Leverage and the Cross‐Section of Equity Returns

Building on theoretical asset pricing literature, we examine the role of market risk and the size, book‐to‐market (BTM), and volatility anomalies in the cross‐section of unlevered equity returns. Compared with levered (stock) returns, unlevered market beta plays a more important role in explaining the cross‐section of unlevered equity returns, even after controlling for size and BTM. The size effect is weakened, while the value premium and the volatility puzzle virtually disappear for unlevered returns. We show that leverage induces heteroskedasticity in returns. Unlevering returns removes this pattern, which is otherwise difficult to address by controlling for leverage in regressions.     

Assessing Project Risk

Finding the appropriate discount rate, or cost of capital, for evaluating investment projects requires an accurate estimate of project risk. This can be challenging because project risk cannot be estimated directly using the CAPM, but must instead be inferred from a set of traded securities, typically the equity betas of comparable firms in the same industry. These equity betas are then unlevered to undo the effect of comparable companies' financial leverage and obtain estimates of “asset” betas, which are then used to estimate project risk. The authors show that asset betas estimated in this way are likely to overestimate project risk. The equity returns of companies are risky not only because of their existing projects but also because of their growth opportunities. Such growth opportunities often include embedded “real options,” such as the option to delay, expand, or abandon a project. Because such real options are similar to leveraged positions in the underlying project, a company's growth opportunities are typically riskier than its existing projects. Therefore, to properly assess project risk, analysts must also unlever the asset betas derived from comparable company stock returns for the leverage contributed by their growth options. The authors derive a simple method for unlevering asset betas for growth options leverage in order to properly assess project risk. They then show that standard methods for assessing project risk significantly overestimate project costs of capital—by as much as 2–3% in industries such as healthcare, pharmaceuticals, communications, medical equipment, and entertainment. Their method should also be applied to stock return volatility to derive project volatility, an important input for determining the value of a firm's growth opportunities and the appropriate time for investing in these opportunities.     

Corporate Investment and Asset Price Dynamics: Implications for the Cross-section of Returns

We show that corporate investment decisions can explain the conditional dynamics in expected asset returns. Our approach is similar in spirit to Berk, Green, and Naik (1999) , but we introduce to the investment problem operating leverage, reversible real options, fixed adjustment costs, and finite growth opportunities. Asset betas vary over time with historical investment decisions and the current product market demand. Book‐to‐market effects emerge and relate to operating leverage, while size captures the residual importance of growth options relative to assets in place. We estimate and test the model using simulation methods and reproduce portfolio excess returns comparable to the data.     

Equilibrium "Anomalies"

Many empirical “anomalies” are actually consistent with the single beta capital asset pricing model if the empiricist utilizes an equity‐only proxy for the true market portfolio. Equity betas estimated against this particular inefficient proxy will be understated, with the error increasing with the firm's leverage. Thus, firm‐specific variables that correlate with leverage (such as book‐to‐market and size) will appear to explain returns after controlling for proxy beta simply because they capture the missing beta risk. Loadings on portfolios formed on relative leverage and relative distress completely subsume the powers of the Fama and French (1993) returns to small minus big market capitalization (SMB) portfolios and returns to high minus low book‐to‐market (HML) portfolios factors in explaining cross‐sectional returns.     

Risk-taking incentives of executive stock options and the asset substitution problem

Various theoretical models show that managerial compensation schemes can reduce the distortionary effects of financial leverage. There is mixed evidence as to whether highly levered firms offer less stock‐based compensation, a common prediction of such models. Both the theoretical and empirical research, however, have overlooked the leverage provided by executive stock options. In principle, adjusting the exercise prices of executive stock options can mitigate the risk incentive effects of financial leverage. We show that the near‐universal practice of setting option exercise prices near the prevailing stock price at the date of grant effectively undoes most of the effects of financial leverage. In a large cross‐sectional sample of Canadian option‐granting firms, we find evidence that executives' incentives to take equity risk are negatively rather than positively related to the leverage of their employers.     

Safety Transformation and the Structure of the Financial System

This paper studies how a financial system that is organized to efficiently create safe assets responds to macroeconomic shocks. Financial intermediaries face a cost of bearing risk, so they choose the least risky portfolio that backs their issuance of riskless deposits: a diversified pool of nonfinancial firms' debt. Nonfinancial firms choose their capital structure to exploit the resulting segmentation between debt and equity markets. Increased safe asset demand yields larger and riskier intermediaries and more levered firms. Quantitative easing reduces the size and riskiness of intermediaries and can decrease firm leverage, despite reducing borrowing costs at the zero lower bound.     

