Capital structure theory and practice

Jonah Whanau

2022-03-15 10:32:00 Tue ET

Capital structure theory and practice 

The genesis of modern capital structure theory traces back to the seminal work of Modigliani and Miller (1958, 1963). This work not only leads to the core testable propositions but also sets the research agenda for the subsequent decades. These propositions shine light on the nexus between a corporation’s market value and the choice of debt versus equity in the absence of taxes, agency costs, financial distress costs, information asymmetries, and other market frictions.

  1. A corporation’s market value is independent of its capital structure or relative mix of debt and equity.
  2. The relative riskiness of a corporation’s equity increases with the degree of financial leverage.


Modigliani and Miller’s propositions suggest that the costs of different forms of capital do not change independently, so there is no gain from opportunistically switching between debt and equity. The above Modigliani-Miller propositions can be synthesized with the CAPM to yield a formula for the required rate of return on a corporation’s equity.


Trade-off theory 

By adding a few market frictions to the baseline Modigliani-Miller model, the trade-off theory determines an optimal capital structure. These frictions include taxes, distress costs, and agency costs. Higher taxes on dividends indicate more debt (Modigliani and Miller, 1963; Miller and Scholes, 1978). Higher non-debt tax shields indicate less debt (DeAngelo and Masulis, 1980). Higher distress or business disruption costs suggest that equity is more important than debt for a firm to survive. Agency problems also call for more or less debt. Too much equity can result in free cash flows and potential conflicts of interest between corporate managers and shareholders (Jensen, 1986). Too much debt can lead to asset substitution and conflicts of interest between managers and bondholders (Fama and Miller, 1972; Jensen and Meckling, 1976). Leland (1994) and Leland and Toft (1996) derive an equilibrium model of optimal capital structure that weighs a reasonable trade-off between interest tax shields and business disruption costs. To the extent that the costs and benefits of debt usage offset one another, the corporation faces an optimal mix of debt and equity in accordance with shareholder wealth maximization.

The key testable prediction of the trade-off theory is that capital structure fully or partially adjusts toward some target leverage ratio. The empirical evidence thus far offers polemic views of this capital structure puzzle with large heterogeneity in the speed of partial adjustment toward an unobservable target mix of debt and equity (e.g. Fama and French (2002, 2005), Flannery and Rangan (2006), Antoniou, Guney, and Paudyal (2008), Lemmon, Roberts, and Zender (2008), and Huang and Ritter (2009)). The crux of this issue is that the estimates of target leverage convergence speed are quite sensitive to the variation in the econometric methodology. As a result, this issue remains a major puzzle in the capital structure literature.


Pecking order theory 

In the pecking order theory of Myers (1984) and Myers and Majluf (1984), there is no optimal capital structure. If there is an optimum, the cost of deviating from this optimum is insignificant in comparison to the cost of raising external finance. Raising external finance is costly because corporate managers have better information about the firm’s recent prospects. Due to this information asymmetry, outside investors rationally discount the firm’s stock price when the firm issues equity in lieu of debt. To avoid this discount, corporate managers view equity as the last resort. This rationale suggests that each firm follows a pecking order of capital structure. The Myers-Majluf firm uses up internal funds first, then uses up debt, and finally resorts to equity. In the absence of profitable investment opportunities, the firm retains profits and builds up financial slack to avoid having to raise external finance in the future. A firm raises debt to finance its investment opportunities if there are insufficient internal funds to support these opportunities. Following the pecking order, a firm adjusts the debt ratio due to the need for external funds, but not because of an attempt to reach an optimal mix of debt and equity (Myers, 1984; Myers and Majluf, 1984; Shyam-Sunder and Myers, 1999).   

Shyam-Sunder and Myers (1999) conduct the first empirical test of the pecking order theory against the static trade-off theory. The econometrician regresses the variation in the debt-to-assets ratio on the funds-flow deficit and the deviation of debt-to-assets from the target capital structure, which can be quantified as the firm’s moving average debt ratio or the industry average debt ratio. The pecking order coefficient turns out to be higher than the target adjustment coefficient by an order of magnitude (i.e. β=0.73>γ=0.15). This model captures most of the variation in the debt-to-assets ratio (R2=0.76). Shyam-Sunder and Myers (1999) interpret this evidence as empirical support for the pecking order theory of capital structure.

