Can Operating Leverage Be the Cause of the Value Premium

Can Operating Leverage be the Cause of the Value Premium?

Luis García-Feijóo*

Florida Atlantic University College of Business

Liberal Arts Building 2912 College Avenue

Davie, FL 33314 Phone: (954) 236-1239 Fax: (954) 236-1298

E-mail: [email protected]

Randy D. Jorgensen Creighton University

Department of Economics & Finance College of Business Administration

2500 California Plaza Omaha, NE 68178-0308 Phone: (402) 280-5513

E-mail: [email protected]

_____________________________________________________________________________ Abstract: Recent theoretical models (Carlson, Fisher and Giammarino, 2004) predict an association between the book-to-market equity ratio (BE/ME) and operating leverage in the cross-section. Consistent with these models, we find a positive association between BE/ME and the degree of operating leverage (DOL), between DOL and stock returns, and between DOL and systematic risk. Overall, our findings provide support for a risk-based explanation for the value premium that is consistent with existing theoretical models. The evolution of systematic risk associated with firm-level investment activity, rather than financial distress, seems to be the main determinant of the value premium. JEL classification: G12 Keywords: Expected returns; book-to-market; operating leverage; value premium; anomalies. _____________________________________________________________________________

*Corresponding Author. We acknowledge very helpful comments of an anonymous referee, Bill Christie (the editor), Brad Jordan, and participants at the 2007 Financial Management Association meetings in Orlando.

2

Can Operating Leverage be the Cause of the Value Premium?

Recent theoretical models (Carlson, Fisher and Giammarino, 2004) predict an association

between the book-to-market equity ratio (BE/ME) and operating leverage in the cross-section.

Consistent with these models, we find a positive association between BE/ME and the degree of

operating leverage (DOL), between DOL and stock returns, and between DOL and systematic

risk. Overall, our findings provide support for a risk-based explanation for the value premium

that is consistent with existing theoretical models. The evolution of systematic risk associated

with firm-level investment activity, rather than financial distress, seems to be the main

determinant of the value premium.

3

There is considerable evidence that stocks with high book-to-market equity ratios

(henceforth BE/ME) have historically earned higher returns than stocks with low BE/ME.

However, researchers disagree as to whether this value premium reflects compensation for

systematic risk (Fama and French, 1996) or mispricing based on cognitive biases (Lakonishok,

Shleifer, and Vishny, 1994; Daniel and Titman, 1997). Recently, a number of theoretical papers

have endogenously linked the dynamics of expected returns and risk to firm-level investment

decisions. In these models, BE/ME is associated with operating leverage; thus, value stocks earn

higher average stock returns as they have higher levels of systematic risk (Carlson et al., 2004;

Zhang, 2005; Cooper, 2006).1

We report three major findings. First, we find a positive association between BE/ME and

DOL, both at the firm- and the portfolio-level using sorting procedures as well as regression

We provide broad empirical evidence regarding these theoretical models by examining

the association among BE/ME, the degree of operating leverage (DOL), and the cross-section of

average stock returns. Evidence of a positive correlation would be consistent with the general

predictions of the models and would support a risk-based explanation for the value premium.

The existing literature also debates whether the systematic risk underlying the value

premium is associated with financial distress or with investment activity. Fama and French

(1996) and Chen and Zhang (1998), argue that the BE/ME effect is due to priced financial

distress risk. In contrast, Berk, Green, and Naik (1999) and Carlson et al. (2004), among others,

suggest that the value premium is related to firm-level investment activity. In our analysis, we

also include the degree of financial leverage (DFL) in an attempt to shed light on the nature of

the systematic risk associated with the value premium.

1 Lev (1974) and Mandelker and Rhee (1984) predict and find evidence of a positive association between operating leverage and systematic risk.

4

analysis. Second, we find a positive relationship between DOL and beta, and between DOL and

average stock returns in the cross-section. These findings offer support for the recent theoretical

models of Carlson et al. (2004), Zhang (2005), and Cooper (2006). Third, we find a positive

relation between size (i.e., market equity) and DFL, and a positive association between BE/ME

and DFL after controlling for size. We also find a positive, but weak, relation between DFL and

stock returns. Taken together, these results do not support the hypothesis that the value premium

reflects compensation for financial risk, in contrast to the argument in Chen and Zhang (1998).

To the extent that higher DFL is associated with greater financial distress risk, our conclusion is

consistent with recent evidence (e.g., Campbell, Hilscher, and Szilagyi, 2008).

While we follow the existing literature and estimate DOL and DFL using a time-series

regression approach (Mandelker and Rhee, 1984), we obtain similar results when we use book

measures of leverage, namely, the ratio of fixed assets divided by total assets and the ratio of

total debt divided by total assets. Additionally, when we examine the evolution of other

underlying fundamentals, such as profitability, sales, or capital expenditures, we find that high

(low) DOL stocks display firm characteristics typically associated with value (growth) stocks. In

the last section, we discuss the results of numerous robustness checks of our methods and

variable definitions.

The evidence we report is consistent with the results of two recent studies. Novy-Marx

(2007) finds support for the hypothesis that operating leverage is related to the value premium.

He reports a positive association between operating leverage and stock returns and between

operating leverage and loadings on the value factor. Gulen, Xing, and Zhang (2008) find

evidence that value firms are less flexible than growth firms in adjusting to worsening economic

conditions. They report that value firms have higher operating leverage, higher ratios of fixed

5

assets to total assets, greater frequency of disinvestment, and higher financial leverage than

growth firms.

Overall, our findings are consistent with the broad implications of recent theoretical

models and provide support for a risk-based explanation for the value premium. Furthermore, the

evolution of systematic risk associated with firm-level investment activity seems to be the main

determinant of the value premium.

This study proceeds as follows. In Section I, we review the related literature. We describe

our data and methods in Section II and provide initial results in Section III. In Section IV, we

investigate the association between DOL and stock returns, and between DOL and beta while in

Section V, we investigate the association between DOL and BE/ME. We discuss the results of

robustness checks in Section VI and provide our conclusions in Section VII.

I. Related Literature

Our investigation belongs to a long-standing line of research concerned with the real

determinants of systematic risk. Researchers have long been aware that operating leverage is one

of the determinants of systematic risk of common stock. In particular, building on Hamada

(1972) and Rubinstein (1973), Mandelker and Rhee (1984) decompose a firm’s systematic risk

into DOL, DFL, and business risk. DOL measures a firm’s reliance on fixed costs, DFL

measures a firm’s reliance on debt, and business risk is the systematic risk of a firm’s basic

operations.

Recently, a number of theoretical papers have linked the evolution of systematic risk to

firms’ capital investment decisions and to the value and size effects of stock returns.2

2 The literature includes the models of Berk et al. (1999), Gomes, Kogan, and Zhang (2003), Carlson et al. (2004), Zhang (2005), Cooper (2006), Novy-Marx (2007), and Aguerrevere (2009).

In

6

particular, Carlson et al. (2004) model the optimal investment behavior of monopolistic firms

facing stochastic market demand conditions. In their model, beta is linear in the ratio of fixed

costs to total firm value (i.e., operating leverage) and the ratio of growth opportunities to assets

in place. Intuitively, BE/ME measures invested capital levels relative to market demand and

relates to risk through operating leverage; size captures the importance of finite growth

opportunities relative to assets in place.

Cooper (2006) develops a model in which the book-to-market ratio depicts the deviation

of a firm’s actual capital stock from its target capital stock. This, in turn, measures the sensitivity

of the return on the firm to aggregate market conditions. If capital investment is irreversible, the

book value of assets of a distressed firm remains constant, but its market value falls increasing its

book-to-market. A high book-to-market firm is sensitive to aggregate shocks as its extra installed

capacity allows it to expand production easily without new investment providing a high payoff to

equity holders. Low book-to-market firms, in contrast, would need to undertake investment

providing a lower payoff. Therefore, high book-to-market stocks have greater systematic risk.

Zhang (2005) examines equilibrium in competitive product markets and demonstrates

that firms’ optimal investment, together with costly reversibility and the countercyclical price of

risk, can generate the observed value premium. Specifically, he emphasizes that capital invested

is riskier than growth options in economic downturns as it is difficult to disinvest. In contrast,

assets in place are as risky as growth options in economic booms. Hence, value stocks are riskier

than growth stocks, particularly in economic downturns when the price of risk is high.

Although the mechanics of the models differ, they share the essential prediction that there

is a positive relation among operating leverage, BE/ME, and stock returns in the cross-section.

Intuitively, in the absence of operating leverage, growth stocks, whose value is derived primarily

7

from growth options, would be riskier than value stocks. We empirically examine the broad

predictions of these models.

As noted, two recent studies report findings closely related to ours. Novy-Marx (2007)

finds support for the hypothesis that operating leverage is related to the value premium. He

reports a positive relation between operating leverage and stock returns and between operating

leverage and loadings on the value factor (Fama and French, 1993). This is consistent with what

we find. However, he reports no association between his measure of operating leverage and

BE/ME, contrary to what we observe. As we discuss below, he uses a direct measure of

operating leverage that is different from the one typically used in the literature, which may

explain the different results. Novy-Marx (2007) also develops an equilibrium model that does not

require measuring operating leverage directly. The model predicts that if the operating leverage

hypothesis holds, there should be a strong correlation between stock returns and BE/ME within

industries, but a weak association across industries. He finds support for this prediction.

