xsect TS Q #1 Q #4
Debt-Ratio Levels:mknegcash 0.910 0.115 0.103 0.045 0.804 0.981mklev 0.240 0.253 0.239 0.087 0.046 0.496mkliab 0.365 0.269 0.249 0.090 0.134 0.622
bknegcash 0.866 0.176 0.148 0.053 0.707 0.974bklev 0.268 0.257 0.252 0.086 0.060 0.530bkliab 0.410 0.260 0.245 0.083 0.181 0.646
Debt-Ratio Simple Changes:schg.mknegcash 0.000 0.066 0.060 0.048 –0.053 0.053schg.mklev 0.005 0.113 0.106 0.080 –0.087 0.105schg.mkliab 0.008 0.109 0.100 0.082 –0.084 0.107
schg.bknegcash 0.002 0.072 0.066 0.053 –0.057 0.065schg.bklev 0.004 0.108 0.103 0.076 –0.084 0.102schg.bkliab 0.007 0.098 0.091 0.073 –0.076 0.097
Debt-Ratio Extreme Changes:xchg.mklev 0.030 0.678 0.605 0.381 –0.401 0.527xchg.bklev 0.036 0.622 0.581 0.351 –0.349 0.508
Instrumented Debt-Ratio Changes Non-IV Q MeansR.schg.mklev –0.005 0.064 0.058 0.042 –0.054 0.046 –0.043 0.049R.schg.mkliab –0.008 0.075 0.067 0.053 –0.068 0.055 –0.038 0.054
Explanations: These are descriptive statistics for the key independent debt-ratio variables. All data are fromCompustat and CRSP, 1962–2015. There are six measures of indebtedness: “mk”-based measures use market-basedequity values (preferably from Compustat, but also CRSP if former is not available); “bk”-based measures usebook-based equity values. “negcash” is one minus cash (preferably CHE, but CH if not available) divided by bookor market-assets. “lev” is financial leverage: netdebt/(netdebt + equity), where netdebt is debt (itself [Compustat]DLTT plus DLC) minus cash, and equity is either the (modestly adjusted) book value of equity (CEQ) or a market-value of equity from Compustat or CRSP. “liab” are liabilities (LT) net of cash divided by total assets (AT). Alldebt-ratios are also winsorized to lie between 0.001 and 0.999. The first four rows describes leverage in levels, thenext four rows in simple changes, the next two rows in “extreme” changes, and the final two rows for stock-returnimputed capital-structure changes (explained later). The bottom right four values show the non-instrumentedchanges in debt ratios for the two quartiles. The quartiles themselves are based on a sort of stocks to spread thekey debt ratio (or ratio change) while maintaining balance by year and firm-size. That is, stocks are sorted byyear, assets, and then by the variable itself. Within each group of four stocks, the least levered stock is assigned toquartile #1, the highest to quartile #4.
40
Table 2: Corporate Debt-Ratio Levels and Subsequent Rates of Return
tbl:famatables-lvls in v4-xsect/famatables-lvls.tex, January 31, 2017
Panel A: Fama-French Alphas for Quartile Portfolios Spread By Debt Ratios, Year and Book-Asset Balanced
Raw XMKT XMKT,SMB,HMLXMKT,SMB,HML,
RMW,CMAXMKT,SMB,HML,RMW,CMA,UMD
Alpha (T-stat) Alpha (T-stat) Alpha (T-stat) Alpha (T-stat) Alpha (T-stat)
mknegcash –0.395 (−5.41) –0.316 (−4.70) –0.345 (−5.45) –0.448 (−7.74) –0.464 (−7.91)mklev 0.076 (+0.74) 0.128 (+1.26) –0.145 (−1.86) –0.200 (−2.56) –0.138 (−1.78)mkliab 0.154 (+1.43) 0.212 (+2.00) –0.078 (−0.98) –0.151 (−1.92) –0.107 (−1.36)
bknegcash –0.186 (−2.02) –0.077 (−0.93) –0.231 (−3.33) –0.365 (−5.82) –0.371 (−5.82)bklev –0.139 (−1.70) –0.120 (−1.46) –0.306 (−4.37) –0.336 (−4.79) –0.291 (−4.14)bkliab –0.072 (−0.78) –0.039 (−0.42) –0.242 (−3.04) –0.323 (−4.26) –0.300 (−3.91)
Panel B: Fama-Macbeth Regressions, Coefficient Reported Only For Key Debt Measure
Solo Solo Incl. Cntrls Incl. Cntrls (TSσ)DT Qrtl (T-stat) DT Ratio (T-stat) DT Ratio (T-stat) DT Ratio (T-stat)
mknegcash –0.116 (−4.61) –1.778 (−4.54) –1.411 (−3.96) –1.404 (−3.93)mklev –0.030 (−0.93) –0.235 (−1.23) –0.418 (−2.57) –0.417 (−2.58)mkliab 0.002 (+0.05) 0.122 (+0.59) –0.218 (−1.22) –0.220 (−1.23)
bknegcash –0.069 (−2.27) –0.755 (−2.41) –1.140 (−3.92) –1.139 (−3.92)bklev –0.088 (−3.31) –0.583 (−3.62) –0.455 (−3.19) –0.453 (−3.19)bkliab –0.057 (−1.92) –0.386 (−2.07) –0.369 (−2.30) –0.366 (−2.29)
Explanations: This table shows the (abnormal) post-measurement average rate of return performance, in percent,for stocks with high debt-ratios levels net of the converse. The four debt ratios (leverage and liability ratios in bothmarket and book values) are explained in Table 1. The dependent stock returns begin four to five months after thefiscal year end, and usually last for twelve months. All data is from Compustat and CRSP, 1962–2015.
Panel A shows Fama-French intercepts for zero-investment portfolios sorted into quartiles, long high-leverage, shortlow-leverage, both year- and asset-balanced.
Panel B shows Fama-Macbeth coefficients and T-statistics (Newey-West with 1 Lag) on debt ratios, using the sameleverage quartile indicators (in the first two data columns), or the debt-ratio itself (in the second two data columns),or the debt ratios themselves either when no other variables or when further variables are included (coefficientsnot reported): the book-market ratio, the firm size, investment, operating profitablity, and the rate of return inlagged months 2–12 (non-advancing) with respect to the fiscal year (in the third two data columns).
Interpretation: Stocks with higher book-leverage have worse subsequent performance. Stocks with higher market-leverage have worse performance only with further controls.