Frank and Goyal (2003) offer an alternative view of the horse race between the trade-off theory and the pecking order theory. Contrary to the pecking order theory, net equity issuance tracks the financing deficit more closely than does net debt issuance. While large corporations exhibit some aspects of pecking order behavior, the evidence is not robust to the inclusion of conventional explanatory factors such as changes in asset tangibility, market-to-book, sales as a proxy for firm size, and profitability (Rajan and Zingales, 1995). Specifically, Frank and Goyal (2003) report that Shyam-Sunder and Myers’s (1999) evidence is quite sensitive to changes in both sample selection and factor design. When the panel regression model includes the above explanatory factors (Rajan and Zingales, 1995), the pecking order coefficient sharply declines to β<0.25 for large firms and β<0.05 for small firms. Therefore, the pecking order phenomenon exists primarily among large firms and is not as robust as Shyam-Sunder and Myers (1999) suggest. The contradictory evidence points to an empirical void that both the static trade-off and pecking order theories cannot fill in practice.

Fama and French (2002) establish some empirical regularities with respect to the trade-off and pecking order theories of capital structure. While the joint predictions of these theories attract supportive evidence, the Fama-MacBeth cross-sectional regression tests shed skeptical light on the issues that reflect disagree-ment between these theories. For better exposition, the bullet points below sum up the joint predictions:

  1. Firms with more investment opportunities have lower book or market leverage.
  2. There is a positive relationship between firm size and financial leverage.
  3. There is a negative relationship between target dividend payout and financial leverage.  


Fama and French (2002) design a set of Fama-MacBeth leverage regressions to distinguish the trade-off and pecking order models. The framework is a standard partial adjustment model in which the change in book or market leverage partially absorbs the difference between target leverage and past leverage.

The leverage gap moves in response to the target leverage gap at the speed of adjustment per year with firm characteristics such as current and past corporate income and investment. The initial target leverage regression takes into account the joint effect of fundamental firm attributes such as firm size, stock market valuation, investment, profitability, and dividend payout. The econometrician then uses the fitted values of target leverage from this first-stage cross-sectional regression as a useful proxy for target leverage in the second-stage cross-sectional regression.

Controlling for investment opportunities, the trade-off model predicts that profitable firms can afford to have higher book or market leverage. Fama and French (2002) find a significantly negative relationship between profitability and leverage. This evidence contradicts the trade-off model but supports the pecking order theory. On the other hand, Fama and French (2002) report a significantly positive link between the target and future leverage gaps. This evidence suggests the existence of an optimal debt ratio in stark contrast to the pecking order theory. However, the mean reversion of leverage is 7%-10% per year for dividend payers and 15%-18% per year for dividend non-payers. This slow speed of partial adjustment toward target leverage bolsters the trade-off model or the dynamic pecking order model with a soft target leverage ratio.

Contradicting the central predictions of the pecking order model, Fama and French (2005) find that net equity issues are commonplace (i.e. equity is not a last resort). From 1973 to 1982, 54% of the U.S. firms make net equity issues each year, and this proportion rises to 62% for 1983 to 1992 and 72% for 1993 to 2002. Because equity issues are so pervasive, most firms that issue equity are not under financial duress. On average, equity issues are material. Among small firms with high growth potential, net equity issues are on average larger than net debt issues. However, the equity issuance process is lumpy and therefore results in a right-skewed distribution of stock issues. One story for the above results is that the pecking order model breaks down at least in part because there are many ways for firms to issue equity with low transaction costs and modest information asymmetries (Fama and French, 2005). In fact, any forces that lead to equity issuance not as a last resort invalidate the pecking order model.

Overall, Fama and French (2002, 2005) empirically find that both the trade-off and pecking order models have serious problems. It is probably time to stop running horse races between these competing models as standalone stories of capital structure. Perhaps it would be better to view these models as stable mates, and each has some elements of truth that help explain some aspects of corporate financing decisions.


Market timing theory 

In the dynamic version of the pecking order theory, high-growth firms reduce leverage in order to avoid raising equity as investment opportunities arise in the future (Myers, 1984). Baker and Wurgler (2002) report empirical results that are difficult to reconcile with this interpretation. Past values of market-to-book serve as important determinants of financial leverage. On this basis, Baker and Wurgler (2002: 27) assert that capital structure evolves as the cumulative outcome of past attempts to time the stock market. Corporate managers tend to recommend stock issuance when they believe the cost of equity is irrationally low. Conversely, corporate managers tend to recommend stock repurchase when they believe the cost of equity is irrationally high. This market timing theory of capital structure rests upon the behavioral basis of extreme or irrational investor expectations (La Porta, 1996; La Porta, Lakonishok, Shleifer, and Vishny, 1997; Frankel and Lee, 1998; Shleifer, 2000). If corporate managers attempt to exploit extreme investor expectations, net equity issuance should be positively related to the market-to-book ratio. In the absence of an optimal capital structure, corporate managers need not reverse their leverage decisions when the firm seems to be correctly valued and the cost of equity appears to be normal. The persistence of cumulative capital structure decisions leaves transient fluctuations in the market-to-book ratio with permanent effects on financial leverage. The market timing theory accords with Graham and Harvey’s (2001) anonymous survey that many CFOs admit to trying to time the stock market through net equity or debt issuance.