Gulen et al. (2008) find evidence that the value premium displays countercyclical time

variation. They speculate that the expected returns of value firms co-vary more with recessions

than the returns of growth firms as value firms are less flexible than growth firms in adjusting to

recessionary shocks. Consistent with the results of our investigation, they find a positive

association between BE/ME and measures of real inflexibility including operating leverage, the

ratio of fixed assets to total assets, and the frequency of disinvestment.

In a recent paper, Aguerrevere (2009) extends the model of Carlson et al. (2004) to

consider the effects of competitive interaction on firms’ investment decisions. He finds that the

effect of competition on a firms’ systematic risk is conditional upon the level of demand for the

industry output. In his model, firms in competitive industries are riskier than firms in

8

concentrated industries when demand is low because the value of growth options decreases with

more firms in the market and operating leverage makes assets in place riskier than growth

options. When demand is high, firms in competitive industries are less risky than firms in

concentrated industries. Aguerrevere (2009) notes that his model is consistent with a negative

association between operating leverage and BE/ME. Alternatively, we find evidence of a positive

association between DOL and BE/ME. However, a proper empirical analysis of the model’s

implications for the association between operating leverage and BE/ME would likely require the

inclusion of controls for industry structure and market demand, which is beyond the scope of our

investigation.

In sum, the operating leverage hypothesis for the value premium predicts that DOL

should be positively associated with BE/ME and stock returns. However, empirical evidence is

sparse. In the sections that follow, we present new evidence regarding the operating leverage

hypothesis.

II. Data and Methods

In this section, we review the existing literature regarding operating and financial

leverage and explain our methods for estimating DOL and DFL.

A. A Review of the Literature on Operating Leverage

The impact of financial and operating leverage on a firm’s equity risk has been the

subject of a stream of research extending over a number of years.3

3 Early studies tend to proceed with limited theoretical grounds. Darrat and Mukherjee (1995) and Ryan (1997) review these early studies in the finance and accounting literature, respectively.

Most of the modern research

in this area stems from studies utilizing a theoretical basis for testing the impact of operating

9

and/or financial leverage on beta. Much of this follows the theoretical work of Hamada (1972),

Rubinstein (1973), Lev (1974), and Bowman (1979), who demonstrate analytically that there

exists a positive relation between a firm’s operating and financial leverage and the systematic

risk of its stock. As a result of this theoretical work, researchers generally agree that operating

leverage and financial leverage are two real determinants of the systematic risk of common

stock.

Additionally, Gahlon and Gentry (1982) discuss the difficulties of estimating equity betas

using return data (see also Jagannathan and Wang, 1993), and note that managers will benefit

from an understanding of the real determinants of the cost of capital. Because of the theoretical

and practical relevance of operating and financial leverage, introductory finance textbooks

routinely contain a basic discussion of the two types of leverage and their effect on risk. The

literature, however, has no unified approach to estimating the degree of operating leverage and

the degree of financial leverage.

Specifically, to measure DOL and DFL, the literature starts by making a series of

assumptions in the classical ex ante model to conclude that DOL and DFL should be estimated as

elasticity measures.4

The time-series regression approach was pioneered by Mandelker and Rhee (1984) and

Ang and Peterson (1984), and has been used more recently by DeYoung and Roland (2001),

Griffin and Dugan (2003), and Ho, Xu, and Yap (2004). This approach uses a regression of

earnings before interest and taxes (EBIT) on sales to estimate DOL. The point-to-point approach

Then, studies proceed to use one of two approaches: 1) a time-series

regression approach or 2) a point-to-point approach.

4 Regarding DOL, these assumptions include linear, deterministic, and independent revenue and cost functions, a stable product mix, output as the only stochastic variable, and prices determined in a perfectly competitive market for the firm’s product. The difficulty in classifying externally reported costs into fixed and variable components leads to the common definition of DOL as an elasticity measure of EBIT given a change in unit demand. However,

10

estimates DOL as a ratio of changes in earnings to changes in sales, or fixed assets to total assets

(Ferri and Jones, 1979; Lord, 1998). The time-series regression estimates seem to be more

appropriate theoretically (Dugan and Shriver, 1989), although both approaches suffer from

similar biases (Lord, 1998)5

Furthermore, previous studies using the time-series regression approach to estimate DOL

have either ignored or applied a different estimation method to firms with negative earnings

(Mandelker and Rhee, 1984; Griffin and Dugan, 2003; Ho et al., 2004; Rossett, 2001). In

. As we discuss below, we use a time-series regression approach as

our main empirical method, but also use a point-to-point approach as a robustness check. Our

point-to-point estimate equals the ratio of net fixed assets to total assets (Ferri and Jones, 1979;

Mandelker and Rhee, 1984).

O’Brien and Vanderheiden (1987) recommend an adjustment for growth in the time-

series regression approach before estimating DOL. In particular, they recommend detrending the

series of earnings and sales to control for a spurious correlation between growth in both earnings

and sales that would bias DOL estimates toward a value of one. Dugan and Shriver (1992)

compare the two techniques [Mandelker and Rhee (1984) and O'Brien and Vanderheiden,

(1987)] and conclude that O'Brien and Vanderheiden's (1987) estimates are more consistent with

the classical ex-ante model. As we explain below, we follow O'Brien and Vanderheiden (1987)

and detrend the series before estimating DOL and DFL using the time-series regression approach

of Mandelker and Rhee (1984). This is also the approach followed by DeYoung and Roland

(2001) and Griffin and Dugan (2003). We discuss the sensitivity of our results to the estimation

methods in the last section.

many firms do not report data on unit output (or manufacture multiple products), so it is common to use sales rather than output (Lord, 1998). 5 According to theory, DOL estimates should be higher than one if the firm is operating above breakeven point and could be negative if the firm is operating below breakeven. However, a very large proportion of DOL estimates take values less than one (Dugan and Shriver, 1992).

11

contrast, we use a transformation common in the accounting literature to compute logs of

negative earnings (Ljungqvist and Wilhelm, 2005), and subsequently treat similarly firms with

positive or negative earnings.

Taken as a whole, the existing literature supports a positive association between DOL and

systematic risk (Mandelker and Rhee, 1984, Lord, 1996; Ho et al., 2004). However, the majority

of the existing studies suffer from limited sized samples.

As noted in the previous section, a number of theoretical papers have recently put

forward an operating leverage hypothesis to explain the value premium (Carlson et al., 2004).

Empirically, Novy-Marx (2007) finds support for the hypothesis, but reports no association

between his measure of operating leverage and BE/ME. We find a strong correlation between

DOL and BE/ME. Novy-Marx (2007) measures operating leverage as operating costs (costs of

goods sold plus selling, general, and administrative expenses) divided by assets, a measure that

has not been used in the literature. As reviewed, we measure operating leverage (DOL) following

the existing literature.

Our investigation complements that of Novy-Marx (2007) in a number of ways. First, we

emphasize direct tests of the operating leverage hypothesis using DOL, while he focuses on

indirect tests based on the predictions of a model he puts forward. Second, we examine the

fundamental characteristics of firms with different degrees of operating leverage, while he

provides evidence using factor-mimicking portfolios. Third, we include a measure of financial

leverage in our analysis, while he ignores financial leverage effects. Nevertheless, we both find

that there is a positive relationship between operating leverage and stock returns, and, more

generally, conclude that operating leverage is likely to be the cause of the value premium.

12

Furthermore, Gulen et al. (2008) report a positive correlation between their measure of

operating leverage and BE/ME, and between operating leverage and stock returns. To measure

operating leverage, they use the three-year moving average of the ratio of the percentage change

in operating income before depreciation divided by the percentage change in sales. In contrast,

we estimate operating leverage following the time-series approach of Mandelker and Rhee

(1984) over a five-year rolling window. Despite the different variable definitions, however, the

two studies report entirely consistent results that support the operating leverage hypothesis.

B. A Review of the Literature on Financial Leverage

As noted, researchers have known since at least Hamada (1972) and Bowman (1979) that

financial leverage is one of the determinants of systematic risk. Empirical evidence, however, on

the association between DFL and beta is mixed. While Mandelker and Rhee (1984) find a

positive relationship, Darrat and Mukherjee (1995) and Lord (1996) find no association.

Similarly, evidence regarding the correlation between financial leverage and stock returns is

weak, with leverage often becoming insignificant in regressions that include other firm

characteristics (Fama and French, 1992).

Furthermore, theoretical models and empirical studies that have considered interactions

between investment and financing decisions indicate that there exists a trade off (Dotan and

Ravid, 1985; Trezevant, 1992) or a U-shaped relation (Huffman, 1983; Prezas, 1987; Kale, Noe,

and Ramirez, 1991) between operating and financial leverage. This literature suggests that we

should include DFL as a control variable in our investigation regarding the operating leverage

hypothesis.

13

Moreover, some authors (e.g., Fama and French, 1996) conjecture that the value premium

reflects compensation for financial distress risk. According to this literature, financial distress is

related to a state-variable risk of special concern to investors due to its negative effects on

unmeasured components of wealth such as human capital. Although our focus is on financial

leverage (DFL), which is different from financial distress, we would expect the two to be highly

correlated. For example, the literature on financial distress costs has often used high levels of

financial leverage, in combination with other variables, to measure financial distress (Opler and

Titman, 1994). Thus, to the extent that financial leverage is correlated with financial distress, our

study can shed additional light on the hypothesis that the value premium is associated with

financial distress risk.

Empirically, the literature has typically found that financially distressed stocks are

associated with anomalously low returns and that financial distress risk is largely due to

idiosyncratic factors. In a recent study, Campbell et al. (2008) conclude that the value premium

does not reflect compensation for financial distress risk. We similarly conclude that the value

premium is associated with operating leverage, rather than financial leverage.