41
Table 3: Changes in Leverage, Annual Daily Return Volatility, and Annual Average Returns — Controllingfor Assets
tbl:ltxcategtables-chgs in v4-xsect/ltxcategtables-chgs.tex, January 31, 2017
Panel A: schg.mknegcashAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.340 1 –0.059 0.493 0.502 0.497 0.004 0.018 –0.019 0.047 0.030
$3.230 2 –0.008 0.473 0.478 0.480 0.007 0.030 0.013 0.034 0.004
$3.180 3 0.021 0.472 0.476 0.485 0.013 0.043 0.048 0.015 –0.028
$3.150 4 0.060 0.496 0.497 0.504 0.008 0.059 0.061 0.005 –0.054
Panel B: schg.mklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.290 1 –0.093 0.499 0.475 0.465 –0.034 0.088 0.190 0.037 –0.051
$3.240 2 –0.011 0.467 0.463 0.465 –0.002 0.053 0.063 0.028 –0.025
$3.180 3 0.041 0.473 0.487 0.496 0.023 0.011 –0.044 0.026 0.014
$3.190 4 0.111 0.496 0.528 0.540 0.044 –0.003 –0.105 0.011 0.014
Panel C: xchg.mklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.320 1 –0.600 0.505 0.481 0.470 –0.035 0.077 0.184 0.040 –0.038
$3.190 2 –0.034 0.461 0.457 0.459 –0.002 0.063 0.067 0.027 –0.036
$3.210 3 0.190 0.468 0.481 0.490 0.023 0.020 –0.041 0.023 0.003
$3.170 4 0.832 0.501 0.535 0.548 0.047 –0.011 –0.107 0.012 0.023
Panel D: schg.mkliabAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.320 1 –0.089 0.498 0.475 0.466 –0.032 0.100 0.200 0.033 –0.067
$3.240 2 –0.010 0.468 0.466 0.467 –0.001 0.050 0.059 0.031 –0.019
$3.200 3 0.045 0.472 0.488 0.496 0.024 0.002 –0.045 0.026 0.024
$3.140 4 0.112 0.495 0.525 0.537 0.041 –0.004 –0.110 0.011 0.015
42
(Table 3 continued)
Panel E: schg.bknegcashAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.340 1 –0.061 0.490 0.489 0.483 –0.007 0.055 0.074 0.037 –0.018
$3.230 2 –0.008 0.477 0.482 0.484 0.006 0.015 0.034 0.038 0.022
$3.180 3 0.025 0.475 0.482 0.491 0.016 0.025 0.007 0.021 –0.004
$3.150 4 0.070 0.492 0.501 0.508 0.016 0.054 –0.012 0.005 –0.048
Panel F: schg.bklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.270 1 –0.089 0.491 0.478 0.473 –0.018 0.085 0.107 0.041 –0.044
$3.280 2 –0.011 0.468 0.467 0.467 –0.001 0.043 0.047 0.032 –0.012
$3.230 3 0.037 0.475 0.488 0.493 0.018 0.009 –0.009 0.026 0.017
$3.120 4 0.109 0.499 0.521 0.532 0.033 0.011 –0.043 0.003 –0.009
Panel G: xchg.bklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.280 1 –0.750 0.497 0.483 0.478 –0.018 0.079 0.107 0.042 –0.037
$3.230 2 –0.027 0.463 0.460 0.461 –0.002 0.049 0.049 0.030 –0.019
$3.240 3 0.204 0.471 0.483 0.489 0.017 0.014 –0.007 0.024 0.011
$3.150 4 1.140 0.503 0.527 0.539 0.035 0.006 –0.046 0.004 –0.002
Panel H: schg.bkliabAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.300 1 –0.081 0.490 0.476 0.471 –0.019 0.087 0.096 0.036 –0.050
$3.260 2 –0.009 0.471 0.472 0.473 0.003 0.032 0.043 0.037 0.006
$3.180 3 0.039 0.476 0.488 0.494 0.017 0.010 –0.002 0.023 0.012
$3.160 4 0.102 0.497 0.518 0.528 0.030 0.020 –0.033 0.004 –0.016
Explanations: Variables and quartiles are explained in Table 1. The first column shows average book assets,intended to be held constant. The third column shows the sort criterion (identified in the panel header), intendedto be spread. The next four columns describe annual (fiscal-year) statistics for average daily stock-return volatility,during the year. Stock returns are always own returns minus the value-weighted stock-market return. The sortitself occurs at the end of the “Cntmp” period (and uses the Lag debt ratio to calculate the change). The deltacolumn highlights the return changes between lag and lead. The next four columns describe annualized excessreturns. Not reported, simple T-statistics for the differences between #4 and #1 in the “Lead” columns are allhighly statistically significant, permitting focus on economic rather than statistical significance.
Interpretation: Except for schg.mnknegcash, stocks with increasing leverage have subsequently higher volatility.Stocks with increasing leverage have subsequently lower average returns.