Baker and Wurgler (2002) find that the market timing coefficient is significantly negative up to 10 years after the IPO. An alternative measure of market-to-book, the external-finance-weighted-average market-to-book ratio, can be incorporated as an explanatory factor that increases for corporations whose recent past equity issuance tends to be high at the time of high stock market-to-book and vice versa. The evidence suggests that the market timing coefficient is significantly negative in almost all of the above Fama-MacBeth regressions. Baker and Wurgler (2002) estimate that the half-life of convergence toward target capital structure is well over 10 years. This persistence lends credence to the market timing theory that may serve as a plausible substitute for the trade-off and pecking order theories.


Subsequent responses to Baker and Wurgler’s (2002) influential study 

There are several subsequent responses to Baker and Wurgler’s market timing thesis. Kayhan and Titman (2007) point out that the significance of the historical market-to-book series in leverage regressions may be due to the noise in the current market-to-book ratio. Specifically, Kayhan and Titman decompose the external-finance-weighted-average market-to-book ratio into the average historical market-to-book ratio and the covariance between the market-to-book ratio and the financing deficit. The persistence result of Baker and Wurgler (2002) is largely driven by the persistence of the average market-to-book ratio rather than the covariance between the market-to-book ratio and the financing deficit. Also, Leary and Roberts (2005) empirically find that firms attempt to rebalance leverage to stay within an optimal range of capital structure. This evidence refutes Baker and Wurgler’s interpretation of the permanent effect of the market-to-book ratio on structural shifts in the leverage ratio.

Hennessy and Whited (2004) derive a dynamic trade-off model with no market timing opportunities and then apply this model to replicate the empirically observed nexus between the historical market-to-book series and the current leverage ratio. In this model, a high market-to-book firm finances its growth with equity to avoid financial distress. Once this firm becomes profitable, a subsequent leverage increase is unattractive for personal tax reasons, since debt issuance necessitates an increase in dividend payout to shareholders. This dynamic trade-off model operates with a soft and flexible target leverage ratio.

Alti (2006) focuses on the IPO as a major financing event to capture the impact of market timing attempts on capital structure. High IPO volume defines a hot market while low IPO volume defines a cold market. Alti’s (2006) analysis rests on the idea that if market timing attempts have a permanent effect on leverage, then the cumulative change in leverage from its pre-IPO level should continue to reflect the hot-market effect in the post-IPO period. To test this idea, Alti (2006) uses a set of variables to explain the cumulative change in leverage:

Although the hot-market effect suggests a significant 3.53% decline in leverage on average, there is little persistence in this hot-market effect. The hot-market coefficient is –1.46 (t-ratio=1.47) one year after the IPO and +0.51 (t-ratio=0.44) two years after the IPO. In other words, more than half of the hot-market effect is reversed in the first year after the IPO, and the hot-market effect completely vanishes by the end of the second year after the IPO. Overall, Alti’s (2006) results indicate that the hot-market firms pursue an active policy of reversing the past market timing effect on leverage. The reversal begins immediately after the IPO and takes about two years to complete. While cumulative market timing attempts can be an important determinant of financing activity in the short term, the long-term effect is rather limited. Over the long run, corporate capital structure policies seem to be largely consistent with the existence of target leverage ratios.

Flannery and Rangan (2006) offer another response to Baker and Wurgler’s (2002) market timing thesis. A panel regression specification that tests for any particular trade-off leverage behavior must permit each firm’s target debt ratio to change over time. This specification must also recognize that deviations from target leverage may not be offset within a short time window. These requirements are both met in a mean-differencing panel regression model with incomplete adjustment toward target leverage that depends on a unique set of firm characteristics. In turn, this model suggests that the firm’s actual debt ratio eventually converges to the target debt ratio. The implicit assumption is that all firms face the same adjustment speed toward target leverage.