In sum, although the theoretical papers linking operating leverage and the value premium

do not consider any financial leverage effects, we include a measure of DFL in our analysis to: 1)

control for financial leverage following the literature on the determinants of systematic risk, and

2) shed additional light on whether the value premium is related to financial distress risk. For

consistency and to facilitate comparisons with the previous literature, we estimate DFL using the

time-series regression approach. As a robustness check, however, we also consider a point-to-

point measure, defined as the ratio of total debt to total assets (Mandelker and Rhee, 1984).

14

C. Estimating DOL and DFL

We collect data on sales, EBIT, and earnings after interest and taxes (EAIT) for all

companies included in COMPUSTAT in fiscal years 1981-2002. To estimate DOL, we follow

Mandelker and Rhee (1984) and O'Brien and Vanderheiden (1987) and proceed in two steps, as

explained below. Because we are interested in relating DOL to BE/ME and stock returns each

year, we need an estimate for DOL at the end of each year for each firm. Therefore, all of our

regressions are run at five-year overlapping intervals (i.e., 1982-1986, 1983-1987, etc.) at the

firm level. The choice of a five-year window is arbitrary, but it allows us to work with a

relatively long sample period (1986-2002), while at the same time taking into account possible

changes in a firm’s cost structure over time. To avoid giving the impression of data mining, we

have not examined any other window length.

More specifically, we first run the following regressions:

Ln EBITt = Ln EBIT0 + gebit t + μt, ebit

Ln Salest = Ln Sales0 + gsales t + μt, sales

where EBIT0 and Sales0 are the beginning levels of EBIT and Sales, respectively. To compute

logs of negative earnings, we use a transformation common in accounting research (Ljungqvist

and Wilhelm, 2005), ln (1+EBIT) if EBIT ≥ 0, and –ln (1-EBIT) if EBIT < 0.

Second, once the μt, ebit, and μt, sales residual series are produced by the regressions, we

estimate the following equation:

μt, ebit = OL μt, sales + et

15

where et is an error term. OL, the estimate of DOL, measures the average sensitivity of the

percentage deviation of EBIT from its trend relative to the percentage deviation of sales from its

trend.

For consistency, we estimate DFL similarly. That is, we run the following two additional

regressions:

Ln EAITt = Ln EAIT0 + geait t + μt, eait

μt, eait = FL μt, ebit + ut

FL, the estimate of DFL, measures the average sensitivity of the percentage deviation of EAIT

from its trend relative to the percentage deviation of EBIT from its trend.

Therefore, we end up with firm-level estimates of DOL and DFL from 1986-2002 (we

lose the year 1981 when we detrend the series). Note that the methodology we use can result in

negative values for DOL and DFL. We follow Reilly and Brown (2003) and measure DOL in

absolute value. In addition, because negative DFL values are economically irrational, we do not

include firms for which DFL is negative.6

6 In sensitivity checks at the end of the paper, we report that the results do not materially change if we include firms with negative DFL estimates, retain the sign of the negative DOL estimates, or delete observations with negative DOL estimates or with negative earnings.

In an attempt to create a variable that combines

operating and financial leverage effects, we also examine the degree of total leverage (DTL),

defined as the product of DOL times DFL.

D. Sample Description

16

After estimating DOL and DFL, we obtain data on market value and stock returns from

the Center for Research in Security Prices (CRSP). We compute BE/ME as the ratio of book

value of equity (computed as in Fama and French, 1992) at the end of the fiscal year divided by

the market value of equity at the end of the previous December from COMPUSTAT from 1986-

2002. We compute market capitalization (ME) using market equity from CRSP at the end of

June in the calendar year following the end of the fiscal year. Market capitalization and stock

returns are from CRSP over the period June 1987-December 2003. To compute BE/ME, we

ignore companies with negative book values. In addition, we do not include financial firms or

utilities (SIC in the 6000-6900 or in the 4000-4900).

Following the previous literature, we do not include firms until they are in the

COMPUSTAT database for five years to reduce survival biases. In addition, to mitigate

survivorship bias in returns for firms delisted from CRSP for performance reasons, we follow the

prescriptions of Shumway (1997) and Shumway and Warther (1999). That is, for firms delisted

for performance reasons, we use –30% as the last return for NYSE/AMEX firms and –55% as

the last return for NASDAQ firms. These requirements should reduce the influence of small,

young growth stocks on the results.

To prevent extreme observations from influencing our results, we follow the literature

(Fama and French, 1992; Dichev, 1998) and set the top 99.5% and bottom 0.5% of the DOL,

DFL, BE/ME, and monthly stock returns distributions equal to the 99.5% and 0.5% percentiles.

The resulting sample data is summarized in Table I. The descriptive statistics in the table are

similar to those in Dichev’s (1998) over a similar period, despite the fact that we do not include

firms without valid estimates of DOL and DFL. Thus, our results are unlikely to be driven by the

sample selection.

17

Insert Table I about here.

As a first step in analyzing the data, we compute the correlations between the variables.

As demonstrated in Table I, Panel B, DOL and DFL are negatively correlated. In addition,

BE/ME is positively associated with DTL and DOL, and negatively associated with DFL. In

contrast, ME is positively related to DTL and DFL, and negatively related to DOL.

III. Initial Results

In this section, we present preliminary results on the cross-sectional association between

BE/ME, size, and DOL and DFL. In Table II, we report equally-weighted monthly stock returns,

and mean DOL, DFL, and DTL estimates for 25 portfolios based on BE/ME and ME, as in Fama

and French (1993).

Insert Table II about here.

High BE/ME stocks have consistently outperformed low BE/ME stocks over the sample

period. For example, average monthly stock returns are 1.38% for the highest and 0.65% for the

lowest BE/ME quintile across all firms, 1.39% and 0.25%, respectively, within small firms, and

1.22% and 1.09% within large firms.

In contrast, there does not seem to be an association between size and returns in our

sample. For instance, average monthly stock returns are 1.11% for the smallest and 1.01% for the

largest quintile across all firms, 0.25% and 1.09%, respectively, within the low-BE/ME quintile,

18

and 1.39% and 1.22% within the high-BE/ME quintile. The “disappearance” of the small-size

effect has also been reported by the literature (Dichev, 1998; Schwert, 2003).

In Table II, and graphically in Figure I, we also report DOL estimates by BE/ME and size

groups. Consistent with the theoretical models, there is a clear positive association between DOL

and BE/ME.7

The relation between DFL and BE/ME is more complicated. Unconditionally, there does

not seem to be an association between DFL and BE/ME. DFL estimates increase from 1.17 to

1.31 as BE/ME increases from the first to the third quintile, but then decrease to 1.19 in the fifth

Unconditionally, DOL estimates increase monotonically from 2.86 to 5.20 as

BE/ME increases from the lowest to the highest quintile. Conditioning on market value, DOL

estimates increase monotonically from 2.76 to 4.98 across BE/ME quintiles within small stocks,

and from 2.34 to 7.09 across BE/ME quintiles within large stocks. However, there does not seem

to be an association between DOL and size.

Insert Table II and Figure I about here.

In Table II, and graphically in Figure II, there is evidence of a positive association

between DFL and size. DFL estimates increase monotonically from 1.04 to 1.98 as size

increases. Conditionally, DFL estimates increase from 0.96 to 1.55 within the low-BE/ME

quintile, and from 1.08 to 3.79 within the high-BE/ME quintile.

Insert Figure II about here.

7 The associations among BE/ME, size, DOL, and DFL are similar when we examine medians rather than the reported means.

19

quintile. Conditionally, however, DFL estimates appear to be positively associated with BE/ME.

For example, DFL estimates increase monotonically from 0.96 for low BE/ME to 1.08 for high

BE/ME stocks within the smallest market value quintile, and from 1.55 to 3.79 within the largest

market value quintile.

When we combine operating and financial leverage into a total leverage measure, DTL,

we find there is a positive relation between DTL and BE/ME and between DTL and size. These

initial findings are consistent with a risk-based explanation for the value effect.

As a sensitivity check, we consider a point-to-point measure of operating leverage, book

DOL, defined as net fixed assets divided by total assets; and a point-to-point measure of financial

leverage, book DFL, defined as total debt divided by total assets. As demonstrated in Table II,

the general associations reported previously for DOL and DFL can also be observed for their

book value estimates. That is, there is evidence of a positive relation between operating leverage

and BE/ME, and between financial leverage and size. In addition, there is generally a positive

association between financial leverage and BE/ME after conditioning for size.

While the evidence from Table II is suggestive, it does not constitute formal evidence.

Thus, we assess the statistical significance of the previous results in Table III. Because the

average monthly sample sizes shown in Table II are small, particularly among large and high

BE/ME stocks, in Table III, we form quintiles based on either BE/ME or size, and compare the

two extreme quintiles. High BE/ME stocks have DOL levels that are typically 2.33 higher than

those of low BE/ME stocks. This difference is statistically significant at the 1% level. Similarly,

when DOL is measured as fixed assets divided by total assets, the difference is 0.04 and is also

highly significant. In contrast, there is no evidence that high BE/ME stocks have higher DFL

levels than low BE/ME stocks. Although the DFL difference is 0.04, it is not significantly

20

different from zero. Therefore, there is strong evidence that high BE/ME stocks have greater

DOL levels than low BE/ME stocks, but there is no clear association between BE/ME and DFL.

Insert Table III about here.

