Three Essays on Corporate Asset Growth, Bond Pricing, and Implicit Government Guarantees

The purpose of my dissertation is to identify factors driving corporate bond pricing and government guarantees on corporate liabilities. In the first manuscript, I identify the driving sources of asset growth from the perspective of debt financing and examine the asset growth effect on bond pricing. There are competing views on potential drivers for corporate asset growth. Researchers in favor of optimal investment attributes a higher asset growth rate to lower cost of capital and richer investment opportunities. Alternatively, the agency problem argument attributes high asset growth to over-investments. Building on that firms often heavily rely on debt to grow their assets, we differentiate these perspectives by studying the relation between the bond yields and issuers’ asset growth rates. We do not find that yields of bonds issued by high asset growth firms are lower than those of low-growth firms. Moreover, we find that bonds issued by high asset growth firms are potentially overvalued – they experience poor performance in years afterwards. Overall, the results are aligned with the agency problem explanation for corporate asset growth. The second manuscript offers a novel approach to estimate the value of the implicit government guarantee by combining the contingent claim pricing with the likelihood of the government intervention. We find in our sample that the cost of this implicit protection can go beyond tens of billions of dollars with an average of about $13 million per company, per year, and it rises to about $24 million if the government is assumed to intervene with certainty. We then investigate the relationship between the implicit government guarantee and the funding costs of small and large banks. The funding costs for both small and large banks are related to the value of the implicit government guarantee. Moreover, we show that the spread of the funding costs of small banks over large banks is strongly associated with the value of the implicit government guarantee, especially after the crisis. The corporate bond sector has grown tremendously over the past decade. Rapid growth in Chinese corporate indebtedness and corporates ability to pay back their liabilities have become a persistent concern for regulators and investors in recent years. In the third manuscript, we examine the determinants of the pricing of Chinese corporate bonds and potential agency costs arising from implicit government guarantees (IGG) for state owned enterprises (SOEs). We show that the yield of central government SOE bonds is 85 bps lower than that of nonSOE bonds after controlling for firm-specific, bond-specific characteristics, and macroeconomic variables. Further, quantifying IGG with (the lack of) bond yield sensitivity to equity volatility, we present evidence on the dark side of IGG high IGG firms are subject to greater agency costs; they are more likely to over-invest to negative NPV project, suffering poor operating performance.


LIST OF TABLES
Firms differ substantially in their asset growth rates. Based on the Compustat database, from 1994 to 2014 the average asset growth rate weighted by corporate market capitalization for firms in the top corporate asset growth decile group is 62% while the average asset growth rate of firms in the bottom decile group is -18%.
What may account for the large difference in corporate asset growth? This is a very important issue to corporate profitability and efficiency. Regarding this topic, people heatedly debate about whether there is an optimal asset growth and how is asset growth associated with costs of capital and firm growth opportunities. Researchers in favor of rational expectation suggest that asset growth is a realization of a firm's growth opportunities. Thus, firms with better investment opportunities and a relatively lower cost of capital would have a higher asset growth rate (see, e.g., Hou, Xue, Zhang, 2015). On the other hand, behavioral economists attribute firm asset growth to over-investments -if managers have empire-building incentives, they may fund investment projects beyond the level that maximizes shareholders' value . Under this view, corporate asset growth may not be negatively associated with the costs of capital.
The optimal-investment and over-investment explanations have the same prediction on corporate investment: asset growth and future stock performance are negatively associated with each other. Such equivalence makes it hard to differentiate between alternative explanations; To date the literature based on stock performance remains unsettled on the main drivers for corporate asset growth. 1 1 Researchers in the behavioral camp attribute investors' excessive extrapolation on past growth to the negative asset growth effect on equity returns (e.g., Lakonishok, Shleifer, and Vishny, 1994;Titman, Wei, and Xie, 2004;Cooper, Gulen and Schill, 2008). Alternatively, researchers in the rational expectation camp focus on the association between investment and expected return (Cochrane 1991(Cochrane , 1996Li, Livdan, and Zhang, 2009;Liu, Whited, and Zhang, In this study, we shed direct light on the debate by analyzing yields and performance of corporate bonds. The key rationale lies in that corporates heavily rely on debt financing to grow assets. Therefore, bond yield is potentially a good proxy for a firm's marginal cost of capital. Further, a careful examination of bond yields helps us understand the relationship between bondholders and shareholders, a critical source of agency conflicts. Moreover, biased investor beliefs play a role in determining the value of corporate bonds. Recent studies show that bond investors may overextrapolate past growth realizations in corporate bond markets, leading to time-varying mispricing of corporate bonds (Greenwood and Hanson, 2013;Greenwood and Shleifer, 2014;and Greenwood, Hanson and Jin, 2016). Such excessive extrapolation results in overvaluation of firms with high past growth and these expectations will be revised after a period of relatively low asset growth, resulting in a sharp decline in bond price.
Empirical predictions under rational expectation and agency problem explanations are starkly different. Optimal investment suggests a negative relation between yield spread and corporate asset growth, i.e. high asset growth firms tend to have low yield spread holding expected cash flow constant. In contrast, the agency problem explanation indicates that high asset growth firms are not necessary to be those with low cost of capital due to the over-investment and empire-building tendencies. Further, when investors act irrationally and invest in overpriced bonds, we expected a positive asset growth effect on yield changes after the asset growth year. In other words, we expect to see that yields of corporate bonds increase afterwards for high asset growth firms.
How much does a high asset growth firm use debt to finance their growth? To address this question, we breakdown firm asset growth into major financing side of the balance sheet. All firms combined, the contribution of retained earnings to 2009). High asset growth implies low cost of capital, predicting low future stock returns. financing activities of asset growth is 30% and the contribution of debt financing is 74% for value weighted portfolios. In contrast, the contribution of equity is -4%.
Moreover, for firms in the top ten percentile of asset growth rates, nearly 80% of financing activities of asset growth comes from debt; 8% is from internal funds (i.e, retained earnings); new equity financing accounts for 12% of grown assets. These findings confirms that high asset growth firms heavily reply on debt financing, justifying the use of corporate bond yields as a proxy for the firm's marginal cost of capital.
We examine the determinants of asset growth rates by performing several sorts. First sorting on lagged bond yields, we find an inverse U-shaped between yield spread ranks and asset growth rates. Highest asset growth rates are not firms in the lowest yield spread group. We then control for asset growth in the prior year and check the relation between asset growth rates and lagged yield spreads. Again, higher asset growth rates are not firms with relatively lower yield spreads. The finding does not support the optimal investment argument. Second, we sort firms based on asset growth rates and look at the yield spreads prior to portfolio formations. Here we identify a U-shaped relation between corporate bond yield spreads and corporate asset growth rates. Finally, to control for the effects of growth opportunities and bond credit risk, we construct two-way sorts based on asset growth rates and lagged returns on earnings (ROEs) (a measure of firm growth opportunities used in Hou, Xue, and Zhang, 2015) and on asset growth rates and bonds' credit rating. The finding still suggests a nonlinear relationship between lagged bond yields and firm asset growth rates.
We perform further analysis at the firm level to control for other factors that potentially influence asset growth. The dependent variable is firm asset growth rates. Besides lagged bond yield spreads, other explanatory variables include squared yield spreads, firm size, leverage, ROE, credit ratings, and bond maturity.
The coefficient on squared yield spreads captures the nonlinear relation between lagged bond yield spreads and asset growth rates. We find that, consistent with conventional wisdom, firm size is negatively associated with asset growth. Also, asset growth are significantly positively associated with firm ROEs, suggesting asset growth to be positively related to future cash flow. Most importantly, we find the coefficient on yield spreads is significantly negative while the coefficient of squared yield spreads is significantly positive. There is a U-shaped relationship between asset growth rates and yield spread in the prior period.
What does the U-shaped relation tell us? It says that when the lagged yield spread is low, corporate asset growth tends to be high. On the other hand, when the lagged yield spread is high, corporate asset growth also tends to be high. This basically suggests that when a firm has relatively low cost of debt, it may issue more debt and pursue higher asset growth. This is consistent with the optimal investment story. However, when a firm has a relatively high cost of debt, the optimal investment rule no longer applies. This potentially suggests a role of the agency problem based explanation for asset growth.
We look at, the bond level, how corporate asset growth rates affect yield spread changes in the year after the asset growth formation year. Note that the yield spread changes and bond performance in years afterwards help us identify if information asymmetry between corporate insiders and bond investors indeed exists. If bond investors are fully aware of issuers' incentives, we would see that bond yields stay constant after the asset growth year. 2 On the other hand, when investors cannot see through issuers' incentive, we may observe the yields of bonds issued by high-asset growth firms significantly drop in years afterwards. Our empirical 2 From the firm perspective, if a firm decides to issue bonds to finance asset growth when bond investors have the ability to see through managerial incentive, it pays a relatively high cost to raise money. The risk appetite of such firms would be high. findings support the latter. We document a strong positive relation between asset growth and yield spread changes after controlling for bond-specific characteristics, firm-specific characteristics and macroeconomic factors. One percent increase in asset growth rate is associated with 0.3 basis point increase in yield spread.
Furthermore, we find that the asset growth effect on bond yield spread changes remains intact separately for firms with positive and negative asset growth rates.
For negative asset growth firms, a positive relation between asset growth rates and yield spread changes indicates the most negative asset growth firms actually have a most negative adjustment in bond yields. It appears that investors over-react to the negative asset growth rates in year t (by setting a higher yield spread) and correct it afterwards.
Our sample is rich in the sense that it includes the financial crisis period and bonds of different credit quality, allowing us to perform further analysis. First, we breakdown the entire sample period into three sub-periods: i) pre-crisis, ii) crisis, and iii) post-crisis. We find that asset growth is negatively associated with yield spread changes during the crisis period, while asset growth is positively associated with yield spread changes during non-crisis period. The implication is that corporate managers are more cautious in their investments and are less likely to overinvest during financial crisis. Meanwhile, investors tend to be rational and make conservative investments when market condition is hard. We show that asset growth has a negative effect on yield spread changes during financial crisis when the agency problem and over-investment tendency are less pronounced. Second, we separately look at the asset growth effects among investment grade and speculative grade bonds. We show that the asset growth effect remains positive in both rating categories.
Finally, we address the question whether asset growth can forecast excess corporate bond return, which is estimated 6 months after the formation of asset growth portfolios. Controlling for both bond and firm specific variables, we find that asset growth is negatively associated with future bond return. A standard deviation increase in asset growth is associated with 0.5% decrease in bond annual bond return. Note that bond return consists of two elements: one related to yield spread changes and the other related the level of bond yields. As we are interested in the change in bond yields after the asset growth measurement year, we further decompose bond returns into these two elements. The finding indicates that the negative association between bond return changes and asset growth rates is mainly attributed to yield changes. Overall, our findings are in aligned with the agency problem based explanation.
This paper contributes to the current literature of asset growth effect and corporate bond pricing in several ways. First, we investigate the potential driving sources of asset growth using corporate bond data. Using yield spread as the proxy of cost of capital, we empirically distinguish rational investment expectation and over-investment explanation by examining bond yields and corporate asset growth.
The existing literatures have debated whether asset growth anomaly is due to over-investment or the evidence of rational expectation (Cooper, Gulen and Schill, 2008;Lipson, Mortal and Schill, 2011;and Watanabe, Xu, Yao and Yu, 2013).
Our evidence suggests that the asset growth effect is more likely due to the agency explanation of corporate bonds pricing rather than rational expectation. Second, we extend the study to changes in yield spreads. , , and Chen et al. (2007) show that macroeconomic factors, equity volatility and liquidity are important determinants of yield spread changes. We find that an increase in asset growth is significantly and positively associated with yield spread regardless of controlling for changes in credit rating, liquidity, macroeconomic influences, or other firm specific factors. The explanatory power of asset growth persists for both investment grade and speculative grade bonds. Third, this study is among the first to examine mispricing of individual bonds. Using aggregate bond data, Greenwood and Hanson (2013) show that investors tend to overextrapolate past growth realizations, leading to mispricing of corporate bonds. In contrast, we extend the study of mispricing of corporate bond pricing literature by examining the performance of individual bonds.
The remainder of our paper is organized as follows. Section 2 develops the hypothesis. Section 3 introduces data and summary statistics. Section 4 explores the driving sources of asset growth and examines the asset growth effect on bond performance. Finally, section 5 concludes.