43
Table 4: Changes in Leverage, Annual Daily Return Volatility, and Annual Average Returns — Controllingfor Lag Returns
tbl:ltxcategtables-chgs-rc in v4-xsect/ltxcategtables-chgs.tex, January 31, 2017
Panel A: schg.mknegcashAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.180 1 –0.058 0.492 0.497 0.492 0.000 0.038 –0.017 0.045 0.007
$3.620 2 –0.009 0.458 0.464 0.466 0.007 0.038 0.018 0.031 –0.007
$3.840 3 0.019 0.468 0.472 0.478 0.010 0.038 0.046 0.018 –0.020
$2.270 4 0.061 0.514 0.520 0.529 0.014 0.038 0.056 0.007 –0.031
Panel B: schg.mklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.580 1 –0.088 0.497 0.479 0.469 –0.028 0.038 0.181 0.040 0.002
$3.260 2 –0.011 0.468 0.464 0.465 –0.003 0.038 0.056 0.025 –0.013
$3.120 3 0.041 0.469 0.484 0.490 0.020 0.038 –0.038 0.025 –0.013
$2.950 4 0.106 0.498 0.525 0.541 0.043 0.038 –0.097 0.011 –0.027
Panel C: xchg.mklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$4.080 1 –0.569 0.499 0.480 0.470 –0.028 0.038 0.173 0.042 0.004
$2.750 2 –0.027 0.466 0.463 0.463 –0.004 0.038 0.062 0.023 –0.015
$2.750 3 0.239 0.468 0.482 0.488 0.021 0.038 –0.034 0.022 –0.016
$3.340 4 0.716 0.500 0.528 0.544 0.044 0.038 –0.097 0.014 –0.024
Panel D: schg.mkliabAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.150 1 –0.084 0.500 0.482 0.475 –0.025 0.038 0.195 0.035 –0.004
$3.760 2 –0.011 0.465 0.462 0.462 –0.003 0.038 0.056 0.034 –0.004
$3.540 3 0.045 0.467 0.479 0.487 0.020 0.038 –0.045 0.021 –0.017
$2.460 4 0.107 0.501 0.529 0.542 0.041 0.038 –0.103 0.011 –0.026
44
(Table 4 continued)
Panel E: schg.bknegcashAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.140 1 –0.059 0.491 0.489 0.483 –0.008 0.038 0.077 0.035 –0.003
$3.970 2 –0.008 0.463 0.466 0.469 0.006 0.038 0.033 0.033 –0.006
$3.350 3 0.024 0.470 0.477 0.483 0.013 0.038 0.008 0.026 –0.012
$2.450 4 0.069 0.509 0.519 0.530 0.021 0.038 –0.015 0.007 –0.030
Panel F: schg.bklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.660 1 –0.086 0.489 0.478 0.474 –0.015 0.038 0.105 0.041 0.003
$3.280 2 –0.012 0.470 0.468 0.468 –0.002 0.038 0.045 0.029 –0.009
$3.070 3 0.037 0.474 0.486 0.491 0.017 0.038 –0.009 0.026 –0.012
$2.900 4 0.105 0.500 0.520 0.533 0.033 0.038 –0.039 0.005 –0.033
Panel G: xchg.bklevAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$4.100 1 –0.721 0.489 0.478 0.475 –0.015 0.038 0.101 0.039 0.001
$2.900 2 –0.016 0.469 0.468 0.467 –0.002 0.038 0.048 0.030 –0.008
$2.670 3 0.270 0.474 0.485 0.489 0.015 0.038 –0.006 0.024 –0.014
$3.240 4 1.007 0.501 0.521 0.534 0.034 0.038 –0.040 0.008 –0.030
Panel H: schg.bkliabAnnlzd Vltlty (TSσ) Net Return
Assets # sort Lag Cntmp Lead ∆Lead–Lag Lag Cntmp Lead ∆Lead–Lag
$3.170 1 –0.077 0.491 0.481 0.476 –0.015 0.038 0.095 0.037 –0.001
$3.900 2 –0.010 0.467 0.466 0.468 0.001 0.038 0.041 0.035 –0.003
$3.510 3 0.039 0.471 0.481 0.486 0.016 0.038 –0.004 0.022 –0.016
$2.330 4 0.100 0.504 0.523 0.535 0.031 0.038 –0.030 0.006 –0.031
Explanations: This table is identical to the previous one, except that quartiles are now sorted to control for the lag net return(instead of sorted to control for assets).
Interpretation: Firms increasing leverage are experiencing declines in average net returns.
45
Table 5: Annual Stock Return Characteristics Surrounding Changes in Debt Ratios
tbl:ltxregtables-schgs in v4-xsect/ltxregtables-schgs.tex, January 31, 2017
Panel A: Regression Coefficients Explaining Lead Daily Non-Annualized Volatility (SD) With Own Lag and (Reported)Change in Leverage Ratio
Fama-Macbeth Panel RegressionsCoef (T-NW) Coef (T-DC)
schg.mknegcash 0.002 (2.77) –0.001 (−0.52)schg.mklev 0.019 (8.30) 0.023 (13.34)schg.mkliab 0.021 (7.80) 0.025 (13.83)
schg.bknegcash 0.010 (8.29) 0.012 (11.88)schg.bklev 0.013 (9.41) 0.014 (14.82)schg.bkliab 0.015 (8.90) 0.017 (16.06)
Panel B: Regression Coefficients Explaining Lead Daily Average Annual Returns With Own Lag and (Reported)Change in Leverage Ratio
Fama-Macbeth Panel RegressionsCoef (T-NW) Coef (T-DC)
schg.mknegcash –0.230 (−4.07) –0.316 (−3.71)schg.mklev –0.069 (−1.08) –0.048 (−0.56)schg.mkliab –0.042 (−0.62) –0.007 (−0.08)
schg.bknegcash –0.123 (−2.49) –0.080 (−2.27)schg.bklev –0.107 (−2.13) –0.087 (−1.91)schg.bkliab –0.091 (−1.58) –0.054 (−1.19)
Explanations: The regressions use the same annual data as the previous “category” Table 3. Let R y be eitherthe the average daily equity return (net of the market) volatility over year y in Panel A, or the compound return(net of the market) in panel B; and let L y be the leverage measure at the end of the year. The regression isRt+1 = a+ b · Rt−1 + c · (Lt − Lt−1) + e. It is the coefficient c that is reported in the two panels. The coefficientsin the second column are from Fama-Macbeth regressions (albeit on annual returns), with T-statistics based on3 Newey-West lags in the third column. The coefficients in the fourth column are from OLS regressions, withdouble-clustered and White heterogeneity-adjusted T-statistics in the fifth column.
Interpretation: Except for schg.mknegcash, which is unrelated, volatility increases with leverage. Annual returnsare too weak to be predicted reliably, but the sign is usually negative and some specifications are significant.
46
Table 6: The Effect of Changes in Debt Ratios on Subsequent Monthly Stock Returns, All Stocks
tbl:famatables-schgs in v4-xsect/famatables-schgs.tex, January 31, 2017
Panel A: Fama-French Alphas for Quartile Portfolios Spread By Debt-Ratio Changes, Year and Book-Asset Balanced
Raw XMKT XMKT,SMB,HMLXMKT,SMB,HML,
RMW,CMAXMKT,SMB,HML,RMW,CMA,UMD
Alpha (T-stat) Alpha (T-stat) Alpha (T-stat) Alpha (T-stat) Alpha (T-stat)
schg.mknegcash –0.334 (−7.15) –0.357 (−7.73) –0.312 (−7.02) –0.252 (−5.68) –0.253 (−5.62)schg.mklev –0.230 (−3.16) –0.272 (−3.81) –0.366 (−5.39) –0.262 (−3.88) –0.097 (−1.72)schg.mkliab –0.208 (−2.84) –0.246 (−3.40) –0.343 (−4.99) –0.242 (−3.54) –0.076 (−1.33)
schg.bknegcash –0.261 (−5.98) –0.287 (−6.70) –0.274 (−6.55) –0.200 (−4.89) –0.155 (−3.86)schg.bklev –0.325 (−5.90) –0.365 (−6.85) –0.395 (−7.56) –0.294 (−5.82) –0.201 (−4.34)schg.bkliab –0.285 (−5.56) –0.323 (−6.52) –0.348 (−7.23) –0.265 (−5.59) –0.181 (−4.13)
Panel B: Fama-Macbeth Regressions, Coefficient Reported Only For Key Debt Measure
Solo Solo Incl. Cntrls Incl. Cntrls (TSσ)DT Qrtl (T-stat) DT Ratio (T-stat) DT Ratio (T-stat) DT Ratio (T-stat)
schg.mknegcash –0.077 (−4.56) –1.869 (−4.70) –1.636 (−4.33) –1.678 (−4.55)schg.mklev –0.080 (−3.04) –1.332 (−4.48) –0.550 (−2.28) –0.472 (−1.99)schg.mkliab –0.078 (−3.43) –1.106 (−3.27) –0.164 (−0.63) –0.046 (−0.18)
schg.bknegcash –0.075 (−6.79) –1.333 (−3.93) –0.911 (−2.54) –0.885 (−2.46)schg.bklev –0.106 (−5.42) –1.435 (−7.06) –0.528 (−2.79) –0.482 (−2.55)schg.bkliab –0.106 (−8.02) –1.372 (−5.64) –0.421 (−2.06) –0.360 (−1.79)
Explanations: The content and format of these tables is identical to those in Table 2, except that the variable underconsideration is now the simple change in the leverage ratios. All stock returns are measured after the increase inleverage, with a 4-5 months accounting lag.