Additionally, when we compare the two extreme size quintiles, we find that small stocks

have higher DOL levels and lower DFL levels than big stocks. In terms of book values, small

stocks have lower levels of both DOL and DFL estimates. Therefore, small stocks are less

financially leveraged than big stocks, at least in the univariate analysis.

In Table III, we perform two types of sensitivity analyses. First, we note than there does

not seem to be a statistically significant value premium in our sample when stock returns are

value weighted. Although the average monthly difference between high and low BE/ME stocks

is 0.15%, the t-statistic is only 0.48. This contrasts with an average monthly difference of 0.73

(the t-statistic is 2.90) when stock returns are equally-weighted. Therefore, as a sensitivity check,

we examine differences between the high and low BE/ME stocks within the smallest quintile.

Previous research (Petkova and Zhang, 2005) has also focused on the smallest quintile as the

value effect appears to be strongest among small firms.8

As a second sensitivity check, we compute cross-sectional medians by quintile and

average them across the 17 years in our sample period. As shown in Table III, there is evidence

In Table III, we confirm that there exists

a value premium in the smallest quintile of stocks, in terms of both equally-weighted and value-

weighted returns. Similar to the full sample, high BE/ME stocks have significantly greater DOL

levels than low BE/ME stocks in the smallest quintile of stocks.

21

of a statistically significant positive correlation between DOL and BE/ME and between DFL and

size.9

8 Fama and French (2006) find that the value premium is 55% larger for small stocks than for big stocks from 1926-2004. They report no evidence of a statistically significant value premium (based on BE/ME) for big stocks in the U.S. over the 1926-1963 or the 1963-2004 subsample periods. 9 The sample size of 17 is small. However, results are similar when we compare distributions using the Wilcoxon signed rank test with tables for the null distribution of ranks sums based on the sample size.

The results of this section are broadly consistent with recent theoretical models that predict

a positive association between operating leverage and BE/ME.

IV. DOL and the Cross-Section of Average Stock Returns

In this section, we investigate the association between DOL and DFL and the cross-

section of stock returns. Theoretical models predict a positive association between operating

leverage and stock returns because operating leverage increases systematic risk.

In Table IV, we report average monthly percent stock returns by deciles based on

estimates for DOL (Panel A), DFL (Panel B), or DTL (Panel C). Portfolios are formed each June

based on estimates as of the previous fiscal year end. Reported returns are monthly averages over

the twelve months following each June. There is evidence that firms with higher DOL estimates

earn higher subsequent returns. Equally-weighted monthly stock returns increase from an

average of 0.78% for the lowest to 1.15% for the highest DOL decile. In addition, stock returns

for the first five deciles are consistently lower than returns for the higher deciles. The average of

the monthly return difference between stocks in the highest decile and stocks in the lowest decile

is a positive 0.37%, which is significantly different from zero at the 5% level (the t-statistic is

2.35). Consistent with the results of the previous section, BE/ME monotonically increases as

DOL increases.

Insert Table IV about here.

22

In Panel B, there is weak evidence of an association between DFL and realized stock

returns. Although the average stock returns for the highest DFL decile are higher than for the

lowest DFL decile (1.18% and 0.96%, respectively), the association is not monotonic.

Furthermore, the average of the monthly return differences between stocks in the highest and the

lowest deciles is 0.22%, which is marginally different from zero (the t-statistic is 1.71). To the

extent that stocks with higher DFL levels are more likely to experience financial distress, the

finding that there is a weak relation between DFL and stock returns is consistent with previous

research (Dichev, 1998; Campbell et al., 2008). In addition, the association between DTL and

stock returns (Panel C) is positive and significant, but it is not as strong as the one between DOL

and returns.

In Table IV, we also present average beta estimates by decile. We estimate firm-level

betas as in Fama and French (1992). In the univariate analysis, there does not appear to be a

relation between systematic risk and DOL, which is inconsistent with the operating leverage

hypothesis. However, as we discuss below, this result may be due to measurement error in the

estimates of beta and/or DOL.

In Table V, we present regression analysis results at the firm level. Following Fama and

MacBeth (1973), we report the time-series averages of slopes from monthly cross-sectional

regressions of stock returns on beta, size, BE/ME, DOL, and DFL. Because we estimate DOL

and DFL within the sample, inferences are likely to be biased. Nevertheless, the firm-level

regressions indicate that there is, in our sample, a positive association between BE/ME and the

cross-section of stock returns consistent with the previous literature. In addition, the regression

results suggest that there is also a positive relation between DOL and stock returns in the cross-

23

section, but that such an association is weakened when BE/ME is also included in the

regressions. In contrast, there does not seem to be a relation between DFL and stock returns.10

Consistent with our previous results, there is evidence of a positive association between

DOL and the cross-section of stock returns. DOL coefficient estimates are always positive and

Insert Table V about here.

To account for measurement errors in the estimation and testing of DOL and DFL within

the sample, we follow the previous literature and employ a portfolio-grouping approach.

Specifically, each month, we form 50 portfolios based on variables expected to be correlated

with operating and financial leverage, and compute value-weighted portfolio returns, DOL, and

DFL averages. We then run regressions using these value-weighted portfolio averages. Our

instrumental variables, expected to be positively correlated with operating and financial leverage,

include book DOL and book DFL, the variance of sales over the previous five years (White,

Sondhi, and Fried, 2003) and industry groups based on two-digit SIC codes (52 groups). All

variables are measured as of the end of the fiscal year prior to the year of portfolio formation.

We report our results in Table VI. Standard errors are adjusted for autocorrelation assuming that

coefficients follow an AR (1) process (Loughran and Schultz, 2005).

Insert Table VI about here.

10 Because DOL and DFL are related to systematic risk in a multiplicative fashion, it could be argued that the dependent variable should be transformed by taking a logarithm before running regressions. The results shown in Tables V and VI are stronger (i.e., higher significance levels for both DOL and DFL estimates) when the dependent variable is ln(stock returns) or ln(excess stock returns).

24

are statistically significant in three of the four regressions. DOL parameter estimates (t-statistics)

when book DOL and sales variance are used to form portfolios are 0.22% (2.30) and 0.40%

(2.74), respectively. When industry affiliation is the ranking variable, the estimate is 0.20%

(1.76). DOL parameter estimates are insignificant only when book DFL is used to form

portfolios. In contrast, DFL parameter estimates are never statistically significant.

The essence of the operating leverage hypothesis is that the value premium reflects

compensation for higher levels of systematic risk caused by firm-level investment activity. Thus,

it is important to examine whether there is a relation between operating leverage and systematic

risk. Accordingly, in Table VI, we also present the results of cross-sectional regressions of beta

on DOL and DFL. Because researchers have not agreed on how to best estimate beta, we follow

Fama and French (1992), an influential paper on the value premium literature.

There is evidence of a consistent positive relation between DOL and beta when book

DOL, book DFL, industry affiliation, and beta are used to form portfolios. Additionally, there is

evidence of a negative association between DFL and beta for all instrumental variables used to

form portfolios. Although not shown, the results are similar, in sign and statistical significance,

when only DOL or only DFL are included in the regressions. The finding that there is a positive

relation between DOL and beta should be viewed with caution, however. Both DOL and beta are

measured with error and estimated within the sample. Nevertheless, the finding is consistent with

the rest of the evidence we present, and provides further support for the operating leverage

hypothesis. Furthermore, the finding that there is a negative relation between DFL and beta is

consistent with the reported negative association between financial distress risk and returns

(Campbell et al., 2008) and may account for the poor performance of beta estimates in

explaining the cross-section of average stock returns (Fama and French, 1992).

25

Overall, the results of this section suggest that there is a positive relation between DOL

and systematic risk and between DOL and stock returns in the cross-section, which is consistent

with the operating leverage hypothesis. In the next section, we examine the association between

DOL and BE/ME using regression analysis.

V. Operating Leverage and BE/ME

In recent theoretical models (Carlson et al., 2004), operating leverage plays an essential

role in the explanation of the value premium. In this section, we provide direct evidence of a link

between BE/ME and DOL using regression analysis. Specifically, we perform annual cross-

sectional regressions of DOL on BE/ME at the firm level. In Table VII, we report the time-series

average of coefficient estimates and t-statistics based on time-series standard errors adjusted for

autocorrelation following Loughran and Schultz (2005). In the regressions, we set DOL as the

left-hand side variable, so that measurement error can be absorbed by the disturbance term.

Insert Table VII about here.

As reported in the table, when DOL is regressed against BE/ME, the coefficient estimate

of 0.31 is highly significant, statistically and economically. For example, for an increase in the

BE/ME ratio from the median value of 0.62 to the third quintile of 1.03, the regression results

predict an increase in DOL levels from 1.60 to 1.88 or a 20% increase.

As a sensitivity check, we follow Fama and French (1992) and break up BE/ME into the

ratio of total assets to market equity (TA/ME) and the ratio of total assets to book equity

(TA/BE). Because TA/ME can be interpreted as a measure of operating leverage, while TA/BE

26

(i.e., the equity multiplier) is a measure of financial leverage, this regression specification can

provide evidence on the operating leverage hypothesis, controlling for financial leverage. As

demonstrated in Table VII, the TA/ME coefficient estimate of 0.31 is also statistically

significant. The TA/BE coefficient estimate is negative and statistically indistinguishable from

zero. Further, results do not change when we control for size (lnME).

In unreported robustness checks, the results do not change when we include average sales

(i.e., demand levels) or sales variance (i.e., demand volatility) computed over the five years prior

to each cross-section year. These control variables can be motivated within the model of Carlson

et al., (2004).