Hypothesis Development
In the pioneer works, Brainard and Tobin (1968) and Tobin (1969) argue that the rate of investment should be related to its q, which is defined as the value of capital relative to its replacement cost. Firms choose to invest in a project when its q exceeds 1. This is the so-called q theory of investment. Subsequently, Hayashi (1982) shows that in a perfect competition and constant returns to scale economy, a firm's marginal q (the market value of an additional unit of capital divided by its replacement cost) is equal to its average q (the market value of existing capital divided by its replacement cost). 3 Cochrane (1996), Liu, Whited and Zhang (2009) and subsequent works derive the q-theory implications for cross-sectional investment returns, which are tied directly to expected returns of individual stocks to firm asset growth and growth opportunities. The logic is following: firms with greater investment opportunities are more likely to make large investments, i.e. experiencing greater asset growth. Nevertheless, holding firm growth opportuni-ties constant, firms with lower cost of capital will engage in greater investments, and vice versa. Therefore, the q-theory of investment predicts an inverse relation between investments and expected stock returns, holding growth opportunities constant.
There is evidence on the inverse relation between asset growth rates and stock performance in the subsequent period. For instance, Hou, Xue, and Zhang (2015) propose a four-factor asset pricing model based on q-theory and find this empirical factor model can well capture a broad cross section of stock returns. 4 Nevertheless, as noted in the literature, stock performance does not necessarily reflect expected returns. For instance, Greenwood and Shleifer (2014) show that stock returns are inversely related to investor expectations of future stock market returns. This raises serious concerns on the implication of empirical findings in explaining the q-theory implication in the link between asset growth and stock returns. Consequently, various studies alternatively use bond returns to derive equity prices and examine equity pricing models (Campello, Chen andZhang, 2008 andPhillipon, 2009).
Our study follows the same spirit as Campello, Chen and Zhang (2008) and Phillippon (2009). According to the pecking order theory in corporate finance, firms are more likely to use debt to finance a firm's asset growth rather than to issue equity. In particular, when debt is used for asset growth, the cost of capital is correlated with cost of debt. A higher marginal cost of debt leads to a lower future bond performance. In addition, after a relatively high asset growth, marginal q is decreasing, leading to a lower cost of capital.
Following the investment-based model of Liu, Whited and Zhang (2009), firms choose optimal investment to maximize the market value of equity. Let (K it , X it ) denote the maximized operating profits of firm i at time t. The profit function depends on capital, K it , and a vector of exogenous aggregate and firm specific shocks, X it . We assume that the firm i has a Cobb-Douglas production function, however, no longer with a constant returns to scale. End-ofperiod capital equals investment plus beginning-of-period capital net of depreciation: K it+1 = I it + (1 − δ it ) K it , in which capital depreciates at an exogenous proportional rate of δ it . Firm incur adjustment costs when investing. We use a standard quadratic adjustment cost: One-period debt is used to finance investment. Specifically, at the beginning of time t, firm i can issue an amount of debt, B it+1 (which must be repaid at the beginning of period t + 1). In the meantime, firms pay back the bond, B it . The gross return on the bond is r B it . For simplicity, assume the corporate tax rate to be zero. The payout of firm i equals: Let M t+1 be the stochastic discount factor from t to t + 1. Firm i maximizes its cum-dividend market value of equity: It can be shown that the optimal condition in terms of equityholder value maximization is the following: where r I it+1 is the investment return of firm i from t to t + 1.
The expected investment return in equation (3) Jointly considering the above two equations, we expect bond expected returns, , to be inversely related to corporate investment, i it k it , holding the benefit of investment constant. 5 All the securities are rationally priced under the optimal investment perspective. Using the conventional proxy for E(r B it+1 ), bond yield, y it , we have This leads to our first hypothesis: H1. Holding expected cash flow constant, corporate asset growth is negatively associated with bond yields.
The agency problem explanation predicts that firms grow more than the optimal level. Controlling firm growth opportunities stay constant, high asset growth firms potentially have a high cost of capital.
H2. For high asset growth firms, bond yields could positively associated with asset growth rates.
The agency problem are prevalent in an environment with a great deal of information asymmetry. Investors could potentially over-, under-, or appropriately react to the potential managerial over-investment incentives. The second hypothesis is related to bond yield changes in the year after the asset growth measurement year. If investors over-react to the managerial incentive, we would see bond yields drop for high asset growth firms after the asset growth years. If bond investors are fully aware of issuers' incentives, we would see that bond yields stay constant after the asset growth year. Finally, as pointed out by Lakonishok, Shleifer, and Vishny (1994), investors may excessively extrapolate from firms' past growth when they value stocks. When investors cannot see through issuers' incentive, we may observe the yields of bonds issued by high-asset growth firms significantly drop in years afterwards. In case that investors do not fully understand the agency problem of over-investment, they may overvalue a firm with large investments by overvaluing its potential future cash flows. The lower return subsequent to large investment hence reflects a market correction of the initial overvaluation. The hypothesis is as below: H3. For high asset growth firms, bond yields increase in the year after the high asset growth year.
There is a consistent expectation on the relationship between asset growth rates and bond performance. We state the hypothesis alternatively in terms of bond performance.
H3A. High growth firms experience bad bond performance in the year after the high asset growth year.

Data and Summary Statistics 3.1 Data
The data used in this study come from several sources. First, the main trans- We account for reporting errors using standard filtering procedures commonly used for the TRACE transaction data (see, Dick-Nielsen, 2014) ) 6 . Similar to Lin, Wang and Wu (2011), we also extend the sample to January 1994 using the data from the  (2007) and employ a parametric model to estimate yield curve.
The yield curve allows two humps, one at short maturities and the other at long maturities. Yield spread is then defined as the difference between the bond yield and the associated yield of the treasury yield curve at the same maturity. The sample period is from January 1994 to December 2014.
We obtain the bond characteristic data from Fixed Income Securities Database (FISD). This database contains bond issue-and issuer-specific variables such as issue amount, maturity, provisions, coupon and credit ratings on all U.S. corporate bonds maturing in 1990 or later. We merge our transaction data with bond characteristics and eliminate preferred shares, non-U.S. dollar denominated bonds, bonds with odd frequency of coupon payment, and bonds that are mortgage backed, asset 6 These include (i) same-day trade corrections and cancellations; (ii) trade reversals which refer to corrections and cancellations conducted not on the trading day but thereafter; (iii) agency and interdealer transactions. 7 Using the last transaction within the last five trading days of the month instead of that on the last day helps increase the number of non-missing monthly observations. If there are no trades in the last five trading days, the month-end price is missing for that month. backed or part of unit deals. To prevent the confounding effects of embedded options, we also exclude the callable, puttable, convertible, and sinking fund bonds, as well as bonds with a floater. Finally, we mainly use the Moodys rating from the FISD, but, if it is not available, we use the Standard & Poors (S&P) rating when possible and drop bonds whose ratings we cannot identify.
Moreover, we get the financial statements of firms from the Compustat. The firms are required to have positive total assets. To mitigate the backfilling biases, a firm must be listed on the Compustat for 2 years before it is included in the data set (e.g., Fama and French (1993)). We further exclude regulated, financial, or public service firms. The main variable of interest is the asset growth rate (AG).
Following Cooper et al. (2008), the annual firm asset growth rate (AG) for year t is calculated as the percentage change in total assets (Compustat data item 6) from the fiscal year ending in calendar year t-2 to fiscal year ending in calendar year t-1: To compute asset growth rate, we require a firm not have zero or negative total assets in both years t-2 and t-1. We further winsorize asset growth rate at the top and bottom 1% in each year to control for the influence of outliers. The equity volatility is estimated using 252 daily return from the CRSP. Finally, we combine firm accounting information with bond transaction and FISD bond characteristic data using issuer 6-digit cusip. In the final sample, we have 447,543 month-end bond transactions of 8,909 bonds of 1,551 firms from January 1994 to December 2014.

Summary Statistics
Panel A of Table 1  Overall, high asset growth firms are larger in size, higher in profitability, and lower in liabilities. Yield (yield spread) is positively related to liquidity, leverage ratios and equity volatility and negatively related to credit rating and profitability ratios.
Our sample is sorted into deciles based on their year to year annual asset growth rates (AG). Panel A of Table 2 shows bond issuer characteristics of asset growth decile portfolios. The high asset growth portfolio (Decile 10) contains bond issuers with the highest asset growth rate and the time-series average of value-weighted cross-sectional means of growth rates for these firms is substantial at 62 %. Decile 1 issuers are low asset growth firms, with average annual growth rates of -19%. Low asset growth firms tend to be firms that have low profitability ratios (OIS and ROE), low interest coverage rate, high leverage and high equity volatility. The high asset growth firms are the smallest firms in our sample with the yearly average of $42.9 billion, but have the highest operating income to sales.
D7 tends to be the firms with the largest size. Panel B shows the bond specific characteristics. Decile 1 has the largest yield spread with the average rating of 12.8. Decile 6, 7, and 8 contain bonds with the lowest yield spread and highest credit rating. The yield spread of D10 is 2.15 with the rating of 13.66.

Empirical Results
In this section we conduct a series of empirical tests to investigate the potential driving sources of the asset growth effect. Asset growth effect has been well documented in the equity market. However, the drivers of asset growth have been largely ignored in this existing literature. First, we ask how does a firm finance their growth opportunities. To answer this question, we decompose asset growth and look at the subcomponents of asset growth from the financing side. Second, we examine the determinants of asset growth. To do that, we perform several portfolio sorts and conduct regression analysis. Next, we examine the asset growth effect on yield spread changes following the asset growth formation year. We further decompose asset growth into its major components from both the investing side and financing side of the balance sheet and ask whether the asset growth effect can be explained by the subcomponents of asset growth. Lastly, we explore whether asset growth can forecast excess corporate bond return.

Asset Growth Decomposition
Total asset growth captures the aggregate growth of a firm. To explore the potential driving sources of asset growth, we break down asset growth of various components with the emphasis of financing side. Following Cooper et al. (2008), the asset growth financing decomposition is as follows: T otal asset growth(AG) = Operating liabilities growth(∆OpLiab) In Table 3, we report the growth of various asset growth components in each asset growth decile portfolio from the financing side. The number in each cell reports time-series average of yearly means of asset growth component variables from fiscal year t-2 to year t-1 scaled by total asset in the fiscal year ending in calendar year t-2. We sort the sample into deciles each year based on annual asset growth rate at the beginning of year t. There are several notable observations.
First, growth in debts accounts for large fraction of asset growth from the financing side. Specifically, for the high asset growth decile, growth in debts contributes 62.9% (38.9%/62.4%) of the total asset growth for the value-weighted portfolio.
In the last three columns, we show the contribution of each financing component (RE, Equity and Debt) to the total financing activities, including both internal and external financing. For example, debt financing accounts for 79% of total financing activities, while equity financing takes about 13%. This suggests that corporates highly rely on debt as the major tool to finance their growth opportunities. Second, the average growth in stock is -0.2%. More than 70% firms in our sample have negative growth in stock. This is consistent with pecking order theory and suggests that equity financing is not the main source for external financing. According to the first two observations, asset growth firms are more likely to rely on debt financing than on equity financing for asset growth, especially for high asset growth firms. More interestingly, we find that negative growth firms tend to be firms with negative changes in retained earnings and debt. We also note that for decile 5, 6 and 7, these firms tend to buy back their equities by using retained earnings or debt.
The asset growth decomposition provides insights on the driving sources of asset growth. High asset growth firms are more likely to use debt to finance their investments, while negative asset growth firms have negative retained earnings and reduced amount of debt. The overall message is that corporates heavily rely on debt for external financing. Therefore, bond yield is considered as a good proxy for a firm's marginal cost of capital, which indicates an alternative way to re-examine the q-theory explanation by relating bond performance and asset growth firms.