Interpretation: Firms that increased leverage had lower subsequent average rates of return. The magnitude andsignificance depends on the controls.
47
Table 7: The Effect of Changes in Market-Based Debt Ratios on Subsequent Monthly Stock Returns,Cross-Classified Simultaneous Risk (Daily Volatility and Market-Beta) Changes
tbl:xtables-bysigma in v4-xsect/xtables-bysigma.tex, January 31, 2017
schg.mknegcash schg.mklev schg.mkliab
Firm
Year
s∆
Tota
lAnn
lzd
Eqty
Vola
tilit
yA
nnua
lA
vgR
etur
ns
Lev Risk ↓ unclr Risk ↑
1↓ 16,904 4,738 16,1802 16,919 5,134 15,7693 16,866 5,057 15,8774↑ 17,334 4,834 15,632
Lev Risk ↓ unclr Risk ↑
1↓ –0.121 0.021 0.1392 –0.108 0.023 0.1373 –0.105 0.029 0.1434↑ –0.111 0.025 0.150
Lev Risk ↓ unclr Risk ↑
1↓ 0.038 0.034 0.0622 0.035 0.013 0.0393 0.022 0.001 0.0134↑ 0.008 –0.004 0.003
Lev Risk ↓ unclr Risk ↑
1↓ 18,743 4,957 14,1222 17,473 5,147 15,2023 16,276 5,088 16,4364↑ 15,531 4,571 17,698
Lev Risk ↓ unclr Risk ↑
1↓ –0.140 0.015 0.0962 –0.108 0.023 0.1183 –0.097 0.027 0.1564↑ –0.095 0.034 0.188
Lev Risk ↓ unclr Risk ↑
1↓ 0.040 0.028 0.0362 0.030 0.014 0.0303 0.026 0.003 0.0324↑ 0.004 –0.005 0.021
Lev Risk ↓ unclr Risk ↑
1↓ 18,759 4,888 14,1752 17,458 5,246 15,1183 16,217 5,048 16,5354↑ 15,589 4,581 17,630
Lev Risk ↓ unclr Risk ↑
1↓ –0.138 0.020 0.0962 –0.109 0.020 0.1233 –0.097 0.027 0.1564↑ –0.095 0.031 0.184
Lev Risk ↓ unclr Risk ↑
1↓ 0.033 0.026 0.0362 0.035 0.007 0.0353 0.026 0.009 0.0314↑ 0.006 –0.001 0.018
schg.bknegcash schg.bklev schg.bkliab
Firm
Year
s∆
Tota
lAnn
lzd
Eqty
Vola
tilit
yA
nnua
lA
vgR
etur
ns
Lev Risk ↓ unclr Risk ↑
1↓ 17,525 4,911 15,3862 16,878 5,040 15,9043 16,772 5,060 15,9684↑ 16,848 4,752 16,200
Lev Risk ↓ unclr Risk ↑
1↓ –0.124 0.020 0.1262 –0.112 0.024 0.1383 –0.103 0.027 0.1524↑ –0.104 0.027 0.153
Lev Risk ↓ unclr Risk ↑
1↓ 0.030 0.024 0.0512 0.034 0.024 0.0463 0.032 0.000 0.0164↑ 0.007 –0.007 0.007
Lev Risk ↓ unclr Risk ↑
1↓ 18,151 4,929 14,7422 17,296 5,120 15,4063 16,521 5,085 16,1944↑ 16,055 4,629 17,116
Lev Risk ↓ unclr Risk ↑
1↓ –0.129 0.020 0.1112 –0.110 0.022 0.1213 –0.102 0.025 0.1534↑ –0.101 0.032 0.179
Lev Risk ↓ unclr Risk ↑
1↓ 0.038 0.031 0.0472 0.031 0.018 0.0373 0.028 0.005 0.0314↑ 0.005 –0.014 0.005
Lev Risk ↓ unclr Risk ↑
1↓ 18,279 4,910 14,6332 17,158 5,125 15,5393 16,533 5,049 16,2184↑ 16,053 4,679 17,068
Lev Risk ↓ unclr Risk ↑
1↓ –0.128 0.019 0.1102 –0.109 0.022 0.1283 –0.104 0.027 0.1534↑ –0.101 0.030 0.173
Lev Risk ↓ unclr Risk ↑
1↓ 0.033 0.024 0.0442 0.035 0.019 0.0463 0.028 0.008 0.0224↑ 0.005 –0.011 0.008
48
(Table 7 continued)
Explanations: “Risk ↑” (“Risk ↓”) stocks are those that experienced both a daily equity volatility increase(decrease) of at least 0.1%/day (1.6% per annum) from the lag year (–1,0) to the lead year (0,+1).Displayed volatilities and returns are for year (+1,+2). The leverage quartiles are the same four schgcategories as those used elsewhere in the paper. The displayed post-sort monthly average returns andpost-sort total volatility changes are measured monthly over the 12 months following the leverage andstock risk changes.
Interpretation: The cash-change leverage ratios, mknegcash and bknegcash, show only weak changes insubsequent equity volatility, but the two broader leverage metrics show clear volatility increases. Leverageassociates with lower subsequent average returns for all leverage metrics, even for stocks with increasingrisk.