The long-term impact of firm characteristics on the market debt ratio is given by its coefficient scaled by the adjustment speed. The various explanatory firm characteristics include the ratio of operating income before interest and tax expenses to total assets, the market-to-book ratio, the amount of depreciation as a proportion of total assets, the natural logarithm of total assets, the ratio of fixed assets to total assets, the ratio of R&D expenditure to total assets, the binary dummy variable for zero R&D investment, the lagged industry median debt ratio, and firm and year fixed effects. Most of the explanatory variables are highly significant, and the baseline specification captures about 45% of the variation in the market debt ratio.

Flannery and Rangan (2006) provide evidence in support of the view that each year a typical firm closes more than 30% of the gap between the current and target leverage ratios. While cumulative market timing and pecking order attempts serve as an important determinant of financing activity in the short term, the long-term effect is limited. Over the long term, corporate capital structure policies are largely consistent with the existence of target leverage ratios.

Flannery and Rangan’s (2006) baseline analysis entails consistently estimating the adjustment speed in a dynamic panel. Careful attention is given to the serial correlation properties of the dependent variable and the residual term (Baltagi, 2001; Wooldridge, 2002). With the use of lagged book leverage ratios as exogenous instruments (Greene, 2003), Flannery and Rangan (2006) ensure the consistent estimation of the adjustment speed in the range of 30% to 40% per year. This empirical result is robust to the variation in the use of alternative panel regression specifications and robustness checks, the latter of which involve changes in the time horizon for estimation, firm size, and debt ratio measurement.

Flannery and Rangan (2006) provide auxiliary tests in response to some concurrent studies of Baker and Wurgler (2002), Frank and Goyal (2003), Welch (2004), and Lemmon and Zender (2010). Indicators of the pecking order and market timing theories carry significant coefficients, but their economic effects are swamped by partial adjustments toward firm-specific target leverage ratios. Stock price fluctuations have a short-term impact on the market debt ratios, but the typical firm’s cumulative efforts to reach the target leverage ratio offset these transitory effects within a few years. Overall, Flannery and Rangan’s (2006) evidence supports the dynamic trade-off theory of capital structure with rapid partial adjustment toward target leverage.

Antoniou, Guney, and Paudyal (2008) report international differences in the speed of adjustment toward target leverage. Using international panel data and system GMM panel estimation, Antoniou, Guney and Paudyal (2008) find that the adjustment speed depends on the country’s legal origin, financial condition, and market- or bank-orientation. While French firms adjust their capital structure toward the target at the fastest rate, Japanese firms do so at the slowest rate. A firm’s capital structure adjustment reflects country-specific heterogeneity in the broader economic institutions, corporate governance practices, tax systems, borrower-lender relations, and legal rules and institutions for investor protection.

Huang and Ritter (2009) acknowledge that no single theory of capital structure is capable of explaining all of the time-series and cross-sectional patterns in the firm leverage data. Echoing the largely inclusive perspective of Fama and French (2005), Huang and Ritter (2009) suggest that the relative importance of the trade-off, pecking order, and market timing theories has varied in different studies. Using a measure of the equity risk premium, Huang and Ritter (2009) find that firms are more likely to tap into external equity finance when the relative cost of equity is low. In accordance with the market timing theory, the typical firm funds a large proportion of the financing deficit with equity when the equity risk premium is low. This behavior in turn results in lower leverage for many subsequent years.

Huang and Ritter (2009) point out that target capital structure is highly persistent over time. As a result, the system GMM estimator of Antoniou, Guney, and Paudyal (2008) and Lemmon, Roberts, and Zender (2008) is likely to introduce a substantial bias. Hahn, Hausman, and Kuersteiner (2007) propose a long differencing estimator for highly persistent data series. In this estimator, a multi-year difference of the model is taken rather than a one-year difference. Using this long differencing technique, Huang and Ritter (2009) find that firms only slowly rebalance away the undesirable effects of leverage shocks. In essence, it takes about 7.2 or 5.2 years for the typical firm to remove all of the effect of a shock on the respective book or market leverage ratio. These point estimates land within the full gamut of estimates of adjustment speed in the order of 3.2 to 20 years (e.g. Fama and French (2002); Welch (2004); Flannery and Rangan (2006); Antoniou, Guney, and Paudyal (2008); Huang and Ritter (2009)).