Determinants of the asset growth
Q-theory of investment relates corporate investment to their cost of capital. Hou, Xue and Zhang (2015) suggest that lower cost of capital and better investment opportunity imply high marginal q and high corporate investment. According to the conjecture based on q-theory of investment, asset growth is negatively related to the cost of capital given expected profitability or cash flows. In other words, firms are more likely to grow when their cost of capital is low. In contrast, agency theory suggests that corporate managers have the over-investment and empirebuilding tendency. Thus, corporates might grow aggressively even when the cost of capital is high. In this section, we differentiate these two hypotheses by examining the determinants of the asset growth.
First, we explore the relationship between yield spread and asset growth using portfolio analysis. We calculate value-weighted yield spread and credit rating at bond-issuer level. Then we sort bond issuers into quintiles each year based on the yield spread at the beginning of the asset growth year. Results are provided in Table 4, where the reported asset growth rate is the time series average of crosssectional means. The cross-sectional means are calculated using value weight. D1 has the lowest yield spread, while D10 has the highest yield spread. In column 1, we show an inverse U-shaped relation between asset growth rate and yield spread.
D4 group has the highest asset growth rate. As suggested in Cooper et. al (2008), the current asset growth rate is highly related to prior asset growth rate. To control for that, we conduct two-way sorts based on prior year asset growth rate and lagged yield spread. Our findings confirm the inverse-U shaped relation. The only exception is AG 2, which shows a negative relation between yield spread and asset growth rate.
Next, we sort issuers into deciles based on annual asset growth rate in each year and look at yield spread prior to the asset growth formation period. Moreover, we create a no growth portfolio as the benchmark by sorting bond issuers into deciles based on the absolute value of asset growth rate. We define the lowest decile as the no asset growth portfolio. Table 4 reports the results, in which the reported yield spread is the time series average of value-weighted cross-sectional means.
In Panel A, the first column reports average yield spreads of bond issuers on asset growth-sorted deciles. Interestingly, we find a U-shaped relationship between asset growth and yield spread. D1 has the highest yield spread of 3.98. This is consistent with the conjecture of q-theory investment that firms tend to have low growth rates when yield spread is high. Bond issuers tend to have lower yield spreads as asset growth rate increases and reaches the lowest point of 1.59 for D7. However, yield spreads of D9 and D10 are 1.76 and 2.59, respectively. The difference between D10 and D1 is -1.39 and is significant at 1% level (t=-10.23).
We also note that the difference between D10-nogrowth is 0.46 (t=4.87), suggesting that high asset growth decile has a relatively higher yield spread than that of no growth or medium growth portfolios.
To control for the profitability effect, we conduct two-way sorts based on asset growth rates and lagged ROE. We first sort the sample into three ROE groups (low, medium and high). Within each ROE groups, bond issuers are further sorted into asset growth decile portfolios. Results are presented from column 2 to column 4. Consistent with the previous findings, a U-shaped pattern remains across the asset growth portfolios within each ROE group. The difference between D10 and no growth portfolio is 0.38 (t=5.32) and 0.69 (t=3.33) for medium ROE group and high ROE group, respectively.
Following the above procedure, we also examine the asset growth and yield spread relation in rating based subsamples. Specifically, bond issuers are first sorted into quintiles (Q1 to Q5) based on the lagged rating. Q1 firms are rated of B1 or lower; Q2 are rated between Ba3 and Ba1; Q3 are rated between Baa3 and Baa1; Q4 are rated between A3 to A1; Q5 firms receive the highest rating with Aa3 or higher. Within each rating group, bonds issuers are further sorted into asset growth deciles. Again, we confirm a distinct U-shaped of each rating group. The difference between D10 and no growth portfolio is positive, but less significant.
In Panel B, we focus on firms with newly issued bonds during asset growth formation period. The offering yield of new bonds is considered as the marginal cost of capital. We repeat the same process and sort bonds into asset growth deciles. The results are strong and consistent with our findings in Panel A. Overall, high asset growth firms are not the firms with the lowest yield spread. Instead, they tend to have higher yield spread. The difference between D10 and no growth portfolio is 0.4 (t=3.53) for all newly issued bonds.
Furthermore, we use regression analysis to examine the relation between yield spread and asset growth rate. According to prior studies, we control for both firm and bond characteristics that have been shown to be associated with firm asset growth: prior year asset growth, ROE, total assets, and leverage. We also include bond characteristics such as years to maturity and credit rating. The definitions of these variables are provided in appendix. The model is specified as follows: where the subscript i, t refers to bond issuer i and year t. X is the main variables, representing yield spread or bond yield of firm i. AG is bond issuers annual asset growth rate of year t. We include the lagged-year control variables in the regressions. We also consider firm-fixed effects to capture time-invariant heterogeneity across firms, and standard errors to account for clustering at the firm level. In addition, we include year fixed effects to capture the aggregate time-series trends.
We perform panel regressions and present the results in Table 6. First, we examine various model specifications from column 1 to column 5. In column 1, we only include yield spread as independent variable and the coefficient of yield spread is -1.0626 (t=-8.22). To capture the U-shaped effect as we document in the previous section, we include the squared term of yield spread in the regression. We find the coefficient on yield spread is significantly negative and the coefficient of the quadratic term is significantly positive, suggesting a U-shaped relation between yield spread and asset growth rate. In column 3, we examine how firm characteristics affect firm asset growth rate. As expected, current asset growth rate is positive related to the prior year growth rate with the coefficient of 0.0293 (t=2.49). The coefficient of ROE is 0.017 (t=2.93), suggesting that firms with more profits are more likely to grow. Moreover, leverage and firm size are negatively related to firm asset growth. In column 4, we include both yield spread and firm characteristics variables. In column 5, we also add bond characteristics (years to maturity and credit rating). In addition, we show that firms with higher ratings are associated with higher growth rate. The most telling story is that the coefficients on the squared yield spread term are positive and statistically significant across various model specifications. In the last column, we use the bond yield as an alternative measure of cost of capital. Because when firms raise capital, their decisions are based on both the level of capital and risk premium (yield spread). The coefficient on the quadratic term of yield is 5.85 (t=6.03), which is consistent with our findings using yield spread as the proxy of cost of capital.
Overall, our findings document a U-shaped relation between yield spread and firm asset growth. The U-shape relation holds when we control for both bond and firm specific characteristics. Our evidence is not consistent with the hypothesis based on the q-theory of investment. Instead, the potential driving sources of asset growth are more likely due to agency based explanation. In the next section, we examine the asset growth effect on yield spread changes.

Asset Growth Effects on Yield Spread Changes
According to the second hypothesis, the agency problem posits a positive relationship between asset growth and yield spread changes. To test H2, we explore the relation between asset growth and yield spread changes using portfolio analysis.
We sort bond issuers into deciles based on asset growth rate in each year and estimate the yearly average yield spread changes from July of the asset growth year t to July of year t+1. D1 has the lowest asset growth rate, while D10 has the highest. Table 7 reports the results, in which the reported average is the time-series average of cross-sectional means of the yield spread. The cross-sectional means are calculated using value-weight.
In Panel A, we show average yield spread changes for all the bonds in our sample. D1 has negative yield spread changes of -8.5 bps (t=-3.22), while D10 has positive yield spread changes of 11 bps (t=3.7). More interestingly, we note that yield spread changes are statistically insignificant for D3 to D7 deciles. According to agency theory based hypothesis, the agency problem might be more pronounced when the asset growth is positive. Thus, we further divide our sample into positive and negative asset growth sample. Further, we sort bond issuers into deciles within each positive and negative asset growth group.
In the positive asset growth sample, we find that bonds issued by high asset growth firms tend to have positive yield spread changes. For example, yield spread changes are 8.1 bps (t=3.38) and 10.2 bps (t=2.58) for D9 and D10, respectively.
Yield spread changes are positive, but insignificant in other asset growth portfolios.
In the negative asset growth sample, we show that bonds with more negative asset growth rate are associated with negative yield spread changes. Our evidence is consistent with H2 that bonds issued by high asset growth firms tend to have positive yield spread changes, while bonds issued by low or negative growth bonds tend to have negative yield spread changes.
In panel B, we repeat the same process, but focus on the newly issued bonds.
We use the yield spreads of the first available trade after issuance for the current period. We use yield spread in July of the following year as the next period. If there is no trade in July, we use the next available trade. We confirm our previous findings and show that asset growth is positive related to yield spread changes.
The magnitude and statistical significance of yield spread changes are smaller in the newly issued sample.
Next, We conduct regression tests to study whether asset growth is a determinant of yield spread changes. We include a list of independent variables used in , , and Chen et al. (2007). Specifically, we consider credit rating and liquidity. Liquidity is estimated by the Amihud illiquidity ratio. We expect positive changes in liquidity to have positive effect on yield changes. We also include four accounting variables: pretax interest coverage, operating income to sales, long-term debt to assets, and total debt to capitalization. Positive changes of the first two variables indicate financially healthy firms and are likely to produce a low yield spread. Positive changes of the second two variables indicate highly levered firms and imply a high yield spread. We also compute the standard deviation of daily excess returns for each bond issuer's equity over the 252 days during the asset growth period. We expect the positive change in the standard deviation of daily excess returns to have a positive effect on yield spreads. To control for macroeconomic variables, we use 1-year treasury rate, the difference between the 10-and 2-year Treasury rates, and the difference between the 30-day Euro-dollar and Treasury yields. The model is specified as follows: where the subscript i, j, t refers to bond j of firm i at year t, ∆ represents the first difference in each variable for each bond j, asset growth is defined as the year to year annual changes. income to sales is associated with a significant decrease in the yield spread, while higher leverage and higher equity volatility can lead to higher yield spread changes.
In column 3, we include firm specific, bond specific and macroeconomic variables.
The coefficients on asset growth remain significantly positive. One percent change in asset growth is associated with 0.3 percent change increase in yield spread. In addition, the deterioration of bond quality (rating) is related to a significant increase in the yield spread. Similarly, a higher risk in liquidity leads to an increase in the yield spread. This is consistent with the findings from Chen et al. (2007).
Furthermore, based on the unique feature of asset growth, we divide the sample into two subsamples: positive AG and negative AG subsamples. The coefficients on the asset growth are significantly positive. For instance, the coefficients on the asset growth are 0.2276 (t=2.87) for positive AG subsample and 1.7645 (t=2.61) for negative AG subsample.
Columns 6 through 8 show the results using the newly issued bonds for the full sample and two subsamples. The results are similar to those using all the traded bonds. One percent increase in asset growth is associated with 0.24 percent increase in yield spread changes for newly issued bonds. The asset growth growth effects are 0.26 and 1.67 for positive asset growth sample and negative asset growth sample, respectively. Overall, the result in Table 8 shows that asset growth is significantly and positively associated with yield spread changes regardless of whether we include firm-specific, bond-specific, or macro-level variables in different sample settings. Economically, a one percent increase in asset growth results in a 0.29 basis point increase in yield spread. For positive and negative asset growth firms, one percent increase in asset growth indicates a 0.228 and 1.76 basis point increase.
We also conduct robustness checks by examining the asset growth effect through various sample periods: i) pre-crisis, ii) crisis, and iii) post-crisis. During the recent financial crisis period, firms tend to have low asset growth rate due to the bad market conditions. Corporate managers face financial constraints and are cautious in how they invest. Thus, we expect that the firms tend to have less over-investment tendency during the crisis. In the meantime, investors are more rational and tend to make safe investments.  Table 8 and test for asset growth effect in different sample periods.
The results are reported in Table 9. Panel A of Table 9 considers the sample of all bonds while Panel B represents the results for the newly issued bonds. We find that the coefficients on asset growth for the full sample are significantly positive in precrisis period and post crisis period while significantly negative in the crisis period. This is consistent with our conjecture. The coefficient of asset growth is -1.64 (t=-3.32), suggesting that asset growth is associated with lower yield spread changes.
Facing higher cost of capital and more financial constrains, agency problem tends to be less pronounced. When we divide the full sample bonds into two subsamples based on the asset growth rate, we find that the coefficients on asset growth are significantly positive except for the negative AG subsample in the pre-crisis period.
In Panel B, the results on the asset growth are similar except that the coefficients on the asset growth are significantly negative for both positive AG and negative AG subsamples. Overall, the results suggest that the asset growth is positively associated with the yield spread change in pre-crisis and post crisis period while negatively associated with the yield spread during the crisis period.
Furthermore, we examine the asset growth effect on both investment and speculative bonds. Since bonds performance varies across various rating groups, we ask whether the asset growth effect holds in investment and speculative grade bonds. Similarly, we repeat the regressions in Table 8 for the bonds in two different rating groups respectively and report the results in Table 10. Panel A of Table 10 considers the full sample bonds while Panel B represents the results for the newly issued bonds. As we expect, the coefficients on the asset growth are significantly positive for investment-grade and speculative grade bonds. They stay significantly positive for the full sample and two asset growth subsample bonds. However, when we look at the regressions for investment-grade and speculative bonds using newly issued bonds, the coefficients on the asset growth become insignificant for the negative AG subsample bonds. Overall, all the results consistently show that the asset growth is positively associated with the yield spread change. In the following section, to explore the driving sources of asset growth effect, we break down asset growth into major balance sheet components from investment and financing aspects.