For completeness, in Table VII, we also report regression results when the left-hand side

variable is DFL. We make two observations. First, consistent with our previous results, there is

evidence of a positive association between BE/ME and DFL, controlling for size. Second, there

is a positive relation between the equity multiplier and DFL, but not between TA/ME and DFL

suggesting that our DFL variable is indeed a measure of financial leverage. Overall, the results of

this section support the main prediction of recent theoretical papers linking operating leverage

and the book-to-market ratio.

VI. Robustness Checks

In this section, we report the results of two types of robustness checks. First, we

demonstrate that firms with high (low) DOL levels display characteristics typically associated

with value (growth) stocks. This evidence offers further support for the operating leverage

hypothesis.

Second, we report the results of a battery of robustness checks of our sample, methods,

27

and variable definitions. Overall, our results are only sensitive to detrending the earnings and

sales series before estimating DOL. However, after controlling for size, there is evidence of a

significantly positive association between DOL and BE/ME even if the series are not detrended.

A. DOL and Value and Growth Characteristics

We examine the evolution of growth in earnings, assets, sales, and capital expenditures

around the portfolio formation year. We compute portfolio growth rates following Fama and

French (1995). In particular, they look at the evolution of the ratio of portfolio equity income to

market equity income, EIp(t)/ EIm(t), around the portfolio formation year (Year 0). The two ratios

are averaged separately across portfolio formation years. In addition, the ratios are standardized

so that they are 1.0 for all portfolios in the year of the portfolio formation. We report our results

in Table VIII.

Insert Table VIII about here.

The evolution of profitability for high and low DOL stocks resemble that of high and low

BE/ME stocks (Fama and French, 1995). Specifically, the profitability of high DOL stocks

deteriorates prior to and improves subsequent to portfolio formation, while the opposite is true

for low DOL stocks. In addition, in unreported results, we also find that low DOL stocks are

consistently more profitable than high DOL stocks.

Previous research has found that low (high) BE/ME stocks experience increases

(decreases) in total assets, sales, and investment prior to portfolio formation (Fama and French,

1995; Lakonishok et al., 1994; Anderson and García-Feijóo, 2006). As illustrated in Table VIII,

28

we find that low (high) DOL stocks experience increases (decreases) in their economic

fundamentals around the portfolio formation year.

B. Sample, Methods, and Variable Definition

Previous research regarding the association between operating leverage and stock returns

has focused on manufacturing firms (Mandelker and Rhee, 1984). Due to our sample

construction requirements, 63% of our firm-year observations belong to the manufacturing

industry (SIC code between 2000-3999). When we repeat the analysis including manufacturing

firms only, the results are very similar to those of the full sample. There is evidence of a weaker

univariate association between DOL estimates and average stock returns. The average equally-

weighted monthly return difference between high and low DOL decile stocks, although positive

(0.30%), becomes statistically indistinguishable from zero (t-statistic of 1.53).

In our analysis, we have followed O'Brien and Vanderheiden (1987) and detrended the

series of earnings and sales before estimating DOL using the time-series regression approach of

Mandelker and Rhee (1984). Our results are sensitive to this adjustment. If we follow the

original approach of Mandelker and Rhee (1984), we find there is a significantly negative

association between DOL estimates and BE/ME, and no significant association between DOL

and stock returns. In Table III, for example, the average DOL estimate for firms in the lowest

B/M quintile is 5.79, while the estimate for the highest quintile is 4.89; the difference of -0.90 is

significantly different from zero at the 1% level. However, there is evidence of a significantly

positive relation between DOL and BE/ME after controlling for size. Within the smallest quintile

in Table III, DOL is 4.46 for the high BE/ME stocks and 3.52 for the low BE/ME stocks; the

difference of 0.94 is significant at the 1% level. Moreover, the estimated coefficient on B/M in

29

Table VII after controlling for size is 0.35%, which is significantly different from zero at the 1%

level.

Our reported results do not include stocks with negative DFL estimates because a

negative degree of financial leverage has no economic meaning. Stocks with negative DFL

estimates represent about 8% of our sample firm-years, and are distributed evenly between

manufacturing and non-manufacturing industries. None of our conclusions regarding DOL,

BE/ME, and stock returns are affected by the inclusion of negative DFL firms. Similarly, our

results do not change if we delete firms with negative DOL estimates, or if we retain the negative

sign (firms with negative DOL estimates tend to be firms with very low values of the book-to-

market equity ratio). Furthermore, our results are not sensitive to the exclusion of firms with

negative earnings. There is a strong positive link between DOL and BE/ME, and a weak, but still

positive relation between DOL and stock returns.

In a previous version of Gulen et al. (2008), Xing and Zhang (2004) estimate DOL at the

portfolio level. If we follow their approach, we find evidence of a negative relation between

DOL and BE/ME. Estimates are 1.00 for the Growth quintile, and 0.72 for the Value quintile;

DOL estimates are not significantly different from one except for the Value quintile. Detrending

the series of sales and earnings leads to generally lower DOL estimates, except for the Value

portfolio. After detrending, there is weak evidence of a positive association between DOL and

BE/ME at the portfolio level. DOL estimates are 0.81 for the Growth quintile and 0.92 for the

Value quintile, with only the estimate for the Growth quintile being (marginally) different from

one.

Finally, when we examine the time-series evolution of the association between DOL and

BE/ME, we find that the link is very persistent. For example, in Figure III, we plot annual

30

median values of DOL estimates by BE/ME quintile (the middle quintile is omitted in the graph).

It should be noted that firms in the higher (lower) BE/ME quintiles have consistently exhibited

higher (lower) DOL levels. This offers further support for the predictions of the existing

theoretical models.

VII. Summary

We test the broad prediction of the models of Carlson et al.(2004), Zhang, (2005), Cooper

(2006), and Novy-Marx (2007) that there should be a positive association between operating

leverage and the book-to-market ratio (BE/ME) in the cross-section. Consistent with the models,

we find 1) a positive association between BE/ME and estimates of the degree of operating

leverage (DOL), 2) a positive association between DOL estimates and subsequent stock returns,

and 3) a positive association between DOL and beta estimates.

To estimate DOL, we use the time-series regression approach of Mandelker and Rhee

(1984), but detrend the series of earnings and sales following the recommendations of O’Brien

and Vanderheiden (1987). If we do not detrend the series, we find evidence of a significantly

negative link between DOL and BE/ME, and no significant relation between DOL and stock

returns. However, after controlling for size, there is evidence of a significantly positive

association between DOL and BE/ME, even if the series of earnings and sales are not detrended.

Further, our results do not materially change if we exclude observations with negative earnings

or negative DOL estimates. Overall, we find support for a risk-based explanation for the value

premium that is consistent with recent theoretical models.

31

References

Aguerrevere, F.L., 2009, “Real Options, Product Market Competition, and Asset Returns,”

Journal of Finance 64, 957-983.

Anderson, C.W. and L. García-Feijóo, 2006, “Empirical Evidence on Capital Investment,

Growth Options, and Security Returns,” Journal of Finance 61, 171-194.

Ang, J. and P.P. Peterson, 1984, “The Leasing Puzzle,” Journal of Finance 39, 1,055-1,065.

Berk, J.B., R.C. Green, and V. Naik, 1999, “Optimal Investment, Growth Options and Security

Returns,” Journal of Finance 54, 1,153-1,607.

Bowman, R.G., 1979, “The Theoretical Relationship between the Systematic Risk and Financial

(Accounting) Variables,” Journal of Finance 34, 617-630.

Campbell, J.Y., J. Hilscher, and J. Szilagyi, 2008, “In Search of Distress Risk,” Journal of

Finance 63, 2,899-2,939.

Carlson, M., A. Fisher, and R. Giammarino, 2004, “Corporate Investment and Asset Price

Dynamics: Implications for the Cross Section of Returns,” Journal of Finance 59, 2,577-2,603.

Chen, N. and F. Zhang, 1998, “Risk and Return of Value Stocks,” Journal of Business 71, 501-

32

535.

Cooper, I., 2006, “Asset Pricing Implications of Non-Convex Adjustment Costs and

Irreversibility of Investment,” Journal of Finance 61, 139-170.

Daniel, K. and S. Titman, 1997, “Evidence on the Characteristics of Cross-Sectional Variation in

Stock Returns,” Journal of Finance 52, 1-33.

Darrat, A.F. and T.K. Mukherjee, 1995, “Inter-Industry Differences and the Impact of Operating

and Financial Leverages on Equity Risk,” Review of Financial Economics 4, 141-155.

DeYoung, R. and K.P. Roland, 2001, “Product Mix and Earnings Volatility at Commercial

Banks: Evidence from a Degree of Total Leverage Model,” Journal of Financial Intermediation

10, 54-84.

Dichev, I.D., 1998, “Is the Risk of Bankruptcy a Systematic Risk?” Journal of Finance 53,

1,131-1,147.

Dotan, A. and S.A. Ravid, 1985, “On the Interaction of Real and Financial Decisions of the Firm

under Uncertainty,” Journal of Finance 40, 501-517.

Dugan, M.T. and K. A. Shriver, 1989, “The Effects of Estimation Period, Industry, and Proxy on

the Calculation of the Degree of Operating Leverage,” Financial Review 24, 109-122.

33

Dugan, M.T. and K.A. Shriver, 1992, “An Empirical Comparison of Alternative Methods for the

Estimation of the Degree of Operating Leverage,” Financial Review 27, 309-321.

Fama, E.F. and K.R. French, 1992, “The Cross-Section of Expected Stock Returns,” Journal of

Finance 47, 427-465.