DeAngelo, DeAngelo, and Stulz (2010) revisit the market timing thesis that corporate managers attempt to sell highly priced shares when stock market conditions permit (Loughran and Ritter, 1995, 1997; Baker and Wurgler, 2002). Their logit regressions help discover the determinants of the probability of a firm’s decision to conduct an SEO. The number of post-listing years serves as a measure of each firm’s lifecycle stage, and the market-to-book ratio and the recent abnormal stock return serve as measures of each firm’s market-timing opportunities. DeAngelo, DeAngelo, and Stulz (2010) find that the typical firm’s lifecycle stage differences have an economically larger impact on SEO probabilities than do differences in market timing opportunities. In the sample of 4,291 SEOs, 90% of the firms conduct no more than 3 SEOs over a 29-year period from 1973 to 2001, thus serial market timers are not the norm. Because the majority of firms would face a near-term cash constraint in the pre-SEO year with no increase in capital investment, debt issuance, or dividend payout, DeAngelo, DeAngelo, and Stulz (2010) infer that most firms conduct SEOs to meet a short-term cash need due to precautionary concerns. Lifecycle stage with a genuine near-term cash constraint affects much of the variation in the likelihood of SEO issuance while market timing motives are secondary considerations.

Lemmon, Roberts, and Zender (2008) employ the pooled OLS regression, the panel regression with firm fixed effects, and the system GMM panel regression (Blundell and Bond, 1998) to benchmark the capital structure adjustment speed estimates with the prior studies. Corporate capital structures tend to be stable over a long period of time: firms with high or low leverage tend to remain so for over 20 years. Although there is some evidence of sluggish convergence toward to the mean, the vast majority of capital structures are invariant over time. Much of this unobservable heterogeneity remains unexplained by many empirical specifications (e.g. Fama and French (2002); Welch (2004); Alti (2006); Flannery and Rangan (2006); Antoniou, Guney, and Paudyal (2008); Huang and Ritter (2009)).

DeAngelo and Roll (2015) note that the previous capital structure literature focuses on firm fixed effects (e.g. Lemmon, Roberts, and Zender (2008)). These fixed effects indicate substantial unobservable time-invariant heterogeneity in corporate capital structure. However, DeAngelo and Roll (2015) empirically find that leverage cross-sections more than a few years apart are dramatically different. While migration over the cross section of leverage quartiles is substantial and pervasive, nearly 70% of the firms appear in different leverage quartiles over a typical 20-year period. In other words, corporate leverage exhibits significant firm-specific variation over time. Moreover, DeAngelo and Roll’s (2015) simulation reports evidence in support of a flexible target leverage model. Perhaps corporate investment, payout, and equity issuance considerations govern the time path of leverage insofar as the firm’s debt-to-equity mix remains within a wide range that the flexible target zone allows over a few years.


Comments and suggestions for future empirical corporate finance research 

The capital structure literature provides a full gamut of estimates of adjustment speed in the order of 3.2 to 20 years (e.g. Fama and French (2002); Welch (2004); Flannery and Rangan (2006); Antoniou, Guney, and Paudyal (2008); Huang and Ritter (2009)). The polemic views of capital structure adjustment speed shed inconclusive light on the relative merits of the trade-off and market timing theories. This issue thus suggests room for future econometric improvements in the measure of target leverage for better estimates of the adjustment speed.

The financial risk literature suggests that a distress risk variable has to be a coherent measure of risk with econometrically rich properties (Artzner, Delbaen, Eber, and Heath, 1999). Also, this literature suggests the use of value-at-risk or conditional value-at-risk that in turns serves as a complex function of default probability (PD), loss given default (LGD), and exposure at default (EAD) in the asymptotic single risk factor model (Vasicek, 1977). This model helps estimate the minimum capital requirement for the firm to sustain its normal business at a particular confidence level. Indeed, this novel estimation can allow the econometrician to reverse-engineer the *optimal* target leverage ratio. This financial risk concept echoes the long-term persistent component of target capital structure (Lemmon, Roberts, and Zender, 2008).

It is informative to identify the negative relation between stock return volatility and subsequent earnings growth (Chen, Wang, and Zhang, 2014). This nexus serves as a potential mechanism through which stock return volatility shocks propagate changes in subsequent earnings growth and these changes then reflect capital structure heterogeneity. At any rate, this nexus makes one reminiscent of the DuPont breakdown of profitability or return on equity: ROE=(profit margin)*(sales turnover)*(financial leverage) where the first term is the ratio of corporate return to total net sales, the second term is the ratio of total net sales to total assets, and the third term is the ratio of total assets to total equity. This tripartite identity suggests that any future earnings growth indicates changes in some or all of these terms. Hence, it is plausible for stock return volatility shocks to correlate with changes in subsequent earnings growth, especially if these shocks represent an increase in the typical firm’s exposure to risk that arises from an increase in financial leverage. It would be fruitful to further develop this economic rationale.


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