Asset Growth Effect: Decomposition Results Explanation
As we have shown above, asset growth has a positive impact on future bond yield changes. Our findings are more consistent with predictions from the agency theory. In this section, we further explore the asset growth effect on bond yield changes by examining various subcomponents of asset growth. In addition, we examine whether the manner in which the growth is financed affects the yield changes. One might expect that agency problem is more pronounced when corporate managers make large investments in physical assets or new equities and less pronounced when firms invest in intangible assets or reserve more cash. Moreover, we expect that large expansion and rapid asset growth are more likely financed with external financing sources.
In addition to the asset growth decomposition from the financing side of balance sheet as specified in equation (7), we decompose asset growth into 6 subcomponents: cash growth, noncash current assets growth, property, plant and equipment (PPE) growth, investment and advances growth, intangible assets growth and other assets growth from the investment side. To maintain an asset growth identity, each asset category difference is scaled by the previous years total asset value.
We perform regressions of yield spread changes on the lagged components of asset growth. We report results of the full sample in Panel A of Table 9. From an asset investment standpoint, we find that increases in non-cash current assets, PPE, investment and advances, intangible assets and other assets are associated with significant positive coefficients. In particular, t-statistics for the coefficients on the significant investment components vary from 2.07 for PPE to 3.87 for investments and advances. When we include all six investment components of asset growth in the same regression, we find that changes in noncurrent assets, PPE and investment and advances are positively significant, with growth in noncurrent assets and investment and advances exhibiting strong effect (the t-statistics for the coefficients is 3.29 and 3.87 respectively). It suggests that when firms make large investments in noncurrent assets, PPE and investment and advances, yield spread increases after the asset growth period. In addition, changes in cash and others assets are negatively significant and the coefficient of changes in intangible assets are not statistically significant. Our findings are consistent with our conjecture.
Corporate managers are more likely to expand in fixed assets, new equities or operating assets when they have the over-investment or empire building tendency, while agency costs would be lower when firms reserve more capital to meet their debt obligations. Another interesting finding is yield spread changes are unrelated to changes in intangible assets.
In equation (7), we decompose total asset growth into 5 components: operating liabilities growth, retained earnings growth, stock financing growth, debt financing growth and others shareholders equity and liabilities growth from the financing side. We find that growth in debt financing and operating liabilities growth are associated with positive yield spread changes. Specifically, growth in operating liabilities and debt are associated with the strongest effect with coefficient of 1.7 (t=4.79) and 1.49 (t=4.14), respectively. As shown in Table 2, growth in debts and growth in operating liabilities accounts for more than 60% and 20% of total asset growth, respectively, suggesting that corporates heavily rely on debts and operating liabilities when they grow rapidly. We show that the agency effects are more likely to occur when firms realize growth opportunities by financing with debts and operating liabilities. When we include all subcomponents of financing growth variables into the regression, both debts and operating liabilities growth variables are statistically significant, while growth in retained earnings and others are negatively insignificant. The agency costs would be lower when firms finance their investments using retained earnings.
We repeat the same process by examining the various growth components in positive asset growth sample and negative growth sample. Results of positive growth sample are reported in Panel B. From the investment standing point, growth in noncurrent assets and intangible assets are positive and significant; whereas growth in retained earnings and other assets are negative and significant. The intangible assets are still insignificant related to yield spread changes.
From the financing side, it is worth noting that changes in both equity and debt financing are positively related to yield spread changes, suggesting that there are more pronounced agency problems when firms use external financing sources.

Asset Growth and Bond Performance
In the previous sections, we have shown that high firm asset growth rate is associated with high yield spread, suggesting that high asset growth is more likely due to the over-investment incentives of corporate managers. Moreover, asset growth is negatively correlated with future yield spread changes. As discussed in H3, biased investor belief can lead to mispricing of corporate bond. Overextrapolation of firm past growth realizations in the presence of agency problem can result in a sharp decline in bond values. In this section, we examine the asset growth effect on bond performance and ask whether asset growth can forecast excess corporate bond return.
Corporate bond return could be contaminated with mispricing. Due to the agency problems, firms tend to make large investments regardless of the cost of capital and growth opportunities. On the other hand, investors may not see through issuer's incentives. Greenwood and Hanson (2013) show that bond investors overextrapolate firms with high asset growth and their expectations will be revised after a period of relatively low asset growth, resulting in lower bond return. For example, investors tend to be too optimistic of the future growth opportunities of high asset growth firm and believe these firms will continue to grow rapidly.
However, these firms tend to over grow in the past and exhaust potential growth opportunities, resulting in a relatively low asset growth in the following period.
Thus, we expect that asset growth is negatively associated with future excess corporate bond return. The annual corporate bond return as of year t+1, Ret t+1 , is computed as: where P t+1 is the bond price at year t+1, which is defined as the bond price at the 18 month after the formation of asset growth portfolios; C is the annual coupon payment; P t is the bond price at year t, which is defined as the bond price at the 6 month after the formation of asset growth portfolios.
Next, we express the above equation in terms of the log return: r = log(1+ret).
Bond return can be decomposed as: where P y t+1 t is the bond price estimated with yield at year t+1, all else being equal. The first term is the yield change effect component on bond return and the second term is the yield effect component on bond return. This is essentially similar to the decomposition in Campbell, Lo, and MacKinlay (1997), however, coupon bonds are used here. In the bond return decomposition, the firm term is analogous to bond price change, i.e. P t+1 /P t . The second term is analogous to bond current yield, which is the ratio of annual coupon payment to the lagged bond price. Bond price at year t is obtained from TRACE. To estimate P y t+1 t , we use bond yield at year t+1 and other bond characteristics from year t.
We perform panel regression to examine the asset growth effect on future excess corporate bond return. The dependent variable is the return Ret i,t+1 of an individual bond i in excess of one year treasury rate at year t+1. We include firm specific variables: asset growth rate, leverage, operating income to sales and market to book (M/B) ratio. We also control for bond specific variables, such as bond ratings, years to maturity and yield to maturity. All independent variables are obtained at the end of the formation of asset growth portfolios. The model is specified as follows:

Conclusion
In this paper, we empirically distinguish rational expectation and mispricingbased explanation on asset growth anomaly by using corporate bond data. First, we document a distinct U-shaped relation between yield spread and corporate asset growth. The pattern holds strong when we control for bond-and firmspecific characteristics using both portfolio and regression analysis. High asset growth firms tends to be firms with relatively higher yield spread. We suggest that asset growth is more likely due to the over-investment and empire building tendency. Second, we show a positive relation between asset growth and yield spread changes. High asset growth firms are more likely to have positive yield changes. The positive asset growth effect remains strong across various sample periods and rating groups. Our evidence is consistent with the conjecture of agency problem. In the asset growth decomposition, we find that agency problem is more significant when firms use debt and operating liabilities for financing and when firm make large investments in fixed assets and new equities. Finally, asset growth is positively associated with future bond return, which is attributed to the yield change effect component. Overall, our empirical finding is more aligned with the agency problem explanation of corporate asset growth. The variables used in the paper are listed below (with Compustat data items in parenthesis).
Asset growth (AG) is the 1-year percentage change in total firm assets , where assets are Compustat data item 6. To compute AG, a firm must have nonzero total asset in both year t-1 and t-2.
Yield spreads are defined as the difference between the yield of bond and the associated yield of the Treasury curve at the same maturity. We employ a parametric model to estimate yield curve following Gurkaynak, Sack and Wright (2007).
Pretax interest coverage is the ratio of [operating income after depreciation (data 178)+interest expense(data 15)] to interest expense.
Operating income to sales is [operating income before depreciation (data 13) to net sales (12).
Long-term debt to assets is [total long-term debt (data 9) to [total assets (data 6)].
Total debt to capitalization is [total long-term debt (data 9)+debt in current liabilities (data 34)+average short-term borrowings (data 104)] to [total liabilities (data 181)+market value of equity (from CRSP)].
Log(Assets) is the natural log of total assets (data 6).
Leverage is the sum of long-term debt and debt in current liabilities, scaled by total assets [(long-term debt (data 9) + Debt in current liabilities(data 34)/total assets(data 6)].
ROE is net income (data 172) scaled by total shareholder's equity (data 144).
SDExret is the equity volatility, which is estimated using 252 daily excess stock returns (from CRSP), for each issuer.
10Yr is the 10-year treasury yield .
Treasury slope: we define the slope of the yield curve as the difference between 10-year and 2-year Treasury yield. We interpret this proxy as both an indication of expectation of future short rates, and as an indication of economic health.
Euro is the difference between the 30-day Eurodollar and 3-month Treasury Bill rate that controls for other potential liquidity effects on corporate bonds relative to Treasury bonds.
Amihud is Amihud illiquidity ratio estimated based on bond returns and trading volume at daily frequencies, for a given year. Specifically, Amihud = 1 N N j=1 R j Q j . N is the number of days with at least one trade on the bond during a year, and R j and Q j are the return and dollar trading volume on day j when there is at least a trade. The return R j is measured as the percentage change in closing clean price, from the most recent day with trading to the last trade on day j.
Panel A of the table reports the distribution of the main variables used in the analysis. Firm characteristics variables include asset growth (AG), total assets (in billion $), book leverage, pretax interest coverage (PIC), long-term debt to assets (LTA), total debt to capitalization (DTC), operating income to sales (OIS), net income to equity (ROE), and standard deviation of excess daily stock return (Sdret). Bond characteristics variables include yield, yield spread (YldSpread), Amihud measure (%), amount issued (in million $), coupon, rating, and maturity. We assign integer numbers to the credit ratings (i.e., Aaa=22, Aa1=2, ..., D=1). The definitions of the variables are provided in the appendix. The distributional attributes include the 5th, 25th, 50th, 75th and 95th percentiles, as well as the mean and standard deviation (Std Dev) of each variable. We obtain each statistic each year and then take the average over time. Panel B of the table reports the correlation matrix of these variables. The sample period is from January 1994 to December 2014.  This table shows summary statistics of bond-issuer (Panel A) and bond-specific (Panel B) characteristics for the deciles based on the asset growth at the fiscal year t. D1 represents issuers with the lowest asset growth rate while D10 represents issuers with the highest asset growth rate. Issuer characteristics include assets (in billions $), leverage, pretax interest coverage (PIC), long-term debt to assets (LDA), total debt to capitalization (DTC), operating income to sales (OIS), ROE and standard deviation of daily excess return (Sdret). We also include bond-specific characteristics, including yield, yield spread (YldSpread), credit rating, amihud measure, amount issued (in millions $), maturity, and coupon rate. We assign integer numbers to the credit ratings (i.e., Aaa=22, Aa1=2, ..., D=1). Details on the construction of these variables are provided in the Appendix. The number in each cell reports time-series averages of yearly cross-sectional means over the full sample period (January 1994 to December 2014) across all bond issues and issuers.    The table shows the average yield spread of portfolios for all bonds and for the newly issued bonds respectively. Each year, we sort issuers into deciles based on asset growth rates. D1 (D10) represents issuers with the lowest (highest) asset growth rate. Yield spread is obtained at the beginning of the asset growth year. All bonds are also sorted into three profitability groups and quintiles (Q1-Q5) rating groups. The yield spread is the difference between the bond yield and the yield of a comparable maturity treasury bond. We repeat the same process, but sort all bonds by the absolute value of asset growth rate. No asset growth portfolio has the lowest absolute value of asset growth rate. Panel A reports yearly average yield spread of asset growth portfolios for all bonds. Panel B reports yearly average yield spread for newly issued corporate bonds. Newly issued bonds are defined as the bonds that are issued during the asset growth year. All numbers are in percentage. Inside the parenthesis are the Newey-West (1987) adjusted t-statistics with a 2 year lag. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.   . T-statistics are in parentheses below each coefficient, and are adjusted for clustering at the firm-level. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.
(1)   The yield spread change determinants are based on firm-specific characteristics, bond-specific effects, macroeconomic variables. Annual changes in all variables are examined for 1994-2014 period. The liquidity is estimated by the Amihud measure. We use a cardinal scale for all bonds, regardless of whether they are investment grade or speculative grade bonds, ranging from 1 for C rated bonds, to 22 for Aaa rated bonds. The firm specific characteristics are operating income to sales, long-term debt to assets, total debt to capitalization, and excess stock daily volatility. T-note rate is the 1 year Treasury rate. Term-slope is the difference between the 10 year and 2 year Treasury rates. Eurodollar refers to the difference between the 30-day Eurodollar rate and the 3-month T-bill rate. More details on the construction of these variables are provided in the Appendix. T-statistics are presented in parentheses. The issuer is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.
Full Sample Newly Issued Bonds   The yield spread change determinants are based on firm-specific characteristics, bond-specific effects, macroeconomic variables. We use a cardinal scale for all bonds, regardless of whether they are investment grade or speculative grade bonds, ranging from 1 for C rated bonds, to 22 for Aaa rated bonds. The firm specific characteristics are operating income to sales, long-term debt to assets, total debt to capitalization, excess stock daily return and equity volatility. T-note rate is the 1 year Treasury rate. Term-slope is the difference between the 10 year and 2 year Treasury rates. Eurodollar refers to the difference between the 30-day Eurodollar rate and the 3-month T-bill rate. More details on the construction of these variables are provided in the Appendix. Investment grade bonds are numbered from 13 (Baa3 rated bonds) to 22 (Aaa rated bonds). Speculative grade bonds are numbered from 1 (C rated bonds) to 12 (Ba1 rated bonds). The issuer is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.   We perform panel regression on the asset growth effect on bond return. In column (1) to column (4), the dependent variable is the excess return of corporate bonds over one year treasury rate. In column (5), the dependent variables is the yield change effect component of bond return. In column (6), the dependent variable is the yield effect component of bond return. We control for firm characteristics: asset growth rate, leverage, income to sales and market to book (M/B) ratio. We also control for bond characteristics: bond ratings, years to maturity, and yield to maturity. More details on the construction of these variables are provided in the Appendix. T-statistics are presented in parentheses. The issuer is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.
(1) Prepared for submission to Journal of Banking and Finance.