Fama, E.F. and K.R. French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds,”

Journal of Financial Economics 33, 3-56.

Fama, E.F. and K.R. French, 1995, "Size and Book-to-Market Factors in Earnings and Returns,"

Journal of Finance 50, 131-155.

Fama, E.F. and K.R. French, 1996, “Multifactor Explanations of Asset Pricing Anomalies,”

Journal of Finance 51, 55-84.

Fama, E.F. and K.R. French, 2006, “The Value Premium and the CAPM,” Journal of Finance

61, 2,163-2,185.

Fama, E.F. and J.D. MacBeth, 1973, “Risk, Return and Equilibrium: Empirical Tests,” Journal

of Political Economy 81, 607-636.

34

Ferri, M.G. and W.H. Jones, 1979, “Determinants of Financial Structure: A New Methodological

Approach,” Journal of Finance 34, 631-644.

Gahlon, J.M. and J.A. Gentry, 1982, “On the Relationship between Systematic Risk and the

Degrees of Operating and Financial Leverage,” Financial Management 11, 15-23.

Gomes, J., L. Kogan, and L. Zhang, 2003, “Equilibrium Cross-Section of Returns,” Journal of

Political Economy, 111, 693-732.

Griffin, H.F. and M.T. Dugan, 2003, “Systematic Risk and Revenue Volatility,” Journal of

Financial Research, 26, 179-189.

Gulen, H., Y. Xing, and L. Zhang, 2008, “Value versus Growth: Time-Varying Expected Stock

Returns,” University of Michigan Working Paper.

Hamada, R.S., 1972, “The Effect of the Firm´s Capital Structure on the Systematic Risk of

Common Stock,” Journal of Finance 27, 435-452.

Ho, Y.K., Z. Xu, and C.M. Yap, 2004, “R&D Investment and Systematic Risk,” Accounting and

Finance 44, 393-418.

Huffman, L., 1983, “Operating Leverage, Financial Leverage, and Equity Risk,” Journal of

Banking and Finance, 7, 197-212.

35

Jagannathan, R. and Z. Wang, 1993, “The CAPM Is Alive and Well,” Staff Report 165, Federal

Reserve Bank of Minneapolis.

Kale, J.R., T.H. Noe, and G.G. Ramírez, 1991, “The Effect of Business Risk on Corporate

Capital Structure: Theory and Evidence,” Journal of Finance 46, 1,693-1,715.

Lakonishok, J., A. Shleifer, and R. W. Vishny, 1994, “Contrarian Investment, Extrapolation and

Risk,” Journal of Finance 49, 1,541-1,578.

Lev, B., 1974, “On the Association between Operating Leverage and Risk,” Journal of Financial

and Quantitative Analysis 9, 627-641.

Ljungqvist, A. and W.J. Wilhelm, Jr., 2005, “Does Prospect Theory Explain IPO Market

Behavior?” Journal of Finance 60, 1,759-1,790.

Lord, R., 1996, “The Impact of Operating and Financial Risk on Equity Risk,” Journal of

Economics and Finance, 20, 27-38.

Lord, R., 1998, “Properties of Time-Series Estimates of Degree of Leverage Measures,”

Financial Review 33, 69-84.

36

Loughran, T. and P. Schultz, 2005, “Liquidity: Urban Versus Rural Firms,” Journal of Financial

Economics 78, 341-374.

Mandelker, G.N. and S.G. Rhee, 1984, “The Impact of the Degrees of Operating and Financial

Leverage on Systematic Risk of Common Stock,” Journal of Financial and Quantitative

Analysis 19, 45-57.

Newey, W.K. and K.D. West, 1987, "A Simple, Positive Semi-Definite Heteroskedasticity and

Autocorrelation Consistent Covariance Matrix," Econometrica 55, 703-708.

Novy-Marx, R., 2007, “Operating Leverage,” University of Chicago and NBER Working Paper.

O’Brien, T.J. and P.A. Vanderheiden, 1987, “Empirical Measurement of Operating Leverage for

Growing Firms,” Financial Management 16, 45-53.

Opler, T.C. and S. Titman, 1994, “Financial Distress and Corporate Performance,” Journal of

Finance 49, 1,015-1,040.

Petkova, R. and L. Zhang, 2005, “Is Value Riskier than Growth?” Journal of Financial

Economics 78, 187-202.

Prezas, A.P., 1987, “Effects of Debt on the Degrees of Operating and Financial Leverage,”

Financial Management 16, 39-44.

37

Reilly, F.K. and K.C. Brown, 2003, Investment Analysis and Portfolio Management, Mason,

OH: Thomson South-Western.

Rosett, J.G., 2001, “Equity Risk and the Labor Stock: The Case of Union Contracts,” Journal of

Accounting Research 39, 337-364.

Rubinstein, M.E., 1973, “A Mean-Variance Synthesis of Corporate Financial Theory,” Journal

of Finance 28, 167-182.

Ryan, S.G., 1997, “A Survey or Research Relating Accounting Numbers to Systematic Equity

Risk with Implications for Risk Disclosure Policy and Future Research,” Accounting Horizons

11, 82-95.

Schwert, G.W., 2003, Anomalies and Market Efficiency in G. Constantinides, M. Harris, and R.

Stulz, Ed., Handbook of the Economics of Finance, Vol. 1B, Amsterdam, Elsevier Science.

Shumway, T., 1997, “The Delisting Bias in CRSP Data,” Journal of Finance 52, 327-340.

Shumway, T. and V. Warther, 1999, “The Delisting Bias in CRSP’s Nasdaq Data and Its

Implications for the Size Effect,” Journal of Finance 54, 2,361-2,379.

38

Trezevant, R., 1992, “Debt Financing and Tax Status: Tests of the Substitution Effect and the

Tax Exhaustion Hypothesis Using Firms’ Responses to the Economic Recovery Tax Act of

1981,” Journal of Finance 47, 1,557-1,568.

Xing, Y. and L. Zhang, 2004, “Cyclical Variations in Expected Returns,” University of Michigan

Working Paper.

White, G.I., A.C. Sondhi, and D. Fried, 2003, The Analysis and Use of Financial Statements,

Hoboken, NJ: Wiley.

Zhang, L., 2005, “The Value Premium,” Journal of Finance, 60, 67-103.

39

Table I. Summary Sample Statistics We collect data on sales, earnings before interest and taxes (EBIT), and earnings after interest and taxes (EAIT) for all companies included in COMPUSTAT over fiscal years 1981-2002. We estimate DOL and DFL from 1986-2002 by running the following regressions at five-year overlapping intervals (i.e., 1982-1986, 1983-1987, etc) at the individual-firm level:

Ln EBITt = Ln EBIT0 + gebit t + μt, ebit Ln Salest = Ln Sales0 + gsales t + μt, sales

where EBIT0 and Sales0 are the beginning levels of EBIT and Sales, respectively. To compute logs of negative earnings, we use the following transformation: ln (1+EBIT) if EBIT ≥ 0, and –ln (1-EBIT) if EBIT < 0. Once the μt, ebit, and μt, sales residual series are produced by the regressions, we estimate the following equation:

μt, ebit = OL μt, sales + et where et is an error term. OL, the estimate of DOL, measures the average sensitivity of the percentage deviation of EBIT from its trend relative to the percentage deviation of sales from its trend. For consistency, we estimate DFL similarly. That is, we run the following two additional regressions:

Ln EAITt = Ln EAIT0 + geait t + μt, eait μt, eait = FL μt, ebit + ut

FL, the estimate of DFL, measures the average sensitivity of the percentage deviation of EAIT from its trend relative to the percentage deviation of EBIT from its trend. We obtain data on market value and stock returns from the Center for Research in Security Prices (CRSP). We compute BE/ME using end-of-fiscal year values from COMPUSTAT from 1986-2002, ME using market value from CRSP at the end of June in the calendar year following the end of the fiscal year, and stock returns from CRSP over the period June 1987-December 2003. To compute BE/ME, we ignore companies with negative book-values. We exclude regulated and financial firms, and we do not include firms until they are on the COMPUSTAT database for five years to reduce survival biases. To mitigate survivorship bias, we follow Shumway (1997) and Shumway and Warther (1999). We measure DOL in absolute value and delete all firms for which DFL is negative. DTL is defined as DOL times DFL. Book DOL is the five-year average ratio of fixed assets to total assets, and book DFL is the five-year average ratio of total debt divided by total assets.

Panel A. Descriptive Statistics for the Test Variables

Variable Mean Std Dev P5 P25 P50 P75 P95 Returns % 1.07 16.33 -23.08 -7.19 0.00 7.85 28.12 BE/ME 0.82 0.75 0.12 0.35 0.62 1.03 2.15 LnME 4.68 2.21 1.38 3.07 4.48 6.15 8.55 DOL 3.96 7.23 0.11 0.69 1.69 3.92 15.46 DFL 1.23 1.40 0.23 0.71 0.94 1.23 3.11 DTL 4.18 8.19 0.08 0.56 1.58 4.07 17.03 BookDOL 0.30 0.20 0.05 0.15 0.26 0.41 0.73 BookDFL 0.48 0.20 0.16 0.34 0.49 0.62 0.80

Panel B. Pearson Correlation Coefficients for the Test Variables

Returns LnBE/ME LnME LnDOL LnDFL LnDTL LnBook DOL

LnBook DFL

LnBE/ME 0.02 1.00 LnME -0.00 -0.37 1.00 LnDOL 0.01 0.18 0.02 1.00 LnDFL 0.00 -0.00 0.14 -0.08 1.00 LnDTL 0.01 0.16 0.09 0.87 0.42 1.00 LnBookDOL -0.00 0.05 0.18 0.08 0.05 0.10 1.00 LnBookDFL -0.01 -0.01 0.11 0.09 0.09 0.13 0.18 1.00

40

Table II. Average Monthly Percent Returns and Characteristics for Quintile Portfolios Formed on Size and Book-to-Market Equity Each year, we divide NYSE, AMEX, and NASDAQ stocks into five groups based on their size (price times shares outstanding) at the end of June of year t, and into five groups based on ranked values of BE/ME for individual stocks. BE/ME is the ratio of book value equity at the end of fiscal year t-1 divided by market value of equity at the end of December of calendar year t-1. Only positive values of BE/ME are considered. We use NYSE stocks to determine the size and B/M breakpoints. We form 25 portfolios by combining the sorts by size and by BE/ME. DOL, DFL, and DTL are the degree of operating, financial, and total leverage, respectively, which are computed as explained in Table I. Book DOL is the five-year average ratio of fixed assets to total assets, and book DFL is the five-year average ratio of total debt divided by total assets as of the end of the fiscal year prior to the portfolio-formation year.