Oil and stock market activity when prices go up and down: the case of the oil and gas industry

We examine the asymmetric effects of daily oil price changes on equity returns, market betas, oil betas, return variances, and trading volumes for the US oil and gas industry. The responses of stock returns associated with negative changes in oil prices are higher than that associated with positive changes in oil prices. Stock risk measured by market beta is influenced more due to oil price decreases than due to oil price increases. On the other hand, oil risk exposures (oil betas) and return variances are more influenced by oil price increases than oil price decreases. The results of our study indicate that oil and gas firm returns, market betas, oil betas, return variances respond asymmetrically to oil price changes. We also find that relative changes in oil prices along with firm-specific factors such as firm size, ROA, leverage, market-to-book ratio (MBR) are important in determining the effects of oil price changes on oil and gas firms’ returns, risks, and trading volumes.     

Do a firm's equity returns reflect the risk of its pension plan?

This paper examines the empirical question of whether systematic equity risk of US firms as measured by beta from the capital asset pricing model reflects the risk of their pension plans. There are a number of reasons to suspect that it might not. Chief among them is the opaque set of accounting rules used to report pension assets, liabilities, and expenses. Pension plan assets and liabilities are off-balance sheet and are often viewed as segregated from the rest of the firm, with its own trustees. Pension accounting rules are complicated. Furthermore, the role of the Pension Benefit Guaranty Corporation clouds the real relation between pension plan risk and firm equity risk. The empirical findings in this paper are consistent with the hypothesis that equity risk does reflect the risk of the firm's pension plan despite arcane accounting rules for pensions. This finding is consistent with informational efficiency of the capital markets. It also has implications for corporate finance practice in the determination of the cost of capital for capital budgeting. Standard procedure uses de-leveraged equity return betas to infer the cost of capital for operating assets. But the de-leveraged betas are not adjusted for the risk of the pension assets and liabilities. Failure to make this adjustment typically biases upward estimates of the discount rate for capital budgeting. The magnitude of the bias is shown here to be large for a number of well-known US companies. This bias can result in positive net present value projects being rejected.     

How Big is the Tax Advantage to Debt?

This paper uses an option valuation model of the firm to answer the question, “What magnitude tax advantage to debt is consistent with the range of observed corporate debt ratios?” We incorporate into the model differential personal tax rates on capital gains and ordinary income. We conclude that variations in the magnitude of bankruptcy costs across firms can not by itself account for the simultaneous existence of levered and unlevered firms. When it is possible for the value of the underlying assets to jump discretely to zero, differences across firms in the probability of this jump can account for the simultaneous existence of levered and unlevered firms. Moreover, if the tax advantage to debt is small, the annual rate of return advantage offered by optimal leverage may be so small as to make the firm indifferent about debt policy over a wide range of debt-to-firm value ratios.     

Pricing strategy and financial policy

Recent empirical evidence indicates that capital structure changesaffect pricing strategies. In most cases, prices increase followingthe implementation of a leveraged buyout of a major firm inan industry, with the more leveraged firm in the industry charginghigher prices on average. Notable exceptions exist, however,when the leverage increasing firm's rival is relatively unlevered.The first observation is consistent with a model where firmscompete for market share on the basis of price. The second observationcan be explained within the context of a Stackelberg model wherethe relatively unlevered rival acts as the Stackelberg priceleader.     

Systematic risk and the theory of the firm: A reexamination

A recent microeconomic model of the determinants of equity betas (Subrahmanyam and Thomadakis 1980) is generalized by including risky human capital in the market portfolio and allowing a general covariance structure between the model's sources of uncertainty. This provides an explanation of the ambiguous effect of operating leverage on beta by viewing human capital and equity contributors as risk sharers in the firm's output risk. This explanation may help to clarify the apparent conflict with the previous literature. The relationship between systematic risk and monopoly power is rederived and shown to depend upon a plausible condition on the correlation between wage rate and price uncertainty. Finally, the public policy implications of this analysis are presented.     

On the neutrality of debt in investment intensity

This paper examines the interaction between investment and financing decisions of a firm using a real options approach. The firm is endowed with a perpetual option to invest in a project at any time by incurring an irreversible investment cost at that instant. The amount of the irreversible investment cost is directly related to the intensity of investment that is endogenously chosen by the firm. At the investment instant, the firm can finance the project by issuing debt and equity, albeit subject to an exogenously given credit constraint that prohibits the firm’s debt-to-asset ratio from exceeding a prespecified threshold. The optimal capital structure of the firm is determined by the trade-off between interest tax-shield benefits and bankruptcy costs of debt. Irrespective of whether the exogenously given credit constraint is binding or not, we show that leverage has no impact on the firm’s optimal investment intensity, thereby rendering the neutrality of debt in investment intensity. Similar to earlier work, we show that debt is not neutral to investment timing in general, and the levered firm invests earlier than the unlevered firm in particular.     