Abstract
Following the 2008 financial crisis and the government bailout of troubled companies, Too-Big-to-Fail became a standard expression to name a free protection of Wall Street by tax-payers' money. We offer a novel approach to estimate the value of the implicit government guarantee by combining the contingent claim pricing with the likelihood of the government intervention. We find that the cost of this implicit protection on average is about $13 million per company, per year, and it rises to about $24 million if the government is assumed to intervene with certainty. The funding costs for both small and large banks are negatively related to the value of the implicit government guarantee. Moreover, we show that the spread of the funding costs of small banks over large banks is strongly associated with the value of the implicit government guarantee, especially after the crisis.

Introduction
Shedding some light on the 2008 financial crisis, Sorkin (2009) chronicles the story from the beginning of the crisis to the Troubled Asset Relief Program (TARP) and popularizes the concept of "Too Big to Fail" (TBTF). While saving the financial system, TARP was controversial as the cost of the bailout was mainly supported by the US tax payers. The idea of TBTF suggests that large companies enjoy a guarantee that they will be rescued by the government in a bankruptcy situation. As written by Bloomberg There is a common agreement that such an implicit guarantee exists and its cost may be justified due to the potential impact on the overall economy in case of the collapse of the financial system. At the same time, the implicit government guarantee reduces investors' perception about the risk of the financial institution and their expected losses. It also leads to unfair competition due to lower cost of funds, increased risk taking by TBTF institutions and increased potential financial burden on the government. Policy makers have an intention to curb the value of the implicit government guarantee (Schich and Aydin (2014)) which creates a need for having a robust way of measuring it.
The contribution of this article is twofold. First, we propose a novel way to measure the value of the implicit government guarantee. Using our approach we find a confirmation for the above Bloomberg editorial board view that the estimate of the implicit government protection can go beyond billions of dollars for some of the largest companies. Since the implicit government guarantee may potentially involve transfer of billions of dollars from the government to the bailed-out companies, the ability to estimate it remains an important public policy concern. Second, we investigate the relationship between the implicit government guarantee and the funding costs of small and large banks. The funding costs are often used as a proxy for the TBTF effect. Strong association between the spread of funding costs of small banks over large banks with our estimate of the implicit government guarantee serves as an additional confirmation of the validity of our model.
Quantifying the value of the implicit government guarantee has generated a considerable interest in the years following the financial crisis. The more common approaches of assessing the TBTF or the value of implicit government guarantee can be split into three groups: i) The funding cost approach; ii) The CDS-based approach; iii) The contingent claims approach.  (2014)) estimate the reduction in the funding costs based on credit ratings. Credit rating agencies produce two credit ratingsan "individual" credit rating designed to assess institution's strength on a stand-alone basis and a "support" rating which incorporates the probability that the institution will receive government support.
The reduction in the funding costs in this case is estimated as the difference in the cost of funds based on higher "individual" rating and actual "support" rating. The implicit government guarantee is then calculated by multiplying the difference in the funding costs by the assets of the TBTF banks. The main drawback of the first approach is that it doesn't control for the relative risk of different financial institutions and doesn't take into consideration the likelihood of receiving government support. The rating-based approach avoids these problems, it is easy to implement, and the required data is readily available, but it suffers from being subjective and relying on credit rating agency  (2011)). One potential problem related to this approach is the need to estimate the asset value and the asset volatility which are unobservable and should be inferred from the equity market information. The techniques used in the literature estimate the asset value and volatility by simultaneously solving the system of two equations with two unknowns (see, for example, Lucas and McDonald (2009)), some papers rely on oversimplifying assumptions (for example, Noss and Somerbutts (2012) and Oxera (2011) assume that equity constitutes 6% of total assets) or use complex and resource-intensive techniques (for example, Jobst and Gray (2013)). Using the contingent claim approach implicitly assumes that the government will intervene with certainty. However, on an individual basis, as evidence by the collapse of the Lehman Brothers, this intervention may fail to materialize.
Therefore, it is necessary to take into account the likelihood of the government intervention for a given firm. The framework for estimating the likelihood of the government intervention is provided by Beliaeva, Khaksari and Tsafack (2015) who estimate it using the size and the finance industry membership of the company.
In this paper we combine the contingent claim approach with the likelihood of the government intervention to provide an appropriate and robust measure of the implicit government guarantee as the expected value of the contingent claim. 2 This is simply the product of the probability of the government intervention and the value of the put option. We find that the cost of the government protection in our sample is, on average, about $24.5 million per company, per year, and it drops to $13.4 million when we incorporate the fact that the government may not intervene. Our estimates are also consistent with the Bloomberg View's editorials, as we find that the value of the implicit government guarantee can go beyond billions of dollar for very large banks with trillions of dollar in assets and debts. The value of the implicit government guarantee sharply increases after the 2008 financial crisis.
Our empirical analysis reveals a consistently inverse relationship between funding costs and the value of the implicit government guarantee. This inverse relationship means that the decrease in the funding costs is associated with an increase in the value of the government guarantee for both large and small companies.
Furthermore, we find that the spread in funding costs of small banks over large banks and the implicit government guarantee are positively related. In fact, the increase in the difference between the funding costs of small banks and large banks is often considered as a proxy for the too-big-to-fail premium. Therefore, the positive relationship confirms this intuition and reinforces our confidence in the way we estimate the value of the implicit government guarantee. Investigating potential structural break for the period after the crisis mostly confirms our results. The relationship between the funding cost spread and the implicit government guarantee is strong and positive both before and after the crisis for bank holding company data. For the FDIC data the results are only strong and positive after the crisis. Before the crisis the relationship is inverse which can be attributed to the FDIC insurance effect.
The remainder of the paper is organized as follows. Section 2 describes our methodology and the data set used to estimate the implicit government guarantee.
Section 3 describes the methodology, the data, and the variables used for analyzing the relationship between our measures of the implicit government guarantee and funding costs. Section 4 presents and summarizes our empirical findings, and section 5 concludes.

Definition
We define the value of the implicit government guarantee as the expected value of the government intervention to rescue the distressed firm. The value of the implicit government guarantee for company is computed as: Where, ,the probability of the government intervention for company ; ,the value of the government subsidy given that intervention will happen with certainty for company .

Estimating the Probability of the Government Intervention (π i ):
Following Beliaeva, Khaksari and Tsafack (2015), we use a logit model to estimate the probability that the government will step in and rescue a company in distress. In our logit model we use the finance industry indicator, the firm size, and the interaction term between these two variables as explanatory variables. The logit model provides a simple way to describe the relationship between several explanatory variables and a binary dependent variable. We apply our model to an extensive dataset of 1571 bankrupt and bailed out companies between 2000 and 2015. The dependent variable in the logit model estimates the probability that the government will step in and rescue a company in distress. It is defined as follows: The logit model is then specified as follows: Where, F( • )the logit function; lgasset,the natural logarithm of the total assets; ,the dummy variable indicating whether the company belongs to the finance industry or not; * the interaction term between the log of the total assets and the finance industry membership.

The Government Guarantee Data and Results
The data that we use to estimate the implicit government guarantee comes from several major sources: SDC Platinum database, TARP database and ProPublica website. SDC Platinum database includes all US public companies with $10 million or more in assets that file for Chapter 11 bankruptcy protection. We compile a broad sample of Chapter 11 bankruptcy filings spanning the years 2000 through 2015 (SDC coverage begins in 1980). We exclude firms with reported assets under $100 million. database.
[Insert Table 1 Here] Panel A of Table 1 summarizes the number of bailout and bankrupt firms in our sample. We have a total of 1,247 bankruptcy cases, including 175 finance firms, and 324 bailout firms, including 304 finance firms. Panel B of Table 1 provides summary statistics for the variables used in the estimation of the probability of the government intervention. The average of the total assets is $12 billion. We normalize the total assets by taking the natural logarithm of the total assets (lgasset hereafter).
The average of lgasset is 6.79 with the standard deviation of 1.53. Panel C of Table 1 shows the correlation coefficients among these variables. We observe a 0.685 correlation between the finance industry dummy variable and the bailout dummy variable and 0.36 correlation between the log of total assets and the bailout dummy variable.
[Insert Table 2 Here] We analyze four different model specifications of logit regression. In model 1 and model 2 we estimate the effects of the financial industry (finance dummy) and the firm size (log of total assets) on the probability of the government intervention, respectively. We include both variables in model 3. To examine the interaction effect, in model 4 we include an additional interaction variable between the finance industry dummy and the log of the total assets. The results of the logit regression estimation for four model specifications are presented in Table 2. All of the parameter estimates are significant at a 1% level across all models. Although the size and the financial industry membership are the two main factors explaining the probability of the government intervention, the addition of the interaction variable between the firm size and the finance industry dummy increases the explanatory power of the model. In fact, model 4 is the best fitting model out of the four model specifications as evidenced by the lowest AIC criteria of 733.67 and the highest Pseudo R 2 of 64.03%. Therefore, we choose Model 4 specification to estimate the probability of the government intervention for all firms in our full sample. 3 The negative sign for the coefficient of the interaction variable seems counterintuitive as the TBTF is mostly related to the financial institutions. A straightforward interpretation of the negative sign is that while the size matters for a bailout of any firm, it is more important for non-finance firms relative to finance firms.
This result can be justified by the fact that there is a strong correlation between credit risks of large and small banks. This is especially true for our sample. The TARP program for the bailout of the financial system included both very large banks as well as small banks. In contrast, non-finance companies' bailout had more homogeneity: firms rescued in 2001 were mostly big airline companies. Therefore, while the firm size matters for a bailout decision, within the financial system, the size effect for individual financial institutions is overshadowed by the risk of the contagion effect. Due to this, the firm's size is not the main driving factor of the bailout decision within the financial industry.
It also worth noticing that our estimation procedure does not include a dummy variable for the crisis period. Although the bailout is related to the economic environment, including a variable indicator for the crisis period will introduce some endogeneity in the estimation of the likelihood of the government intervention for a given company. In fact, when TBTF companies are in trouble, it tends to trigger both a crisis and a bailout program. This can be seen in our sample as we have bailouts only during the crisis period, which can give a false impression that a bailout cannot occur without a crisis. In our study we are more interested in the probability of the government intervention for a given firm, even if the company is far from a distress situation. We expect the crisis effect to be captured by the value of the contingent claim.
Using the estimated parameters, we fit the data to the following Logistic function: The above equation is used at a company level to derive the likelihood of the government intervention which is then incorporated into the calculation of the value of the implicit government guarantee.