Size

Quintile Book-to-Market Equity (BE/ME) Quintile

Low 2 3 4 High All Low 2 3 4 High All Average Monthly Return

(Percent) Average Degree of Operating Leverage

(DOL) Small 0.25 1.01 1.24 1.32 1.39 1.11 2.76 3.24 3.63 4.03 4.98 3.96 2 0.73 1.06 1.23 1.16 1.20 1.04 3.64 3.53 4.26 4.92 6.44 4.24 3 1.01 1.11 1.24 1.25 1.50 1.13 3.24 3.57 4.76 5.27 7.89 4.16 4 1.23 1.25 1.23 1.39 1.69 1.26 2.97 3.24 4.76 7.38 6.39 4.06 Big 1.09 0.87 1.05 1.07 1.22 1.01 2.34 3.64 5.26 5.28 7.09 3.46 All 0.65 1.02 1.23 1.28 1.38 2.86 3.36 4.05 4.47 5.20

Size Quintile

Book-to-Market Equity (BE/ME) Quintile Low 2 3 4 High All Low 2 3 4 High All

Average Degree of Financial Leverage (DFL)

Average Degree of Total Leverage (DTL)

Small 0.96 1.02 1.04 1.08 1.07 1.04 2.47 2.98 3.47 3.75 4.62 3.67 2 1.08 1.24 1.34 1.44 1.85 1.33 3.44 3.73 4.92 5.77 7.56 4.68 3 1.26 1.27 1.54 1.72 1.86 1.42 3.54 3.91 5.70 6.62 9.30 4.81 4 1.55 1.53 1.79 2.19 2.26 1.68 3.65 4.29 6.70 9.64 9.62 5.36 Big 1.55 1.99 2.61 2.74 3.79 1.98 3.54 6.24 9.17 10.16 14.32 5.92 All 1.17 1.25 1.31 1.30 1.19 3.01 3.70 4.59 4.82 5.11

41

Table II. Average Monthly Percent Returns and Characteristics for Quintile Portfolios Formed on Size and Book-to-Market Equity (Continued)

Size

Quintile Book-to-Market Equity (BE/ME) Quintile

Low 2 3 4 High All Low 2 3 4 High All Average Book DOL Average Book DFL

Small 0.25 0.27 0.28 0.28 0.30 0.28 0.50 0.47 0.47 0.46 0.46 0.47 2 0.27 0.31 0.33 0.32 0.38 0.31 0.43 0.46 0.47 0.49 0.57 0.47 3 0.28 0.33 0.36 0.40 0.43 0.34 0.46 0.47 0.50 0.53 0.55 0.49 4 0.30 0.37 0.41 0.50 0.49 0.37 0.47 0.50 0.54 0.58 0.60 0.51 Big 0.32 0.37 0.43 0.47 0.43 0.36 0.51 0.56 0.62 0.62 0.63 0.55 All 0.27 0.31 0.32 0.32 0.31 0.49 0.48 0.49 0.48 0.48

Size Quintile

Book-to-Market Equity (BE/ME) Quintile Low 2 3 4 High All Low 2 3 4 High All

Average Monthly Number of Firms Average June Market Value Equity($millions) Small 222 172 198 228 433 1,252 57 63 60 53 36 50 2 75 76 72 56 32 312 311 317 302 293 284 304 3 60 58 40 25 12 197 755 756 747 732 736 750 4 61 50 30 19 7 167 2,005 1,981 1,947 1,903 1,863 1,970 Big 79 38 21 10 4 152 22,010 12,115 11,194 7,650 8,393 17,590 All 497 395 361 338 488 5,039 1,715 996 504 173

42

Table III. Characteristics for Quintile Portfolios Formed on Book-to-Market Equity Ratio or Size

The table reports the mean values of monthly equally- and value-weighted stock returns and operating and financial leverage measures for stocks grouped into five portfolios based on BE/ME or size. Only values for stocks in the smallest/largest group and the lowest/highest BE/ME group are shown. Variable definitions are described in Table I.

Time-Series Averages of Monthly Cross-Sectional Means

Book-to-Market Equity Quintiles Market Equity Quintiles High Low Diff t-stat Small Big Diff t-stat Full Sample Full Sample

EWret % 1.38 0.65 0.73*** 2.90 1.11 1.01 0.10 0.33 VWret % 1.25 1.10 0.15 0.48 1.18 1.01 0.18 0.52 DOL 5.20 2.86 2.33*** 31.92 3.96 3.46 0.50*** 4.30 DFL 1.19 1.17 0.02 1.23 1.04 1.98 -0.94*** -15.51 DTL 5.11 3.01 2.11*** 26.03 3.67 5.92 -2.25*** -7.10 BookDOL 0.31 0.27 0.04*** 11.34 0.28 0.36 -0.08*** -25.45 Book DFL 0.48 0.49 -0.01*** -3.36 0.47 0.55 -0.08*** -17.84 Small Quintile EWret % 1.39 0.25 1.14*** 4.33 VWret % 1.43 0.51 0.92*** 2.59 DOL 4.98 2.76 2.22*** 53.25 DFL 1.07 0.96 0.12*** 14.63 DTL 4.62 2.47 2.16*** 59.93 BookDOL 0.30 0.25 0.05*** 27.55 Book DFL 0.46 0.50 -0.04*** -17.19

Time Series Averages of Annual Cross-Sectional Medians

Book-to-Market Equity Quintiles Market Equity Quintiles High Low Diff t-stat Small Big Diff t-stat

DOL 2.43 1.23 1.19*** 14.16 1.82 1.38 0.45*** 6.57 DFL 0.88 0.94 -0.06*** -11.63 0.90 1.13 -0.23*** -7.65 DTL 2.23 1.12 1.11*** 13.14 1.60 1.65 -0.05 -0.37 BookDOL 0.26 0.22 0.04*** 6.49 0.23 0.32 -0.09*** -13.71 Book DFL 0.49 0.48 0.00 0.44 0.47 0.55 -0.08*** -9.33

***Significant at the 0.01 level

43

Table IV. Average Monthly Percent Returns and Characteristics for Decile Portfolios Formed on the Degree of Operating Leverage and the Degree of Financial Leverage At the end of June of each year t, t = 1987-2003 and decile portfolios are formed based on DOL, DFL, or DTL as of the end of fiscal year t-1. Returns are computed over the twelve months following portfolio formation (total of 198 months). Deciles are ranked in ascending order. FFBeta is the beta estimate from rolling regressions (Fama and French, 1992). Other variable definitions are in Table I. The last two columns present the average monthly return difference between the High and Low leverage groups (t-stats based on Newey-West (1987) standard errors are in parenthesis).

Low 2 3 4 5 6 7 8 9 High High-Low (Deciles)

High-Low (Quintiles)

Panel A. Portfolios based on the degree of operating leverage (DOL) EW Return (%) 0.78 1.05 1.02 1.00 1.13 1.18 1.20 1.20 1.23 1.15 0.37** (2.35) 0.27** (2.34) VW Return (%) 0.82 0.96 1.16 1.01 1.32 1.18 0.96 0.68 1.28 1.35 0.53 (1.32) 0.36 (1.09) DOL 0.12 0.39 0.70 1.05 1.47 2.00 2.77 4.00 6.61 20.6 DFL 1.57 1.40 1.22 1.19 1.20 1.27 1.20 1.18 1.13 1.01 BE/ME 0.70 0.71 0.72 0.75 0.77 0.84 0.85 0.94 0.97 1.06 ME ($millions) 1399 2164 2458 2950 2160 1663 1706 1447 800 942 Book DOL 0.29 0.30 0.30 0.29 0.30 0.30 0.31 0.31 0.31 0.33 FFBeta 1.21 1.19 1.18 1.18 1.19 1.20 1.19 1.20 1.22 1.22

Panel B. Portfolios based on the degree of financial leverage (DFL) EW Return (%) 0.96 1.05 1.25 0.99 1.17 1.23 0.92 1.13 1.07 1.18 0.22* (1.71) 0.12 (1.11) VW Return 0.78 1.00 1.23 0.76 1.18 1.06 1.28 0.94 1.10 1.10 0.32* (1.82) 0.16 (0.93) DFL 0.23 0.54 0.71 0.81 0.90 0.97 1.06 1.24 1.63 4.27 DOL 4.28 3.94 4.66 5.34 5.21 4.04 3.66 3.11 2.76 2.70 BE/ME 0.85 0.92 0.94 0.87 0.80 0.68 0.74 0.80 0.82 0.87 ME ($millions) 2376 1995 1071 1166 1172 1017 2080 2125 1986 2704 Book DFL 0.51 0.48 0.45 0.45 0.45 0.41 0.44 0.49 0.53 0.60 FFBeta 1.17 1.17 1.20 1.24 1.25 1.30 1.22 1.16 1.14 1.13