PERSONAL TAXES,INFLATION AND MARKET VALUATION

In an inflation-non-indexed progressive tax system, inflation results in a “bracket-creep” effect that reduces the demand for corporate debt while the tax-deductibility of nominal interest makes the use of debt financing cheaper. The interactive effect of inflation and differential dividend and capital gains taxes on the value of a levered firm is analyzed in this paper. Under a non-indexed progressive tax system, inflation decreases the value of the unlevered firm but the effect of inflation on the firm's debt-to-asset ratio is theoretically indeterminate. The gain from leverage is also derived and compared with other valuation models.     

Is unlevered firm volatility asymmetric?

Asymmetric volatility refers to the stylized fact that stock volatility is negatively correlated to stock returns. Traditionally, this phenomenon has been explained by the financial leverage effect. This explanation has recently been challenged in favor of a risk premium based explanation. We develop a new, unlevering approach to document how well financial leverage, rather than size, beta, book-to-market, or operating leverage, explains volatility asymmetry on a firm-by-firm basis. Our results reveal that, at the firm level, financial leverage explains much of the volatility asymmetry. This result is robust to different unlevering methodologies, samples, and measurement intervals. However, we find that financial leverage does not explain index-level volatility asymmetry. We show that this difference between index-level asymmetry and firm-level asymmetry is driven by the asymmetry of the unlevered covariance component of index volatility.     

The Net Benefits to Leverage

I estimate the market's valuation of the net benefits to leverage using panel data from 1994 to 2004, identified from market values and betas of a company's debt and equity. The median firm captures net benefits of up to 5.5% of firm value. Small and profitable firms have high optimal leverage ratios, as predicted by theory, but in contrast to existing empirical evidence. Companies are on average slightly underlevered relative to the optimal leverage ratio at refinancing. This result is mainly due to zero leverage firms. I also look at implications for financial policy.     

A perfect storm in the financial market

This study provides a model explaining how small changes in asset prices may disrupt an entire financial market. Based on the capital asset pricing model (CAPM), our model implies that during a market crash, asset price changes affect the relative distribution of the CAPM betas of individual assets and force all tradable assets to co-move. Using US stock market data, our empirical results are consistent with the model’s predictions. Overall, the study aids understanding of the price patterns of assets during substantial market downturns, such as financial crises.     

Buyout Transactions in the German‐speaking Region: Determinants of Abnormal Performance and Unlevered Returns

This is one of the first comprehensive studies of drivers of private equity performance in the German‐speaking region known as the DACH, made up of Germany, Austria, and Switzerland. It contributes three things to private equity research: First, it explains how operational value drivers affect operational performance (operational alpha) and unlevered rates of return. Second, it whether the same relationships hold across different kinds of private equity business models (those with either organic or inorganic growth strategies; or whether PE investments are small‐cap or mid‐to‐large‐cap). Third, it distinguished between the periods before and after the global financial crisis of 2008. The authors found that (1) annualised benchmark‐adjusted EBITDA margin growth (i.e. improvement in EBITDA margin) is the most significant determinant in abnormal operational performance and unlevered returns, regardless of the business model; (2) private equity firms executing a buy‐and‐build strategy generate lower unlevered returns than those executing an organic growth strategy when the benchmark company is clearly outperformed, most likely because of limited PE managerial resources; (3) mid‐to‐large‐cap private equity firms generate higher unlevered returns and operational alphas than small‐cap private equity firms when the benchmark company is clearly outperformed, because, we believe, larger companies have a higher fixed cost leverage than smaller ones; and we have found that (4) buyout transactions exited during or after the financial crisis yield higher operational alphas but lower unlevered returns compared to buyout transactions exited before the crisis, when the portfolio company underperforms its benchmark company.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Levered Returns

This paper revisits the theoretical relation between financial leverage and stock returns in a dynamic world where both corporate investment and financing decisions are endogenous. We find that the link between leverage and stock returns is more complex than static textbook examples suggest, and depends on the investment opportunities available to the firm. In the presence of financial market imperfections, leverage and investment are generally correlated so that highly levered firms are also mature firms with relatively more (safe) book assets and fewer (risky) growth opportunities. A quantitative version of our model matches several stylized facts about leverage and returns.     

Capital Structure, Information Acquisition and Investment Decisions in an Industry Framework

This paper analyzes the relationship between a firm's capital structure and its information acquisition prior to capital budgeting decisions. It is found that low-growth industries can sustain a large number of levered firms. In these industries, leverage is negatively related to a firm's incentive to acquire information during the capital budgeting process. In contrast, high-growth industries only sustain a small number of levered firms. In these industries, levered firms acquire more information than all-equity financed firms. The model yields empirical predictions regarding the effects of leverage on the expected amount and the volatility of corporate investment. While leverage does not affect firm value, highly levered firms generate a more volatile cash flow than firms with low debt levels.