# گزینه های رشد، شرایط کلان اقتصادی و سطح مقطع ریسک اعتباری

کد مقاله | سال انتشار | تعداد صفحات مقاله انگلیسی |
---|---|---|

5963 | 2013 | 36 صفحه PDF |

**Publisher :** Elsevier - Science Direct (الزویر - ساینس دایرکت)

**Journal :** Journal of Financial Economics, Volume 107, Issue 2, February 2013, Pages 350–385

#### چکیده انگلیسی

This paper develops a structural equilibrium model with intertemporal macroeconomic risk, incorporating the fact that firms are heterogeneous in their asset composition. Compared with firms that are mainly composed of invested assets, firms with growth options have higher costs of debt because they are more volatile and have a greater tendency to default during recession when marginal utility is high and recovery rates are low. Our model matches empirical facts regarding credit spreads, default probabilities, leverage ratios, equity premiums, and investment clustering. Importantly, it also makes predictions about the cross section of all these features.

#### مقدمه انگلیسی

This paper examines the impact of corporate growth options on credit spreads, equity premiums, firm value, and financial policy choices in the presence of time-varying macroeconomic conditions. The motivation for our study derives from the empirical fact that credit risk, leverage, and equity risk premiums exhibit important cross-sectional variation. First, Davydenko and Strebulaev (2007) show that, controlling for standard credit risk factors, proxies of growth options are all positively and significantly related to credit spreads. Similarly, Molina (2005) finds that firms with a higher ratio of fixed assets to total assets have lower bond yield spreads and higher ratings. Second, firms with more growth options typically have lower leverage (see, e.g., Smith and Watts, 1992, Fama and French, 2002 and Frank and Goyal, 2009). Third, value firms earn higher equity returns than growth firms (see, e.g., Fama and French, 1992). Strikingly, none of these cross-sectional properties can be explained by existing structural models of default. The reason is that these models consider firms with only invested assets, but they ignore the fact that growth opportunities constitute an essential element of asset values and that firms are heterogeneous in their asset composition.1 We provide a model that matches these cross-sectional properties of credit risk, leverage, and equity risk premiums. In particular, we explicitly incorporate expansion options of firms into a structural model of default with macroeconomic risk. We show that heterogeneity in the composition of assets helps explain cross-sectional variation of credit spreads and leverage. Moreover, allowing firms to be heterogeneous with respect to the importance of growth options in the values of their assets explains the aggregate credit spread puzzle, not only qualitatively, but also quantitatively. Importantly, the puzzle is solved while fitting historically reported asset volatilities and default rates for realistic debt maturities. At the same time, the model matches the average equity premium and explains a significant portion of the cross section of equity risk (the value premium). It also generates a countercyclical value premium, as observed in the data. Finally, our model is consistent with aggregate and cross-sectional features of default clustering, investment spikes and busts, and recovery rates. For our analysis, we develop a structural-equilibrium framework in the spirit of Bhamra, Kuehn, and Strebulaev (2010b). Thus, we embed a pure structural model of financial decisions into a consumption-based asset pricing model with a representative agent. Our model simultaneously incorporates both intertemporal macroeconomic risk (building on work by Hackbarth, Miao, and Morellec, 2006; Bhamra, Kuehn, and Strebulaev, 2010c; Chen, 2010), which has been shown to be important for explaining credit spreads and leverage, as well as expansion options. Macroeconomic shocks to the growth rate and volatility of earnings, as well as to the growth rate and volatility of consumption, arise due to switches between two states of the economy: boom and recession. The changes in the state of the economy are modeled via a Markov chain, a standard tool to model regime switches. The representative agent has the continuous time analog of Epstein-Zin-Weil preferences (Epstein and Zin, 1989, Weil, 1990 and Duffie and Epstein, 1992b). Therefore, how he prices claims depends on both his risk aversion and his elasticity of intertemporal substitution. Via the market price of consumption determined by the agent's preferences, we are able to link unobservable risk-neutral probabilities used in the structural model to historical probabilities. This modeling approach allows us to study endogenously the effect of macroeconomic risk on credit spreads and optimal financing decisions. We allow firms to have expansion options. These options are converted into invested assets when the underlying earnings process exceeds the investment boundary. We pinpoint the isolated effect of a firm's asset composition on credit risk and leverage by assuming, in the main analysis, that the exercise price of the growth option is financed through the sale of some assets in place, i.e., without additional funds being injected into the company. We also study equity financing later in the paper. Default occurs when earnings are below the default threshold in a given regime. Shareholders maximize the value of equity by simultaneously choosing the optimal default and expansion option exercise policies. The capital structure is determined by trading off tax benefits of debt against default costs to maximize the ex ante value of equity, i.e., the value of the firm. The first