49
Tabl
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Fam
a-Fr
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Alp
has
for
Qua
rtile
Port
folio
sSp
read
By
Deb
t-R
atio
Cha
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Ass
etB
alan
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tbl:f
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h-by
sigm
ainv4
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ct/f
amaf
renc
h-by
sigm
a.te
x,Ja
nuar
y31
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7
Raw
XM
KT
XM
KT,
SMB
,HM
LX
MK
T,SM
B,H
ML,
RM
W,C
MA
XM
KT,
SMB
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,CM
A,U
MD
Alp
ha(T
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t)A
lpha
(T-s
tat)
Alp
ha(T
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t)A
lpha
(T-s
tat)
Alp
ha(T
-sta
t)
allr
isk-
schg
.mkn
egca
sh–0
.429
(−3.
98)
–0.4
97(−
4.71)
–0.4
70(−
4.46)
–0.2
85(−
2.75)
–0.2
45(−
2.34)
allr
isk-
schg
.mkl
ev–0
.376
(−3.
22)
–0.4
58(−
4.04)
–0.5
83(−
5.29)
–0.3
87(−
3.57)
–0.1
90(−
1.91)
allr
isk-
schg
.mkl
iab
–0.3
52(−
2.98)
–0.4
32(−
3.76)
–0.5
56(−
4.98)
–0.3
57(−
3.26)
–0.1
55(−
1.55)
allr
isk-
schg
.bkl
ev–0
.486
(−4.
45)
–0.5
65(−
5.33)
–0.6
22(−
5.90)
–0.4
34(−
4.19)
–0.3
00(−
3.00)
allr
isk-
schg
.bkl
iab
–0.4
56(−
4.14)
–0.5
41(−
5.10)
–0.5
96(−
5.65)
–0.4
20(−
4.04)
–0.2
75(−
2.75)
allr
isk-
schg
.bkn
egca
sh–0
.375
(−3.
57)
–0.4
44(−
4.33)
–0.4
42(−
4.30)
–0.2
46(−
2.45)
–0.1
57(−
1.58)
Expl
anat
ion
s:Th
ese
are
alph
asfr
omze
ro-in
vest
men
tpor
tfol
ios
that
are
long
inst
ocks
that
incr
ease
din
leve
rage
,idi
osyn
crat
icvo
lati
lity
and
mar
ket-
beta
,and
shor
tin
the
conv
erse
.Th
ecr
iter
iaar
eth
esa
me
asth
ose
inTa
ble
7.
Inte
rpre
tati
on:
Firm
sin
crea
sing
inth
etr
ifect
aof
leve
rage
,vol
atili
ty,a
ndm
arke
t-be
taha
dsu
bseq
uent
lylo
wer
aver
age
retu
rnpe
rfor
man
ce.
50
Table 9: The Effect of Changes in Stock-Implied Not-Firm-Managed Changes in Debt Ratios on SubsequentMonthly Stock Returns
tbl:famatables-ivs in v4-xsect/famatables-ivs.tex, January 31, 2017
Panel A: Fama-French Alphas for Quartile Portfolios Spread By Instrumented Debt-Ratio Changes, Yearand Book-Asset Balanced
Raw XMKT XMKT,SMB,HMLXMKT,SMB,HML,
RMW,CMAAlpha (T-stat) Alpha (T-stat) Alpha (T-stat) Alpha (T-stat)
R.schg.mklev –0.241 (−2.45) –0.306 (−3.19) –0.413 (−4.49) –0.274 (−2.99)R.schg.mkliab –0.261 (−2.48) –0.324 (−3.13) –0.452 (−4.57) –0.308 (−3.12)
Panel B: Fama-Macbeth Regressions, Coefficient Reported Only For (Instrumented) Key Variables
Solo Solo Incl. Cntrls Incl. Cntrls (TSσ)DT Qrtl (T-stat) DT Ratio (T-stat) DT Ratio (T-stat) DT Ratio (T-stat)
R.schg.mklev –0.109 (−3.36) –4.009 (−5.36) –1.545 (−2.68) –1.438 (−2.52)R.schg.mkliab –0.118 (−3.70) –3.370 (−4.76) –1.052 (−1.66) –0.900 (−1.43)
Explanations: The indebtedness variable is not the leverage at the end of the year, but the leverageat the beginning of the year grossed up by the firm’s rate of return. Thus, these leverage changes arewithout active managerial leverage changes instituted during the year. Any stock-return based shock toleverage would therefore not have (yet) been counteracted by managerial capital structure policy.
Interpretation: Even for leverage changes that are not actively set by corporate management, leveragechanges have the same negative influence on subsequent average returns.
51
Table 10: Explaining Market-Adjusted Stock Returns Around Actual Equity-Issue Execution Dates, GivenPrevious Declaration
tbl:sdc in welch4-divstudytbls.tex, January 31, 2017
Panel A: Daily Average Returns and Absolute Average Returns Around Issue, in percent
Event Average Event AverageDay Mean Sd Range Return Abs Return
–7 0.167 4.04
–6 0.031 5.29–5 0.032 4.05–4 –0.085 4.27–3 –0.139 5.39 –6 to –3 –0.041 4.63
–2 –0.359 5.39–1 –0.595 5.210 –1.356 5.81 –2 to +2 –0.448 5.04+1 –0.205 4.98+2 0.258 3.34
+3 0.140 3.28 +3 to +6 0.078 3.46+4 0.148 3.27+5 0.036 3.23+6 –0.018 2.95
7 0.164 3.01
Panel B: Panel Regressions Explaining Daily Market-Adjusted Rates of Return
Intercept “After”-Dummy
Coef (se) (se.het) Coef Stdzd (se) (se-het)
Days |3| to |6| –0.162 (0.014) (0.014) 0.062 0.011 (0.018) (0.017)
Days |3| to |6|, Fixed Eff ———— many ——— 0.062 0.011 (0.018) (0.015)
Days |3| to |8|, Fixed Eff ———— many ——— 0.039 0.008 (0.015) (0.015)
Explanations: This table explores stock return responses net of market returns around seasoned equityoffering issues dates, provided the offerings were announced well in advance. There were about 7,700events per day (in Panel A), for a sample of about 100,000 stock returns in the days from 3 to 6 daysearlier (in Panel B).
Interpretation: Equity return volatilities are lower after equity offerings, but average rates of return arehigher.
52
Table 11: Dividend Event-Study Descriptive Statistics
tbl:divdescriptives in welch4-divstudytbls.tex, January 31, 2017
Panel A: Timespan From Declaration to Payment (Ex-) Date
ObservationsDays Payments Returns
Same 996 434,9231 9,807 433,9262 10,088 424,1193 19,086 414,0314 30,747 394,9455 32,692 364,1986 37,022 331,506
(5-Day Window) 7 30,534 294,484
8 28,790 263,9509 22,703 235,16010 17,988 212,457
(9-Day Window) 11 15,565 194,469
12 13,885 178,904
Panel B: Means, Medians, Standard Deviations of Key Dependent and Independent Variables
Days Variable Median Mean Stddev N
5d tb30ms-adj returns 0.00% 0.059% 2.26% 2,343,7289d ewmktd-adj returns 0.00% 0.057% 2.23% 3,087,4889d ewmktd-adj, abs. returns 0.89% 1.380% 1.75% 3,087,488
(5d) dividend yield 0.75% 0.91% 0.91% 2,343,728
Explanations: The data source is now strictly CRSP. The sample consists of all CRSP “1232” (ordinary cashdividend) distributions with stock return, price, and dividend yield data, from 1926 to 2015.