Estimating the Value of the Government Subsidy Given Intervention (V i )
We estimate the value of the government subsidy given that intervention will happen with certainty (i.e. assuming the "full coverage" by the government) using the contingent claims approach of . Under this approach it is assumed that the firm has a simple capital structure consisting of equity and a single homogeneous class of debt. The firm's equity value is modelled as a call option on the firm's assets with the exercise price equal to the firm's default barrier (firm's liabilities). 4 If at the option's maturity the asset value is less than the strike price, then the option expires worthless, shareholders get nothing and the firm is turned over to the debtholders. The value of the implicit government guarantee is analogous to a put option on the firm's assets with the strike price equal to the default barrier (firm's liabilities). If at option's maturity the asset value is less than the strike price, then the option is in-the-money and the option payoff (i.e. payoff from the government) is equal to the difference between the strike price (the firm's liabilities) and the firm's assets. It is represented as a claim that firms have on the government contingent on their failure, the exercising of which restores their assets to a value necessary to prevent their default. The estimation of the value of the government subsidy is done in two steps: Step 1. Estimate (the value of assets) and (the volatility of assets) by solving a system of two equations based on .

Equation 2:
The relationship between the value of equity and the volatility of assets: Given the equity volatility data, the risk-free rate, the market value of equity, and the face value of debt, it is necessary to solve the system of these two highly non-linear equations to estimate the value of assets and the volatility of assets. We derive an easily implementable solution for the assets value and assets volatility which involves solving only one equation with one unknown.
Technical details on the estimation procedure are provided in Appendix A.
Step 2. Compute the value of the implicit government guarantee given intervention as a put option on the firm's assets with the strike price equal to the default barrier (the firm's liabilities).
For a given company i, this represents the value of the government guarantee given that the intervention will happen with certainty.

The Model Specification
It is often assumed that only large financial institutions will be supported by the government in case of default 5 . Therefore, the difference in the costs of funds between small and large financial institutions can be thought of as a proxy for the implicit government guarantee. In this section we investigate the relationship between our measure of the value of the implicit government guarantee, , and the funding cost variable while also controlling for the GDP growth rate. We use the following model specification: To investigate the potential change in the relationship between of the value of the implicit government guarantee and the funding cost, we introduce an interaction variable between the funding cost and the crisis indicator as follows.
Where, a dummy variable taking a value of one after the crisis and zero otherwise.
To study the relationship between the value of the implicit government guarantee and the funding cost variable, we sort our data sample into two groups by bank size. Following Li, Qu, and Zhang (2011), we define the top 20 in book assets as of December of each year as large banks and the remainder as small banks. We separately analyze the relationship between the implicit government guarantee and the funding costs of large banks, small banks and the difference in the funding costs of small and large banks.
The analysis of the relationship between the implicit government guarantee and the funding cost variable provides an alternative way to assess the robustness of our results.

Funding Cost Measure
The bank's funding cost, i.e. the interest rate charged by the bank's creditors, depends on the lender's perception of the bank's probability of distress. In other words, the lenders assess the bank's default probability and adjust the interest rate they charge accordingly. There are two ways to obtain data on interest rates and default probabilities for any given bank.
First, interest rates and default probabilities can be extracted from the market data. A popular proxy for the bank's funding cost is a CDS spread, which can also be used to imply the bank's default probability. However, the limitation of this approach is that the CDS data is not widely available for small banks. An alternative source of data on the bank's funding cost and default probability is the bank's balance sheet reports. The data on the bank's interest expense on debt allows to construct proxies of funding costs. Baker and McArthur (2009) (2016)). However, these two measures may not be appropriate for our study. The average funding cost measure includes payments made to all of the bank's creditors, including both retail and wholesale depositors. As noted by Araten and Turner (2013), the composition of the average funding cost is different for large and small banks, in which large banks have various sources of funds, while small banks largely rely on regular deposits. As a result, the average funding cost of large banks tends to be upward biased due to the mix of funding cost. The interbank funding cost measure is calculated as a ratio of interest expense on federal funds and repos purchased to the average total federal funds and repos purchased during the reporting period. The large banks are more likely to use federal funds and repos for short-term borrowing, while small banks have limited access to them. In fact, the cost of federal funds makes up only 6% of the overall funding costs of small banks as reported by Araten and Turner (2013). Due to the shortcomings of the alternative funding cost measures, in our study we define the funding cost as the cost of deposit.

Bank Funding Cost Data
The banking data is obtained from the COMPUSTAT Bank database and the

Summary statistics
We provide below the summary statistics for the value of the contingent claim, the expected value of the implicit government guarantee, the leverage, and the funding cost.

Empirical Analysis
In this section we report the results of our empirical analysis. First, we compute the value of the implicit government guarantee using the two-step procedure outlined in section 2. Then, we relate the value of the government guarantee to funding costs of large banks, small banks, and the funding cost spread between small and large banks while controlling for the macroeconomic conditions.

The Value of the Implicit Government Guarantee
Using the firms' equity and liability data at the beginning of the quarter, 7 we estimate the value of the government subsidy given intervention as a put option on the firm's assets with the strike price equal to the default barrier (firm's liabilities). 8 Panel A of Table 3 shows that the average value of the implicit contingent claim over a one year maturity is $23.68 million, with the maximum of $111.2 billion. This value represents the value of the government guarantee under the assumption that the guarantee is explicit, i.e. that the government will rescue the troubled companies with certainty. In practice, as the Lehman Brothers bankruptcy has shown, this is not the case even for large banks. One of the contributions of our study is that we define the value of the implicit government guarantee as an expected value of the government intervention and we estimate it by multiplying the value of the government subsidy given certain intervention by the probability of the government intervention. We estimate the average probability of the government intervention to be 15%. We also find that large firms and financial institutions are more likely to receive government support, while a large number of small firms may not be bailed out by the government. After taking into account the probability of the government intervention, we find that the average expected value of the implicit government guarantee for all firms is $12.91 million but it can be as high as $89.2 billion for certain companies. This can be interpreted as the average annual cost of the Too Big to Fail per company for the tax payers. According to the TARP, the total government disbursement was $623 billion.
Therefore, our measure of the value of implicit government guarantee can well capture the size of the recent government bailout.
In addition, we take the quarterly mean of the estimated government guarantee variables to get the time-series data for the subsequent analysis. Panel A of Table 4 shows that the value of the contingent claim over a one year maturity ranges from about $376,000 to $87 million, with a $24.5 million on average. The probability of the government bailout ranges from 4.53% to 17.73% with an average of 15.32%. The mean (median) of the expected value of the implicit government guarantee for all firms over the sample period is $13.38 ($4.07) million. Also note that the product of the average probability with the contingent claim ($24.5 x 0.1532 = $3.75 million) is much smaller than the average value of the government guarantee ($13.38 million). This can be explained by the fact that big companies with large values of contingent claims also have higher likelihood of the government intervention.
[Insert Figure 3 Here] but it has declined in the following years. The high level of the implicit government guarantee after the financial crisis coupled with the low interest rates reflects the fact that the government continued stabilizing the economy well after the financial crisis was over. While the goal was to restore confidence in the economy and stability of the financial system, such policy came at a cost. It put a fiscal strain on the economy, reduced the GDP and delayed the economic recovery.
[Insert Figure 4 Here] Figure 4 shows that the value of the implicit government guarantee increased drastically with the crisis for both finance and non-finance companies. Since nonfinance companies have larger average size compared to finance companies ($2.7 billion versus $1.6 billion), the average value of the implicit government guarantee for nonfinance companies before the crisis was slightly larger compared to that of the finance companies ($3.1 million versus $2.3 million). After the crisis the situation reversed and the finance companies enjoyed a much larger average implicit government guarantee ($31.6 million) compared to that of the non-finance companies ($24.4 million). When we consider the ratio of the average value of the implicit government guarantee to the companies' average market value, the finance companies had larger ratios both before and after the crisis. The difference in ratios between finance and non-finance companies is more pronounced after the crisis. This is consistent with the financial sector bailout which was done in order to prevent the collapse of the entire economy.

The Relationship between the Value of the Implicit Government Guarantee and the Funding Costs
The spread between the funding costs of the small and large banks is often used as a proxy for the too-big-to-fail effect of the implicit government guarantee (see, for example, Baker and McArthur (2009) and Li, Qu, Zhang (2011)). The intuition behind it is that the decrease in the funding costs of large and small banks and subsequent increase in the funding costs spread can be associated with an increase in the value of the implicit government guarantee. We investigate this relationship for the costs of funds using data at BHC level from Compustat (Table 5 and Table 6) and at depositary level from FDIC (Table 7 and Table 8).
The value of the implicit government guarantee depends on the current economic conditions. To control for the state of the economy we use the GDP growth rate. Empirical evidence shows strong inverse relationship between the implicit government guarantee and the funding costs (see Table 5 and Table 7). There is a significant consistency in our results. The strong negative relationship holds for large and small companies for both BHC and FDIC funding costs measures. The inverse relationship means that a decrease in the funding costs is associated with an increase in the value of the implicit government guarantee for both large and small companies.
[Insert Table 5 Here] In Table 5, the one percent decrease of funding cost of large banks is associated with $744,023 increase of the value of implicit government guarantee using the BHCs data. While this result is secondary and can be influenced by other factors, the most interesting result is the positive relationship between the spread in funding costs of small banks over large banks and the implicit government guarantee.
[Insert Table 6 Here] Table 6 shows the one percentage increase of funding cost spread is associated with the $5.44 million increase of the implicit government guarantee. Since the spread between the funding costs of the small and large banks is often considered as a proxy for the too-big-to-fail premium, the positive relationship confirms this intuition and reinforces our confidence in the way we estimate the value of the implicit government guarantee.
[Insert Table 7 Here] We also observe a strong positive relationship between the banks' size and the implicit government guarantee for both small and large BHCs and FDIC banks. The positive relationship implies that larger companies enjoy higher implicit government guarantee. Finally, we explore the relationship between banks' leverage level and the implicit government guarantee for BHCs. We find strong inverse relationship for both large and small BHCs meaning that highly leveraged banks tend to have lower implicit government guarantee. After the financial crisis many companies reduced the amount of leverage which increased their implicit government guarantee.

Government Guarantee and the Funding Costs
In this section we explore the effect of the financial crisis on the relationship between the value of the implicit government guarantee and the funding cost spread between small and large banks. To explore this relationship we add a structural break to distinguish between before and after the crisis periods. The empirical results, for the most part, are consistent with our prior findings (see Table 6 and Table 8). For BHCs the relationship remains strong and positive both before and after the crisis. Before the crisis, the funding cost spread was increasing and so did the implicit government guarantee. After the crisis there is usually a reversal adjustment as the markets gradually return to normal. The positive after the crisis relationship implies that as the funding cost spread narrowed, the implicit government guarantee decreased. For the FDIC banks the relationship is strong and positive after the crisis but it is negative before the crisis.
This result can be attributed to the FDIC insurance effect which reduces the cost of funds of the FDIC insured financial institutions. As was discussed earlier, the FDIC insurance effect should be stronger for small FDIC banks leading to a decrease in the funding cost spread between small and large banks before the crisis at the time when the implicit government guarantee was growing. The FDIC insurance effect becomes insignificant during and after the crisis which is confirmed by the positive relationship between the value of the government guarantee and the funding cost spread after the crisis.

Robustness Check
We

Conclusion
The contribution of our paper is twofold. First, we provide a robust way to estimate the value of the implicit government guarantee and, second, we investigate the link between the value of the implicit government guarantee and the funding cost spread between small and large banks.
Combining the contingent claim pricing with the likelihood of the government intervention, we estimate the value of a potential bailout enjoyed by the firms. Our estimates support the Bloomberg View's editorials, as we find that the value of the implicit government guarantee can go beyond billions of dollar for very big banks with trillions of dollars in assets and debts. Furthermore, we find that the value of the implicit government guarantee sharply increased after the 2008 financial crisis.
Since the TBTF dynamics is often approximated by the change in the spread of the funding cost of small banks relative to large banks, we assess that by constructing the time-series of funding costs of large and small banks. We find that the funding cost spread is strongly related to our estimate of the value of the implicit government guarantee. When we introduce a structural break in the relationship, we find that the relationship is much stronger and more consistent after the financial crisis.