result the model yields is that, like in other macroeconomic models, default boundaries are countercyclical, i.e., shareholders default earlier in recession than in boom. Thus, default is more likely during recession, which, together with countercyclical marginal utilities and default costs, raises the costs of debt for all firms compared with a benchmark model without business cycle risk. The central new feature of our model is that the asset composition alone matters significantly for the costs of debt. Two forces lead to the cross-sectional prediction that debt is particularly costly for firms with a high portion of expansion options in their assets' values. First, because options represent levered claims, firms with valuable growth options are more sensitive to the underlying earnings process than firms that consist of only invested assets. The volatility of the underlying earnings process would, consequently, underestimate the true default risk of growth firms. While the literature discusses this basic idea within equity-financed firms (Berk et al., 1999 and Carlson et al., 2006), little is known about its impact on debt prices. Our structural model allows us to jointly analyze a firm's expansion policy and financial leverage. We show that the combination of these factors is critical for a full exploration of the quantitative implications of the riskiness of growth options on credit spreads. The second driving force is that option values are more sensitive to macroeconomic regime changes than are assets in place. This higher sensitivity is, to some extent, another consequence of the idea that options represent levered claims. Importantly, an additional effect derives from the fact that the optimal exercise boundary of growth options increases in recession and decreases in boom. Intuitively, it is optimal to defer the exercise of an expansion option when the economy switches to recession, i.e., to wait for better times. Because the moneyness of growth options is regime-dependent, and because options represent levered claims, the continuation value of expansion options is more exposed to the macroeconomic state than the one of invested assets. Moreover, the changing moneyness causes expansion options to be less sensitive to the underlying development of the earnings process in recession than in boom, which reduces the value of the shareholders' option to defer default during bad times. Together, these effects amplify the countercyclicality of default thresholds for firms with a high portion of growth options. As marginal utility is high during bad times, the higher tendency to default in recession causes larger credit spreads under risk-neutral pricing for firms with expansion options than for those with only invested assets. We then investigate the quantitative performance of the model in explaining empirically observed data. The literature suggests that an average BBB-rated firm has a ten-year credit spread in the range of 74–95 basis points (bps). (This range is obtained by starting from the average bond yields reported in Davydenko and Strebulaev, 2007 and Duffee, 1998 and taking into account that around 35% of bond yields are due to nondefault components.) With our main set of parameters, a model without business cycle risk produces a mere 29 bps spread for an average firm. A standard macroeconomic model with optimal default thresholds in the spirit of Bhamra, Kuehn, and Strebulaev (2010c) or Chen (2010) implies a spread of 56 bps for average firms at issue that consist of only invested assets. Our estimate for the average BBB-rated US firm's asset composition is that total firm value is about 60% higher than the value of invested assets, which corresponds (approximately) to a Tobin's q of 1.6.2 For such a firm, we obtain a credit spread of about 66 bps when using optimal default thresholds, optimal expansion boundaries, and an earnings volatility such that the average asset volatility matches the one observed for BBB-rated firms. This spread is remarkably higher than the 39 bps our model implies for a firm with only invested assets. The large difference arises even though leverage is kept constant; we vary only the characteristics of the assets themselves. As the economy consists of a mix of firms, the result that growth firms have higher credit spreads than firms with only invested assets suggests that our model can also explain the aggregate credit spread puzzle. To evaluate this conjecture, note that when relating the implications of capital structure models for average credit spreads to empirical studies, it is crucial to take into account that such studies use aggregate data over cross sections of firms, not average individual firm-level data (Strebulaev, 2007). Following this line of reasoning, Bhamra, Kuehn, and Strebulaev (2010c) investigate how the time evolution of the cross-sectional distribution of firms with different leverage ratios affects credit spreads and default probabilities. Building on their approach, we characterize the aggregate dynamics by simulating over time a cross section of individual firms that is structurally similar to the empirical distribution of BBB-rated firms not only with respect to average leverage ratios but also with respect to asset composition ratios. The average ten- and 20-year credit spreads of 81 and 100 basis points, respectively, from simulating this true cross section in our model reflect their target credit spreads well. To solve the aggregate credit spread puzzle, a model needs to explain observed costs of debt while still matching historical default losses (given by the historical default probabilities and recovery rates) and asset volatilities. We consequently proceed by showing that the model-implied