Panel A describes the time span between the declaration and the ex-date in the sample.
Panel B describes the principal variables of interest. The pre-window was either from –6 to –2 (“5d”) or from –10to –2 (“9d”), but only given that the payment was declared at least 7 days or 11 days, respectively, before thepayment. The post-window was either +2 to +6 (“5d”), or +2 to +10 (“9d”). The ex-day, the day before, andthe day after were always excluded from the event-studies. There were 2,343,728 (3,087,488) daily stock returnobservations in the 5d (9d) window.
“ewmktd-adj.” rows are stock returns net of the CRSP equal-weighted return. “tb30ms-adj.” rows are net of theprevailing 30-day Treasury bill rate (from FRED). The absolute returns are sometimes used as a measure of volatility.The dividend yield is with respect to a single dividend distribution (never annualized) and always calculated onceat the outset of the event window. The windows and samples remain the same throughout most of the dividendpayment study. Unreported robustness checks confirm that neither is critical.
53
Table 12: Risk and Reward Changes Around Dividend Cum-Ex Transitions
tbl:divriskreward in welch4-divstudytbls.tex, January 31, 2017
Panel A: Risk Measures“After-Dividend “Win-Start Cross-
Intercept Dummy” Div Yield” Coefficient
Coef Coef Stdzd Coef Stdzd Coef Stdzd
A.1 5d, tb30ms-adj, SD(R) 1.711 0.010 0.003A.2 9d, ewmktd-adj, ABS(R), Evt FE many 0.014 0.005
A.3 1992- 5d, ewmktd-adj, wins 1.353 0.020 0.006
A.4 By divyield, SD(R), 5d, ewmkt, wins incl 0.000 0.000 –1.385 –0.009 1.386 0.008A.5 same, but 1992- incl 0.009 0.000 2.226 0.015 1.432 0.008
Panel B: Reward Measures“After-Dividend “Win-Start Cross-
Intercept Dummy” Div Yield” Coefficient
Coef Coef Stdzd Coef Stdzd Coef Stdzd
B.1 5d, risk-free-adj 0.076 –0.035 –0.008B.2 9d, ewmkt-adj, Evt FE many –0.030 –0.008
B.3 1992- 5d, ewmkt, Wnsr, –0.003 –0.050 –0.012
B.4 By Div Yield, 5d, ewmkt, Wnsr incl –0.001 0.000 3.116 0.014 –6.137 –0.023B.5 Same, 1992- incl –0.002 –0.001 2.737 0.014 –5.932 –0.024
Explanations: Samples and variables are described in Table 11. Each line contains the coefficients of one panelregression. The “after-dividend” dummy is 0 for days from −T to −2 (inclusive) and 1 for days from 2 to T(inclusive). Other days were excluded. The dividend declaration must have occurred at least two days before thestart of the window. The standard errors, even using many corrections, are so low (given the gigantic number ofobservations) that the reader can focus on the coefficient magnitudes. The column labeled “Stdzd” coefficient isthe plain coefficient multiplied by sd(x)/sd(y). The risk measures are either the standard deviation (SD(R)) or theabsolute value (ABS(R)). When the regressors include the dividend-yield at the start of the event-window, theyalso contain the “cross”-variable, i.e., the Dividend Yield times the “After Dividend” Dummy. When winsorization(Wnsr) was applied, it was for daily returns at +20% and –20%.
Interpretation: (A.1-A.3) The volatility after the dividend payment was higher, by about 1 bp per day. (A.4-A.5)The volatility after the dividend payment was higher for higher-dividend yield events. (B.1-B.3) The average rateof return after the dividend payment was lower by about 2-5 bp per day. With 4-8 day windows, this amountsto about 20-30 bp over the full windows. (B.4-B.5) Only the cross-effect mattered. Firms paying more dividendsappreciated more at the payment and then delivered lower returns thereafter. The dividend payment reduced theaverage daily rate of return by about 3bp for every 1% dividend yield. Over 4-8 day windows, this amounts toabout 20-30bp.
54
Figure 1: Effects of Pre-Announced Dividend Payments on Absolute Rates of Return
fig:divvols in welch4-divstudytbls.tex, January 31, 2017
ε to 1% Dividend 1% to 2% Dividend
−20 −10 0 10 20
1.25
1.30
1.35
1.40
Event Day
Mean N
et
Abs
RR ●●●●●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●●●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
div
yld
= 0
.005;
1/(
1−
div
yld
)= 1
.005
−20 −10 0 10 20
1.24
1.26
1.28
1.30
1.32
Event Day
Mean N
et
Abs
RR
●●●●●●
●
●
●
●
●
●
●●●
●●●●
●
●●●●●●
●
●
●
●
●
●●
●
●●
●●
●
●
div
yld
= 0
.014;
1/(
1−
div
yld
)= 1
.014
More than 2% Dividend All Dividend Events
−20 −10 0 10 20
1.25
1.30
1.35
1.40
Event Day
Mean N
et
Abs
RR
●●●●●●
●●
●
●
●●
●
●●●●●●
●
●●●●●●
●
●
●●●●
●
●
●●
●●●●
div
yld
= 0
.026;
1/(
1−
div
yld
)= 1
.027
−20 −10 0 10 20
1.26
1.28
1.30
1.32
1.34
1.36
1.38
Event Day
Mean N
et
Abs
RR
●●●●●●
●
●
●
●●
●●●
●
●●
●
●●
●●●●●●
●
●
●
●●
●●
●●
●
●●
●
●
div
yld
= 0
.009;
1/(
1−
div
yld
)= 1
.009
Explanations: Samples and variables are described in Table 11. The four plots are, in clockwise order,averages of absolute net-of-market rates of return for low-yield, mid-yield, high-yield (less than 1%,1-2%, and more than 3%), and all dividend payments . The four solid lines represent all the stocks whichhave at least 5, 10, 15, or 20 trading days around the payment date. Thus, the gray line has the fewestnumber of stocks, but extends farthest. The dashed line mixes in all stock returns without requiring aconstant set of firms.