Appendix A. Solving for the Value of Assets, , and the Volatility of Assets,
The value of assets, , and the volatility of assets, , are obtained from the following system of two equations: Combining equations (1) and (2) leads to On another hand, 2 is given by Equating these two expressions [ (3) and (4) volatility, , and risk-free rate, , we use equation (6) to solve for assets volatility, .
Once the value of is obtained, we use equation (5) to back out the value of assets, .
Following Levine and Wu (2016) and Vassalou and Xing (2004), we assume an estimation window of one year, i.e. = 1, and estimate the face value of debt as the sum of debt due within the next year and one half of the long term debt. The risk-free rate is given by the one-year Libor rate obtained from Bloomberg. is estimated using the EWMA filter to estimate from quarter to quarter, starting with the volatility estimated on the entire series for each company.

Variable Definition
Value of the contingent claim (  0.36*** 0.397*** 1 Note: Dum_Bailout is the dummy variable taking the value of 1 if the firm is bailed out, and 0 otherwise. Dum_Finance is the dummy variable taking the value of 1 for finance firms, and 0 for non-finance firms. Lgasset is the natural logarithm of the total assets of the firm. *** p<0.01, ** p<0.05, * p<0.1.

Table 2: Logit Regression for the Probability of the Government Intervention
This table shows parameter estimates of the logit regression of the probability of the government intervention. The sample includes 1571 bankrupt and bailed out companies between 2000 and 2015. Dum_finance indicates whether or not the firm belongs to the finance industry. lgasset is the natural log of the total assets.

Variables
Model 1

Table 3: Summary Statistics of Company Level Data and Funding Cost Variables
This table provides summary statistics for listed firms, BHCs, and FDIC banks. Vg is the value of the contingent claim. is the probability of the government bailout. Evg is the expected value of the implicit government guarantee. Leverage is the ratio of the total debt to the total assets. Funding cost is the ratio of the total interest expenses to the average total interest bearing liabilities. Market value, total assets, total liabilities, Vg and Evg are in million. Panel A presents the descriptive statistics of firms' fundamentals and estimated government guarantee variables. Panel B presents the descriptive statistics of fundamentals and funding cost variable for BHCs. Panel C presents the descriptive statistics of fundamentals and funding cost variable for FDIC banks.    For funding cost, size and leverage, models below show the relationship between their averages and the average value of the government guarantee, which represent the expected value of the put option enjoyed by a firm under the implicit government guarantee. Independent factors are built here using data at the BHC Level from Compustat. A parameter for a variable with suffix "ACt" represents the change after the crisis. All variables are quarterly form 2000 Q1 to 2015 Q4. Robust t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%.

Table 7: Implicit Government Guarantee and FDIC Funding Cost
For funding cost, size and leverage, models below show the relationship between their averages and the average value of the government guarantee, which represent the expected value of the put option enjoyed by a firm under the implicit government guarantee. Independent factors are built here using data at the depository Level from FDIC. All variables are quarterly form 2000 Q1 to 2015 Q4. Robust t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%.

A v e r a g e v a l u e o f i m p l i c i t g o v e r n m e n t g u a r a n t e e f o r f i n a n c e a n d n o n -f i n a n c e c o m p a n i e s b e f o r e a n d a f t e r t h e c r i s i s ( i n $ m i l l i o n )
Finance Non Finance

A v e r a g e M a r k e t v a l u e f o r f i n a n c e a n d n o n -f i n a n c e c o m p a n i e s b e f o r e a n d a f t e r t h e c r i s i s ( i n $ m i l l i o n )
Finance Non Finance

Finance Non Finance
Prepared for submission to Journal of Corporate Finance.

Abstract
The corporate bond sector has grown tremendously over the past decade. Rapid growth in Chinese corporate indebtedness and corporates' ability to pay back their liabilities have become a persistent concern for regulators and investors in recent years.
In this paper, we examine the determinants of the pricing of Chinese corporate bonds and potential agency costs arising from implicit government guarantees (IGG) for state owned enterprises (SOEs). We show that the yield of central government SOE bonds is 85 bps lower than that of non-SOE bonds after controlling for firm-specific, bondspecific characteristics, and macroeconomic variables. Further, quantifying IGG with (the lack of) bond yield sensitivity to equity volatility, we present evidence on the dark side of IGGhigh IGG firms are subject to greater agency costs; they are more likely to over-invest to negative NPV project, suffering poor operating performance.

Introduction
The rapid growth in Chinese corporate indebtedness and corporates' ability to pay back their liabilities have become a persistent concern for regulators and investors in recent years. The annual issuance of corporate debt in the amount of 4.3 trillion CNY as of the end of 2017, from 8.5 billion CNY in 2000 1 . Of this total, about 28.6% are central government bonds, 53.5% are local government bonds, and the rest are non-state owned enterprise bonds. It is well known that government tends to bail out state owned enterprises (SOEs) when they are in trouble. In this paper, we examine the determinants of the pricing of Chinese non-financial corporate bonds, which are publicly traded in the interbank bond market as well as the exchange markets, and potential agency costs of implicit government guarantees.
A salient feature of the Chinese financial system is the active involvement of the China's government in the economy (Brunnermeier, Sockin, and Xiong, 2017 Nevertheless, the existence of IGG reduces the connection between bond yields and equity volatility. We, accordingly, measure IGG using bond yield sensitivity to equity volatility. In the subsequent empirical analysis, we demonstrate that the yield spread sensitivity to equity volatility measure can largely capture the benefit of implicit government guarantees. Defining the IGG as the negative equity volatility betas, we show that IGG is positively related to SOE dummy and negatively non-SOE dummy.
Next we examine the effect of government guarantees on firm operating performance. This analysis is motivated by the fact that the presence of implicit government guarantees may foster the agency conflicts between shareholders and bondholders. We find an inverse relation between the magnitude of implicit guarantee of a firm and its operating performance, i.e. the operating performance is relatively lower for SOEs while higher for non-SOEs. We further study the implicit government guarantee effect on stock performance. Interesting, although the difference in operating performance, we find that there is no significant difference in stock performance between SOEs and non-SOEs, suggesting that the implicit government guarantees are perceived by investors. After controlling for bond and firm characteristics, IGG is associated with positive stock performance.
The paper contributes to the literature on implicit government guarantee in several perspectives. First, we find that SOEs enjoy lower debt financing cost than non-SOEs because of the implicit government guarantees from the central and local governments. Second, we propose a simple model and use yield spread sensitivity to equity volatility to quantify the implicit government guarantees. Third, we are among the first to look at the agency cost of implicit government guarantees from the perspective of corporate debt.
The remainder of the paper is organized as follows. Section 2 describes the background of Chinese non-government bond market and reviews the related literature of implicit government guarantees. Section 3 provides empirical framework and hypothesis. Section 4 introduces the data and summary statistics. Section 5 presents our empirical results, and section 6 concludes.

Overview of the Chinese non-government bond market
The Chinese bond market is dominated by government and government-related issues. According to Wind 2016 annual report, the size of the government and government related bonds is about $25 trillion at the end of 2016. While the market share of the corporate bonds is small, it has increased significantly over the last two decades.  (Liao, Liu and Wang, 2014).
According to Zhou and Wang (2000), more than 90% SOE managers are directly appointed by their superior government official. The politician can manipulate the SOEs' behavior through the managers that they appointed. The incentives of SOE managers is to pursue political goods rather than to maximize firm's value. Moreover, local governments are heavily involved in most of the investment decisions of SOEs.
The heavy policy burden, the manager's incompetence, and the collusion between two state agencies (local official and SOE manage) cause the low productivity and poor performance of a SOE.
In addition, the ill-functioning managerial incentive scheme have caused an abnormally high agency costs. SOEs offer low salaries and inflexible compensation to managers. The line between government official and SOE manager is ambiguous, and there are specified salaries for different ranks of government officials. It often happens that a SOE manager is paid according to her rank as government official instead of on her real managerial effort.

Empirical Framework for Implicit Guarantee
We approach the value of implicit guarantee from the perspective of equity volatility. We assume that the value of firm assets (v) follows Geometric Brownian motion. A firm issues debt and the face value of the debt is D. Assume that the bond only defaults at maturity. The value of the firm's debt (d) has the following payoff: We further rewrite the above equation as the following: where p has the following payoff: It should be noted that p is a put option with its exercise price at D. We name it as the default option. In words, debt may be considered as a risk free debt, D, minus value of the default put option. This is consistent with  that the holders of risky corporate bonds can be thought of as owners of riskless bonds who have issued put option to the holders of the firm's equity.
A phenomenon is that Chinese firms, particularly state owned enterprises (SOEs), rarely default their bonds. The first SOE default in 2015 indicates that the government will not fully back the debt of state-owned enterprises. Similarly, few defaults occur in the municipal bond market, and studies attribute the low default of municipal bonds as evidence to potential existence of an implicit government guarantee (IGG). We model IGG (in a particular form) below. If the firm asset value falls below D, but above K (<D), the government will bail out the firm. In other words, the government will not bail out a firm when its asset value is too low (below K, which is the lower bound for a firm to receive implicit guarantee from the government). As a result, we have the following expression for the value of the debt: Accordingly, the value of the guarantee is: g 0  v  K Jointly considering (4) and (5), the presence of guarantee lowers the firm's default probability. We may consider the combination of the default put and the implicit guarantee as a straddle --to short a put option at the exercise price of D (same as the default put) and in the meantime long a put option at the exercise K. The default put option value is reduced by the amount of IGG. We may consider g as a (different) put option that firm obtains from government (a free insurance). With IGG, value of the put option is p -g. Consequently, bond value increases by g, resulting in a lower yield relative to a similar firm without IGG.

Hypotheses
The above framework following  has a clear implication --based on Eq (2), when volatility increases, the value of put option increases, benefiting equityholders at the expenses of bondholders. Bond yields would be highly correlated with equity volatility (precisely, it should be asset volatility). Implicit government guarantees benefit bondholders, increasing bond value and lowering yields of bonds.
This will make bond yields less connected with equity volatility.
Hypothesis 1: Higher IGG indicates lower sensitivity to equity volatility.
A side benefit is that the relationship between bond yields and equity volatility offers us a potential measure of a firm's IGG. Following this idea, we quantify IGG of a firm using the lack of sensitivity in bond yields and equity volatility. This allows us to explore the dark side of an IGG.   In addition, SOEs are more profitable in term of return on assets and return on equity.
The equity volatility is estimated using the 252 days stock daily return.