default rates and asset volatilities of BBB-rated firms are similar to the ones historically reported for realistic debt maturities. The nature of assets, thus, has a powerful impact on costs of debt. Not surprisingly, it also affects the observed features of leverage. At initiation, we find that a firm with an average growth option optimally holds about 4–5% lower leverage than one with only invested assets. In addition, we obtain procyclical optimal leverage decisions of firms, in line with Covas and DenHaan (2006) and Korteweg (2010). The reason is that the default risk is higher in recession than in boom. The negative relation between growth options and leverage also maintains when simulating over time our model-implied true cross section of BBB-rated firms. In this simulation, however, firms deviate from their initially optimal leverage in a way such that the aggregate market leverage of the whole sample becomes countercyclical, consistent with Korajczyk and Levy (2003) and Bhamra, Kuehn, and Strebulaev (2010c). We derive additional testable predictions when studying the aggregate dynamics of our model economy. Credit spreads and default rates are countercyclical, as reported in the literature. Next, aggregate investment patterns are strongly procyclical, with investment spikes often occurring when the regime switches from recession to boom, reflecting the findings in the empirical investment literature (Barro, 1990 and Cooper et al., 1999). Our model also makes specific cross-sectional predictions. For example, realized recovery rates are lower for growth firms. Finally, we show that the model's intuition is consistent with the literature on the value premium for equity. In the true cross section, our model implies an annual value premium, i.e., a difference between the average value-weighted equity premium of the firms in the lowest decile of the asset composition ratio and the premium of those in the highest decile, of 3.47%. Importantly, the model also explains the empirically reported countercyclical pattern of the value premium. Our paper contributes to several streams of previous research. First, the fact that growth options are empirically strongly associated with observed leverage has also prompted other explanations. The most prominent of these additional explanations, agency, comes in two primary forms: a shareholder–bondholder conflict and a manager–shareholder conflict. Appealing to the former, Smith and Watts (1992) and Rajan and Zingales (1995) suggest that debt costs associated with shareholder–bondholder conflicts typically increase with the number of growth options available to the firm due to underinvestment (Myers, 1977) and overinvestment by way of asset substitution (Jensen, 1986; see also Sundaresan and Wang, 2006).3 According to Leland (1998), however, optimal leverage even increases when firms can engage in asset substitution. Similarly, Parrino and Weisbach (1999) conclude that stockholder–bondholder conflicts are too limited to explain the cross-sectional variation in capital structure. Childs, Mauer, and Ott (2005) show how short-term debt reduces agency costs. Hackbarth and Mauer (2012) demonstrate that the joint choice of debt priority structure and capital structure can virtually eliminate the suboptimal investment incentives of equity-holders. Neither of the papers incorporates macroeconomic risk. As for manager–shareholder conflicts, Morellec (2004) shows that agency costs of free cash flow can explain the low debt levels observed in practice and the negative relation between debt levels and the number of growth options; see also Barclay, Morellec, and Smith (2006). Morellec, Nikolov, and Schürhoff (2012) conclude that even small costs of control challenges are sufficient to explain the low-leverage puzzle. It is still a matter of debate to what extent conflicts of interest between managers and stockholders cause the empirically observed patterns. Graham (2000), for example, tests a wide set of managerial entrenchment variables and finds only “weak evidence that managerial entrenchment permits debt conservatism” (p. 1931). In any case, our model is not inconsistent with either of these views. It offers a quantitatively important reason for the cross-sectional variation in leverage and credit spreads that derives solely from the nature of assets of firms.4 Second, at the core of our model is the notion that macroeconomic (business cycle) risk matters in powerful ways for the costs of corporate debt and financial decisions, because firms are more likely to default when doing so is costly (see, e.g., Demchuk and Gibson, 2006 and Almeida and Philippon, 2007; Bhamra, Kuehn, and Strebulaev, 2010c; Chen, 2010). What we add to this literature is the idea that the impact of business cycle risk depends on the asset base of a firm. In contemporaneous and independent work, Chen and Manso (2010) set up a model similar to ours with expansion options. Their focus, however, is on the debt overhang problem, not on explaining cross-sectional features or the credit spread puzzle—the central tasks of this paper. Finally, our structural-equilibrium framework draws on insights from consumption-based asset pricing models (Lucas, 1978 and Bansal and Yaron, 2004). The paper proceeds as follows. In Section 2, we set up our valuation framework. We solve the model in Section 3. Section 4 discusses our parameter and firm sample choices, as well as the optimal default and expansion policies. Section 5 outlines qualitative properties of our model for the aggregate economy. We turn to the quantitative implications for BBB-rated firms in Section 6. The predictions of our model for the value premium of equity are discussed in Section 7. Section 8 concludes.