Interpretation: Post-payment volatilities were higher than pre-payment volatilities, but only reliablyso for high-yield dividend events. The selection window influences the reported volatilities, but onlymoderately so. Even the selection-unconditional mix of firms produces roughly the same inference.
55
Figure 2: Effects of Pre-Announced Dividend Payments on Average Rates of Return
fig:divmeans in welch4-divstudytbls.tex, January 31, 2017
ε to 1% Dividend 1% to 2% Dividend
−20 −10 0 10 20
−0.04
−0.03
−0.02
−0.01
0.00
0.01
0.02
Event Day
Mean N
et
RR
●●●●●●●
●●●●
●●●●
●●●●●
●●●●●●
●
●●●●●●●●●●●●●
div
yld
= 0
.005;
1/(
1−
div
yld
)= 1
.005
−20 −10 0 10 20
−0.05
0.00
0.05
0.10
Event Day
Mean N
et
RR
●●●●●●
●
●●●
●●●●●●●●●●
●●●●●●●●●●●●
●
●
●●●
●●●
div
yld
= 0
.014;
1/(
1−
div
yld
)= 1
.014
More than 2% Dividend All Dividend Events
−20 −10 0 10 20
−0.2
−0.1
0.0
0.1
0.2
Event Day
Mean N
et
RR
●●●●●●●●●
●●●●●●●●
●●●
●●●●●●
●
●●●
●●
●●●
●●●●
●
div
yld
= 0
.026;
1/(
1−
div
yld
)= 1
.027
−20 −10 0 10 20
−0.04
−0.02
0.00
0.02
0.04
0.06
Event Day
Mean N
et
RR
●●●●●●
●
●●●●●●●●●●●●●
●●●●●●
●●●●●●●●●●●●●●
div
yld
= 0
.009;
1/(
1−
div
yld
)= 1
.009
Explanations: Samples and variables are described in Table 11. The four plots are, in clockwise order,averages of absolute net-of-market rates of return for low-yield, mid-yield, high-yield (less than 1%,1-2%, and more than 3%), and all dividend payments. The four solid lines represent all the stocks whichhave at least 5, 10, 15, or 20 trading days around the payment date. Thus, the gray line has the fewestnumber of stocks, but extends farthest. The dashed line mixes in all stock returns without requiring thata constant set of firms.
Interpretation: Post-payment average returns were lower than pre-payment volatilities, and only reliablyso for higher-yield dividend events. The selection window influences the reported average returns, butonly moderately so. Even the selection-unconditional mix of firms produces roughly the same inference.The y-scale changes understate the visual impact of the effect.
56
Figure 3: Year-by-Year Coefficients Explaining Stock Return Moments after Payment and highest Individ-ual Dividend Income Tax Rates
fig:byyear in welch4-divstudytbls.tex, January 31, 2017
Panel A: Explaining Volatility (Absolute Return)
1960 1970 1980 1990 2000 2010
−0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Index
vols
coef
Panel B: Explaining Average (Returns)
1960 1970 1980 1990 2000 2010
−0.15
−0.10
−0.05
0.00
Index
avgs
coef
Panel C: Personal Income Tax Rate on Dividends by Year
1960 1970 1980 1990 2000 2010
0
20
40
60
80
100
Index
tax r
ate
Explanations: Samples and variables are described in Table 11. Panels A and B show the regression coefficients ofinterest (analogous to those in Table 12) when each year is run by itself for the market-adjusted 5-day window. Theblue lines in Panel A are for equity volatility: The solid blue line is on the “after-payment” dummy in a bivariateregression. The dashed blue line is on a multivariate regression for the “cross” variable. The red lines in Panel Bare for average returns: The solid red line is on a bivariate regression “after-payment” dummy. The dashed red lineis on a multivariate regression for the cross variable. To fit on the same scale, the cross-coefficients were divided by100. Panel C shows dividend tax rates, as in Sialm (2009), Becker, Jacob, and Jacob (2013), and Jacob, Michaely,and Mueller (2016).
Interpretation: The effects varied year-by-year, but have not changed in a systematic fashion. This also suggeststhat although there may have been contributions of personal dividend income tax-related preferences to thedividend-payment effect, tax effects could not have been too powerful.
57
Table 13: Different Types of Dividends
tbl:divbytype in welch4-divstudytbls.tex, January 31, 2017
Panel B: Controlling for Dividend Characteristics
Coefficients
Div Yield Bivariate Reg Multivariate Regression
δ After-Dummy After-Dummy δ Cross N
Taxable (code 2) 0.94% –0.017 –0.005 0.681 –1.321 9,985,317Nontaxable (code 3) 0.50% –0.011 0.060 6.249 –14.303 247,535
Recurring 0.88% –0.016 0.016 2.668 –3.724 10,105,183Special 4.14% –0.095 –0.090 –0.237 –0.154 139,922
Previous Dividend
0-75 days 0.84% –0.008 0.005 0.905 –1.603 871,62076-120 days 0.89% –0.016 0.027 3.507 –4.927 5,670,443121-200 days 0.87% –0.019 0.031 3.979 –5.812 1,151,275201-500 days 0.93% –0.022 0.008 2.281 –3.183 717,506New 0.97% –0.026 0.004 1.535 –3.061 210,975
Panel B: Controlling for Prevailing Liability Ratio
Coefficients
Liability Div Yield Bivariate Reg Multivariate Regression
Ratio δ After-Dummy After-Dummy δ Cross N
Low (0 < TL/TA < 1/3) 1.02% –0.024 –0.014 0.391 –1.001 1,892,293Medium (1/3 < TL/TA < 2/3) 0.96% –0.024 –0.009 0.868 –1.535 3,712,706High (2/3 < TL/TA < 3/3) 0.90% –0.008 0.004 0.783 –1.337 3,569,510
Explanations: Each line shows coefficients from two panel regressions, analogous to those in Table 12,but using the longest symmetric event window around the payment, and beginning two days after thepublic dividend declaration. Only ordinary dividends (CRSP distcd first digit 1) are used. In Panel A,taxability of dividends is identified in the fourth digit of the distcd. The classification between recurringand special dividends is identified in the second digit of the distcd (codes 2 through 5 for recurrent,7 for special). The length of time since the last paid dividend is calculated from the CRSP panel. AllOLS coefficients are highly statistically significant, except for two italicized entries for special dividends(which are only about 1% of the sample). In Panel B, stocks are classified by financial liabilities (the ratioof total liabilities net of cash divided by the book value of total assets), truncated at zero and one, in thecalendar year before the dividend declaration.
Interpretation: The mean rate of return after the payment is lower than the mean rate of return beforethe payment, regardless of whether the dividend was taxable or nontaxable, regular or irregular; andwhether the firm was modestly or highly indebted.