Empirical Results
In this section, we examine the implicit government guarantees of state-owned enterprises using corporate bond data. First, we examine the relation between bond yield spread and issuer type. Second, following the model described before, we use equity volatility beta as a proxy of implicit guarantee to estimate the size of implicit guarantee. In contrast, we also look at the agency cost of implicit government guarantees by examining their operating and stock performance

Implicit guarantee and yield spread
We begin our empirical analysis by examining the relation between the yield spread and issuer type. Investors have long held the view that the Chinese government would never let large SOEs default since such an event might trigger severe instability or collapse an entire industry or economy. Livingston, Poon and Zhou (2018) find that bonds issued by SOEs receive higher ratings than those by the non-SOEs. We ask whether SOEs can borrow debts at a lower cost than non-SOEs by controlling for firm specific, bond specific and macroeconomic variables. We include a list of independent variables used in , , and Chen, Lesmond and Wei (2007). The regression model is specified as follows: where YS is the bond yield spread of bond i by firm j. The implicit government guarantee effect is estimated by the bond issuer type dummy. We also control a series of independent variables. We consider bond-specific variables, including credit rating, years to maturity and issuance amount. We also include two accounting variables: operating income to sales and long-term debt to assets. To control for macroeconomic variables, we use 1-year treasury rate, the difference between the 10-and 2-year Treasury rates. LG-SOE is a state owned enterprise (SOE) by Chinese local government; and Non-SOE is an issuer not owned by the government. As we discussed earlier, we expect the yield of bonds issued by SOEs is lower than that of non-SOE because of implicit government guarantees. Further, yields of CG-SOE are even lower than that of LG-SOE because these bonds are backed by the central government. We consider bond specific variables: credit ratings, years to maturity and outstanding amount. Bond ratings are divided into 7 categories and we assign integer numbers to the credit rating, AAA=6, AA+=5, AA=4, AA-=3, A+ to A-=2, BBB+ or below=1, not rated=0. Yield spreads are generally negatively related to credit ratings. We also include macroeconomic variables: 1 year treasury rate and the treasury slope, which is the difference between the 10 year and 2 year Treasury rates. Table 5 show the regression results. In column 1 and 3, we use the full sample which includes bonds with all issue types and bond ratings. We find that yield of non-SOE is 103 bps higher than that of CG-SOE after controlling for bond characteristics and macroeconomic variables. In addition, the yield of LG-SOE is about 23 bps point higher than that of CG-SOE. This is consistent with our expectation that SOEs have lower default risk and lower yield spread due to the government support. In column 2 and 4, we use a subsample of enterprise bonds, corporate bonds and medium-term note (MTN), which receive investment grade ratings. The results are consistent with the previous finding. We find SOE bonds tend to have lower yield spread than non-SOE bonds. It may be noted that the coefficient on rating is negative and significant, suggesting that bond yield is negatively related to the credit rating. Issuance amount, which is considered as the measure of liquidity, is negatively related to the yield spread.
In Table 6, we control for both firm and bond specific variables. Since firm specific variables are only available to public listed firms, we end up with a much smaller sample. We have 4975 bond issues in the bond offering sample and 11055 quarter bond trading observations in the bond trading sample. In column 1 and 2, we show the regression results of all bonds issued by public listed firms. Noticeably, the yield spread of non-SOE bonds is 85 bps higher than that of CG-SOE bonds after controlling for bond, firm and macroeconomic variables. Interestingly, in regression 2, equity volatility is not related to yield spread, suggesting that equity volatility has been priced in yield spread or might be explained by other control variables. We further examine the relation between yield spread and issuer type using bond trading data.
The most telling finding is the consistent significance of the issuer type variables. The coefficients on non-SOE and LG-SOE variables are positive and significant, suggesting a higher yield than that of CG-SOE bonds. Consistent with Collin-Dufresne, Goldstein, and Martin (2001) and Chen, Lesmond and Wei (2007), we find that leverage (long term debt to assets) is positively related to yield spread and income to sales are negatively related to the offering yield.

Implicit guarantee and yield spread sensitivity to equity volatility
Following the simple model laid out in the section 3, we use the sensitivity of yield spread to equity volatility to quantify the implicit government guarantee. The sensitivity is estimated as follows: YS = α 0 + β 1 Evol + β 2 Rating + β 3 Size + ϵ where YS is the bond yield spread of bond i by firm j. The equity volatility is estimated using past 252 daily stock return from CSMAR. We further control for bond rating and firm size, which is estimated by the natural log of total assets. Betas are estimated over rolling 4-year periods for each bond and then used in the crosssectional regression. We estimate betas for each corporate bonds that has at least 4 quarterly observations over the 16-quarter window.
In the empirical framework section, we propose the idea that IGG reduce the sensitivity of a firm's bond yields to volatility of the firm's equity. As a result, we quantify the IGG as the negative equity volatility betas.
In Table 4, the average betas of central SOEs and local SOEs are 0.423 and 0.486, respectively; while the average betas of non-SOEs is 0.956. We further examine whether yield spread sensitivity can capture the implicit government guarantee effect. To do so, we estimate the following regression: IGG j = α 0 + β 1 Issuer Dummy + Control + ϵ If IGG is indeed a good proxy of implicit guarantee, non-SOEs would have a high yield sensitivity to equity volatility, while SOEs tend to have relatively low yield sensitivity. The estimated results are reported in Table 7. As expected, non-SOE is associated with lower IGG, i.e. higher yield spread sensitivity. The results remain strong as we use various regression models, including ordinary least square (OLS), random effect, and fixed effect.
With the implicit government guarantees, SOEs can issue bonds at a lower financing cost. On the other hand, IGG may cause high agency cost of SOEs. Debtholders are less concerned with corporate defaults risk because government tends to bail out SOEs when they are financial distress. In addition, the policy burden, incompetence of corporate managers and ill-functioning compensation scheme have caused a significantly high agency costs, which are important contributors to SOE's inefficiency and low productivity.
We examine the operation performance in terms of operating income to sales and return on assets. For each issuer type, we calculate the median operating ratio each year over the sample period from 2006-2016. Figure 1 shows the operating profitability ratios over the sample period. In figure 1.1, the median operating income to sale of non-SOEs (8.03) is significantly higher than that of CG-SOE (5.33) and LG-SOE (6.04), suggesting that non-SOEs are more efficiency in operating income to sales. Similar, we find similar patterns in Figurer 1.2. But the difference of return on assets between SOEs and no-SOEs is narrowing down with the widest spread during 2007-2010. More interestingly, we notice that the difference of return on equity between SOEs and non-SOEs is much smaller in recent years.
We further examine the implicit government guarantee effect on corporate operating profitability. The regression model is specified as follows: OP = α 0 + β 1 IGG + β 2 Control + ϵ where, OP is estimated by three measures of operating profitability: operating income to sales return on assets, and return on equity. We use issue type dummy and yield spread sensitivity as proxy of IGG. We also control for yield spread, leverage (long term debt to assets), natural log of asset, natural log of market capitalization. Table 8 reports regression results. The coefficients in column 1, 3 and 5 on non-SOE and LG-SOE dummy are positive and significant, suggesting non-SOEs and LG-SOE are associated with higher operating profitability ratios than CG-SOEs. It is worth noting that non-SOEs tend to have a much better operating performance after controlling for firm and bond specific variables. For example, the operating income to sales is 6.14% higher than that of central SOEs. In column 2, 4, and 6, coefficients of Beta are negative and significant which shows that SOEs have lower operational profitability when the IGG is high. Consistent with the evidence in Section 5.2, we show that equity volatility Beta is a good proxy to capture the IGG effect. Further, we study the stock performance. Similarly, we calculate the median annual stock return each year for each issuer type. However, in figure 2, we find the annual stock return of SOEs and non-SOEs move almost synchronically over the sample period. Stock return movement reflects the intrinsic value of underlying stock, which is associated with the firm's operating efficiency.
Despite the relatively low operating performance of SOEs, the stock tends to perform similarly non-SOEs. We attribute the synchronically stock performance to the implicit government guarantees. Then we examine the implicit government guarantee effect on stock performance. We estimate the following regression: Ret = α 0 + β 1 IGG + β 2 Control + ϵ where, ret is the stock return in quarter t. We include the IGG proxy (issuer type dummy and yield spread sensitivity), bond and firm-specific characteristics variables. Generally, stock performance is the mirror of the operating performance. In Table 9, we examine the relationship between stock return and IGG proxy. One might expect that investors might perceive the implicit government guarantee. Thus, IGG is associated with positive stock performance. Column 1 is the base model with only bond and firm specific variables. Column 2 we use the issuer type as IGG proxy, while in column 3 we use the equity volatility beta.
Interestingly, we show that coefficient on non-SOE dummy is negative and significant, suggesting that non-SOE is associated with negative stock performance. The coefficient on LG-SOE is negative but insignificant. Central SOEs are backed by the central government with a stronger commitment to bail out the troubled SOEs, but there is no significant difference between LG-SOE and CG-SOE. The equity volatility beta is positive and significant at 5% level, suggesting that Non-SOE firms have poorer stock performance than SOEs, and the less sensitive to equity volatility the higher stock performance. These facts may confirm our thoughts that stock market investors have expectation of implicit government guarantee for SOEs, which results in the higher SOEs stock performance and the contrary operational profits simultaneously.

Conclusion
We examine the determinants of the pricing of Chinese corporate bonds and potential agency costs of implicit government guarantees. We find strong evidence that SOEs enjoy lower debt financing cost. Yield spread of CG-SOE bonds is 14 bps and 85 bps lower than that of LG-SOE and non-SOE, respectively. Our results remain consistent and strong when we control for a series bond-specific, firm-specific and macroeconomic variables.
Building a simple framework which considers the implicit government guarantee as the put option, we use yield spread sensitivity to equity volatility as an proxy for implicit government guarantee. We show that yield spread sensitivity can largely capture the effect of implicit government guarantee. Moreover, we examine the agency cost of implicit government guarantees. SOEs tend to underperform non-SOEs in terms of operating income to sales, return on assets and return on equity. Despite the difference in operating performance, IGG is associated with positive stock performance.

Table 4. Summary Statistics
This table shows summary statistics of bond and firm variables. We include bond offering yield, trading yield, yield spread and credit ratings. Yield spread is then defined as the difference between the bond yield and the associated yield of the treasury yield curve at the same maturity. Bond ratings are divided into 7 categories and we assign integer numbers to the credit rating, AAA=6, AA+=5, AA=4, AA-=3, A+ to A-=2, BBB+ or below=1, not rated=0. We also include total assets (in millions), market cap (in millions), which is the market value of equity, income to sales, return on assets, return on equity, long term debt to assets, daily equity volatility, quarterly stock return and yield spread sensitivity to equity volatility (Beta). LG-SOE is a state owned enterprise (SOE) by Chinese local government; and Non-SOE is an issuer not owned by the government. We consider bond specific variables: credit ratings, years to maturity and outstanding amount. Bond ratings are divided into 7 categories and we assign integer numbers to the credit rating, AAA=6, AA+=5, AA=4, AA-=3, A+ to A-=2, BBB+ or below=1, not rated=0. We also include macroeconomic variables: 1 year treasury rate and the treasury slope, which is the difference between the 10 year and 2 year Treasury rates. We use two different samples: the full sample and a subsample with investment grade enterprise bonds, corporate bonds, and MTN. We use robust standard error to calculate t value. Tstatistics are presented in parentheses. The industry is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively. Offering Yield Spread Trading Yield Spread VARIABLES (1) (2) (3) LG-SOE 0.261*** 0.485*** 0.226*** 0.276*** (16.56) (11.92) (17.21) (9.51) Non-SOE 1.022*** 1.266*** 1.039*** 1.177*** (46.05) (28.05) (52.60) (37.50) Rating -0.054*** -0.364*** -0.460*** -0.351*** (-11.05) (-33.87) (-86.03) (-43.13) Maturity (years) 0.016*** -0.056*** -0.003*** 0.009*** (6.24) (-8.46) (-8.33) (13.66) Log(Amount) -0.385*** -0.198*** -0.274*** -0.403*** (-63.14) (-19  LG-SOE is a state owned enterprise (SOE) by Chinese local government; and Non-SOE is an issuer not owned by the government. We consider bond specific variables: credit ratings, years to maturity and natural log of outstanding amount; firm specific variables: longterm debt to assets and operating income to sales. We also include macroeconomic variables: 1 year treasury rate and the treasury slope, which is the difference between the 10 year and 2 year Treasury rates. We use two different samples: bond offering sample and bond trading sample. We use robust standard error to calculate t value. Tstatistics are presented in parentheses. The industry is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.

Table 8. Regression of IGG and Operating Profitability
This table reports the regression results of IGG effect on operating profitability. The operating profitability are measured by operating income to sales, return on assets and return on equity. We use issuer type dummy and equity sensitivity (beta) as proxy of IGG. CG-SOE is a state owned enterprise (SOE) by Chinese central government; LG-SOE is a state owned enterprise (SOE) by Chinese local government; and Non-SOE is an issuer not owned by the government. We also control other variables, including yield spread, long term debt to assets and the natural log of firm size (assets and market capitalization). We use robust standard error to calculate t value. T-statistics are presented in parentheses. The industry is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively.
(1)  We use issuer type dummy and sensitivity of yield spread to equity (beta) as proxy of IGG. CG-SOE is a state owned enterprise (SOE) by Chinese central government; LG-SOE is a state owned enterprise (SOE) by Chinese local government; and Non-SOE is an issuer not owned by the government. We also control other variables, including bond yield spread, credit rating, long term debt to assets, natural log of total assets, market to boo ratio, and return on equity. We use robust standard error to calculate t value. T-statistics are presented in parentheses. The industry is the fixed effect. *, ** or *** signifies significance at the 10%, 5%, or 1% level, respectively. (1)