#### نتیجه گیری انگلیسی

It is now well accepted that macroeconomic risk is central for understanding credit risk and capital structure choices. Specifically, defaults are more likely during recession, when they are particularly costly and harder to bear. This countercyclicality increases the costs of debt for all firms. But to explain the cross-sectional variation in apparently excessive costs of debt, variation inside the firm is needed. This paper formalizes the role of one particularly important aspect of this heterogeneity: the asset composition of firms. It is not surprising that in principle the asset composition can be important for optimal capital structure. After all, economists have devoted much effort to understanding the difference between value and growth firms in terms of their financial structure, starting with Myers (1977) and Jensen (1986). Little was known, however, about the quantitative importance of this factor and its relation with macroeconomic risk. The present structural equilibrium model allows us to jointly analyze a firm's expansion policy and financial leverage in the presence of macroeconomic risk. We demonstrate that incorporating the combination of these factors goes a long way toward explaining the empirically observed cross-sectional variation in costs of debt, leverage, and equity risk premiums. Our model implies that companies with a high portion of expansion options tend to be riskier in general and, at the same time, particularly sensitive to macroeconomic risk. They are not only more volatile (because growth options represent levered claims), but also have a higher propensity to default in bad times than firms with a low portion of expansion options. Thus, the default probability and its countercyclicality are higher, the greater the ratio of expansion options to total assets. Together with higher marginal utility of the representative agent in recession, this relation (exacerbated by costly liquidation in recession) implies higher costs of debt and more important endogenous shadow costs of leverage for firms with growth options than for those with only invested assets. Thus, our findings explain why the credit spread puzzle is empirically more pronounced for growth firms and why growth firms hold less debt even after controlling for standard determinants of credit risk. Moreover, because the economy is made up of a cross-sectional mix of firms, the model accounts, in quantitatively fairly accurate ways, for the average credit spread puzzle. The model also yields a countercyclical value premium for equity, consistent with the data. We have studied one type of real options of firms, namely, growth options. However, firms have a wide and varying range of options, including abandonment and shut-down options. A model incorporating these options could, therefore, yield further cross-sectional predictions. While recent research has made important progress in enhancing understanding of average credit risk, the cross section of credit risk has not received sufficient attention. Analyzing it empirically is, fortunately, feasible. Liquid credit default swap quotes are now widely available on a firm-by-firm basis, allowing researchers to investigate specific relations between firm-specific characteristics such as growth options and credit spreads. Our paper also provides a theoretical basis that can guide empirical research in this direction.