Panel C. Portfolios based on the degree of total leverage (DTL) EW Return (%) 0.81 0.85 1.09 1.10 1.05 1.16 1.31 1.15 1.31 1.10 0.28* (1.80) 0.37*** (3.36) VW Return 0.90 0.95 0.86 1.20 1.02 1.22 1.29 0.67 1.22 1.11 0.20 (0.63) 0.20 (0.80) DTL 0.08 0.30 0.57 0.91 1.34 1.93 2.76 4.16 7.07 22.90 BE/ME 0.72 0.70 0.76 0.77 0.80 0.80 0.86 0.92 0.97 1.00 ME ($millions) 1591 2450 2455 2089 2068 1815 1416 1189 1029 1586

***Significant at the 0.01 level **Significant at the 0.05 level *Significant at the 0.10 level

44

Table V. Average Parameter Values from Cross-Sectional Regressions of Monthly Returns on Size, Book-to-Market Ratio, and Operating and Financial Leverage Measures

Raw monthly returns are regressed on size (ME), BE/ME, and DOL, DFL, or DTL estimates. Size is the market value (price times shares outstanding) at the end of June of each year t, t = 1987-2003. BE/ME is the ratio of book value equity at the end of fiscal year t-1 divided by market value of equity at the end of December of calendar year t-1. The estimation of DOL and DFL is explained in Table I. DTL is the product of DOL times DFL. FFBeta is the beta estimate from rolling regressions following Fama and French (1992). Average parameter values are the time series averages, and t-statistics are time-series averages divided by time-series standard errors (198 months). Ln denotes natural logarithm.

Regression Specification, Average Parameter Values (%) and t-statistics Specification Ln FFBeta Ln(ME) Ln(BE/ME) Ln(DOL) Ln(DFL) Ln(DTL)

(1) 0.09 (0.27)

0.06 (0.83)

0.38*** (3.83)

(2) 0.07*** (2.62)

(3) 0.05 (1.20)

(4) 0.07*** (2.69)

0.06 (1.39)

(5) 0.00 (0.10) 0.06**

(2.53) 0.05

(1.50)

(6) 0.33*** (3.51)

0.03 (1.16)

0.05 (1.19)

(7) 0.07*** (2.96)

(8) 0.00 (0.10) 0.06***

(2.82)

(9) 0.33*** (3.55) 0.04

(1.44)

***Significant at the 0.01 level **Significant at the 0.05 level

45

Table VI. Average Parameter Values from Cross-Sectional Regressions of Monthly Returns on Operating and Financial Leverage Measures at the Portfolio Level

At the end of June of each year t, t = 1987-2003; 100 portfolios are formed based on the ranking variable measured at the end of fiscal year t-1. Each month, value-weighted monthly portfolio returns (or FFBeta estimates) are regressed on value-weighted portfolios formed based on DOL and DFL estimates. The estimation of DOL and DFL and other variable definitions are in Table I. FFBeta is the beta estimate from rolling regressions following Fama and French (1992). Varsales is the variance of sales over the five years prior to the portfolio formation year. Average parameter values are the time series averages, and t-statistics are time-series averages divided by time-series standard errors adjusted for autocorrelation following Loughran and Schultz (2005). Ln denotes natural logarithm.

Average Parameter Values (%) and t-statistics

Dep. Variable Ranking Variable to Form Portfolios Intercept Ln DOLp Ln DFLp

Returns

Book DOL 0.48 (1.22)

0.22** (2.30)

-0.01 (-0.15)

Book DFL 0.61 (1.63)

0.05 (0.51)

-0.06 (-0.46)

Varsales -0.04 (-0.08)

0.40*** (2.74)

0.27 (1.05)

Two Digit SIC Code 0.23 (0.62)

0.20* (1.76)

0.25 (1.61)

Ln FFBeta

Book DOL 4.89*** (16.51)

0.24*** (3.74)

-6.19*** (-18.68)

Book DFL 0.32 (0.77)

3.92*** (10.05)

-4.69*** (-12.70)

Varsales 0.22*** (37.28)

-19.84*** (-27.40)

-1.63*** (-5.60)

Two Digit SIC Code 1.01*** (2.83)

5.60*** (13.13)

-10.17*** (-19.92)

FFBeta 1.67 (1.40)

11.98*** (15.54)

-19.37*** (-20.08)

***Significant at the 0.01 level **Significant at the 0.05 level *Significant at the 0.10 level

46

Table VII. Annual Regression Results at Individual Firm Level The table displays results of annual cross-sectional regressions of leverage measures on size, BE/ME, total assets divided by market equity (TA/ME), or total assets divided by book equity (TA/BE). Average parameter values are the time series averages, and t-statistics are time-series averages divided by time-series standard errors adjusted for autocorrelation following Loughran and Schultz (2005). Ln denotes natural logarithm. Variable definitions are in Table I.

Average Parameter Values and t-statistics Dep. Variable Intercept Ln ME Ln BE/ME LnTA/ME LnTA/BE

Ln DOL

0.62*** (23.85) 0.31***

(21.36)

0.47*** (14.87) 0.31***

(17.78) -0.09

(-1.55) 0.34*** (5.90)

0.07** (2.14)

0.37*** (13.61)

Ln DFL

-0.10*** (-8.36) -0.01

(0.27)

-0.15*** (-12.83) 0.01

(0.49) 0.06*** (6.55)

-0.35*** (20.35)

0.06*** (8.08)

0.05*** (2.83)

***Significant at the 0.01 level

47

Table VIII. Economic Fundamentals in the 11 Years Around Portfolio Formation At the end of June of each year t, t = 1987-2003, quintile portfolios are formed based on DOL at the end of fiscal year t-1. The estimation of DOL is explained in Table I. EI(t) is earnings before extraordinary items, but after interest, depreciation, taxes, and preferred dividends for the fiscal year ending in calendar year t; A(t) is total assets; S(t) is sales; and CE(t) is capital expenditures. For a portfolio “p”, EI, A, S, and CE are the sums of the stocks in the portfolio. Portfolio measures are relative to the values of the variables for the market portfolio, and then standardized so the ratios are 1.0 in the portfolio formation year following Fama and French (1995). The market portfolio “m” includes all stocks in the five DOL quintiles.

Year i Relative to Portfolio Formation

-5 -4 -3 -2 -1 0 1 2 3 4 5 Earnings: Mean [EIp (t + i)/ EIm (t + i)]/ Mean [EIp (t )/ EIm (t )]

Low DOL 0.939 0.967 0.910 0.936 0.970 1.000 1.002 0.955 0.996 1.050 1.080 2 0.849 0.901 0.910 0.912 0.967 1.000 0.948 0.921 0.918 0.968 0.980 4 1.136 1.087 1.131 1.147 1.038 1.000 0.979 0.970 0.940 0.853 0.851 High DOL 3.310 2.570 2.060 1.820 1.210 1.000 2.250 3.110 3.340 3.130 2.940

Assets: Mean [Ap (t + i)/ Am (t + i)]/ Mean [Ap (t )/ Am (t )] Low DOL 0.996 1.023 0.975 0.973 0.985 1.000 1.022 1.032 1.063 1.101 1.122 2 0.888 0.913 0.968 0.964 0.975 1.000 1.027 1.045 1.068 1.102 1.162 4 1.075 1.047 1.042 1.023 1.017 1.000 1.000 0.979 0.901 0.857 0.961 High DOL 1.121 1.131 1.108 1.086 1.049 1.000 0.967 0.960 0.982 0.962 0.961

Sales: Mean [Sp (t + i)/ Sm (t + i)]/ Mean [Sp (t )/ Sm (t )] Low DOL 1.045 1.047 1.015 0.992 0.993 1.000 1.010 1.004 1.021 1.038 1.038 2 0.872 0.906 0.947 0.966 0.994 1.000 1.001 1.012 1.040 1.068 1.108 4 1.041 1.021 1.022 1.006 1.005 1.000 1.009 0.991 0.937 0.934 0.875 High DOL 1.168 1.163 1.128 1.085 1.038 1.000 0.984 0.986 1.004 0.990 0.997

Capital Expenditures: Mean [CEp (t + i)/ CEm (t + i)]/ Mean [CEp (t )/ CEm (t )] Low DOL 1.030 1.035 1.003 0.963 0.979 1.000 1.026 1.063 1.063 1.100 1.070 2 0.912 0.950 0.987 1.008 1.028 1.000 1.000 0.994 1.021 1.054 1.104 4 1.010 1.011 1.017 1.001 1.012 1.000 1.014 0.983 0.903 0.889 0.809 High DOL 1.180 1.149 1.110 1.061 1.025 1.000 0.985 1.014 1.061 1.033 1.066

48

Small2 ME

3 ME4 ME

Big

Low

2 BE/ME

3 BE/ME

4 BE/ME

High

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Figure I. Average DOL by BE/ME and ME Quintiles

49

Small2 ME

3 ME4 ME

Big

Low

2 BE/ME

3 BE/ME

4 BE/ME

High

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Figure II. Average DFL by BE/ME and ME Quintiles

50

Figure III. Median DOL by BE/ME Quintile

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Fiscal Year

High BE/ME 4th 2nd Low BE/ME