58
Table 14: Cum-To-Ex Association?
tbl:divwithmorecontrols in welch4-divstudytbls.tex, January 31, 2017
Variable Coef Std.Err T (se-het) Stdzd
Reg1 Intercept –0.007 0.001 –6.39“After-Dividend” Dummy –0.018 0.001 –11.94 –0.004
Reg2 Intercept –0.006 0.001 -5.55“After-Dividend” Dummy –0.018 0.001 –11.93 –0.004Single-Day Cum-To-Ex Return –0.004 0.000 –6.79 –0.004
Reg3 Intercept –0.006 0.001 -4.87“After-Dividend” Dummy –0.019 0.002 –12.55 –0.004Single-Day Cum-To-Ex Return –0.007 0.001 –7.73 –0.007“After-Dividend” Dummy × Cum-To-Ex Return 0.005 0.001 4.37 0.004
Explanations: These three panel regressions predict the market-adjusted event day rate of return withthe post-event dummy, and the payment day cum-to-ex return, analogous to those in Table 13. Theycontain 81,058,017 observations, balanced to have an equal number of stock returns on either side up to21 days and with the requirement of knowledge of the declaration. All OLS coefficients are statisticallyhighly significant.
Interpretation: Events with more positive cum-to-ex returns also had (modestly) lower post-dividendaverage returns. However, this makes no difference to the dividend inference in my paper. The coefficienton after-dividend remains the same.
59
Figure 4: Explaining Average Trading Liquidity Patterns around Previously Declared Payment Dates
fig:liquidity in welch4-divstudytbls.tex, January 31, 2017
−10 −5 0 5 10
0
5
10
15
Payment Evt Day
#
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●Log Number of Trades
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●Log Dollar Volume of Trades
Explanations: Samples and variables are described in Table 11. These are plots of the by-event-dayaverages of the log number of trades and log value of dollar trades.
Interpretation: Liquidity-related trading explanations are unlikely to play a role.
60
Tabl
e15
:Il
lust
rati
veN
umer
ical
Exam
ple
of(P
ost-
Ann
ounc
emen
t)A
t-Pa
ymen
tC
hang
es
tbl:i
llust
rate
inwe
lch4
-app
endi
xtbl
s.te
x,Ja
nuar
y31
,201
7
Firm
Low
Leve
rage
(D0=
$5,
E 0=
$95,δ=
1.05
%)
Hig
hLe
vera
ge(D
0=
$95,
E 0=
$5,δ=
20%
)
Ris
kyP
Safe
C$0
$100
NoRisk
[$10
0,$1
00]
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$5)
$5($
5,$5
)Eq
uity
Cum
T=
0.9
$95
($95
,$95
)±
0.00
%Eq
uity
ExT=
1.1
$94
($95
–$1,
95–$
1)±
0.00
%
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$95)
$95
($95
,$95
)Eq
uity
Cum
T=
0.9
$5($
5,$5
)±
0.00
%Eq
uity
ExT=
1.1
$94
($5–
$1,5
–$1)
±0.
00%
Ris
kyP
Safe
C$2
$98
LowRisk
[$99
.8,$
100.
2]
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$5)
$5($
5,$5
)Eq
uity
Cum
T=
0.9
$95
($94
.8,$
95.2
)±
0.21
0%Eq
uity
ExT=
1.1
$94
($94
.8–$
1,95
.2–$
1)±
0.21
3%
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$95)
$95
($95
,$95
)Eq
uity
Cum
T=
0.9
$5($
4.8,
$5.2
)±
4.0%
Equi
tyEx
T=
1.1
$94
($4.
8–$1
,5.2
–$1)
±5.
0%
Ris
kyP
Safe
C$9
8$2
HighRisk
[$90
.2,$
109.
8]
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$5)
$5($
5,$5
)Eq
uity
Cum
T=
0.9
$95
($85
.2,$
104.
8)±
10.3
2%Eq
uity
ExT=
1.1
$94
($85
.2–$
1,10
4.8–
$1)±
10.4
3%
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$100
.8)
$95
($89
.2,$
100.
8)Eq
uity
Cum
T=
0.9
$5($
1,$9
)±
80%
Equi
tyEx
T=
1.1
$94
($1–
$1,9
–$1)
±10
0%
Ris
kyP
Safe
C$1
00$0
OnlyRisk
[$90
,$11
0]
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$5)
$5($
5,$5
)Eq
uity
Cum
T=
0.9
$95
($85
,$10
5)±
10.5
3%Eq
uity
ExT=
1.1
$94
($85
–$1,
105–
$1)±
10.6
4%
Secu
rity
T=
0T=
2R
isk
@T
Deb
t(FV=
$101
)$9
5($
90,$
101)
Equi
tyC
umT=
0.9
$5($
1,$9
)±
80%
Equi
tyEx
T=
1.1
$94
($1–
$1,9
–$1)
±10
0%
•A
ssum
eth
atth
epr
evio
usly
-ann
ounc
eddi
vide
ndto
bepa
yed
outa
ttim
eT=
1is
$1,t
hatr
isky
proj
ects
will
earn
anr̃
ofei
ther
–10%
or+
10%
,for
ari
skof±
10%
,and
that
cash
isri
sk-f
ree.
Dou
ble
num
bers
inpa
rent
hese
sre
pres
ent
poss
ible
rand
omou
tcom
es.
•If
risk
isze
roor
leve
rage
isze
ro,t
hese
are
the
mar
gin
case
sin
whi
cheq
uity
risk
does
not
incr
ease
.
•If
risk
islo
w,t
heas
sum
ptio
nof
am
inim
umra
teof
retu
rnof
–10%
assu
res
full
paym
ent.
•If
leve
rage
islo
w,t
heas
sum
ptio
nof
am
inim
umra
teof
retu
rnof
–10%
assu
res
full
paym
ent.
•C
onsi
der
high
-ris
k,hi
ghle
vera
ge.
The
debt
face
valu
eof
$100
.8is
pinn
eddo
wn
byth
ede
bt-e
quit
yra
tio
of$9
5-to
-$5
and
cons
iste
ncy
ofth
eex
ampl
e.Th
eeq
uity
rece
ives
$98·(
1+
r̃)+
$2−
$5fr
oma
$5in
vest
men
tfo
rra
tes
ofre
turn
of≈(−
10.3
2%,+
10.3
2%)
wit
heq
ualp
roba
bilit
y.A
fter
the
payo
ut,t
heeq
uity
isw
orth
$94
(not
$95)
,and
the
equi
vale
ntca
lcul
atio
nyi
elds(−
10.4
3%,+
10.4
3%).
61