Implicit Government Guarantee and the CDS Spreads

It is commonly agreed that the government is more likely to step in and rescue some troubled companies labeled as “too big to fail” or “too interconnected to fail.” Since there is no formal contract between these companies and the government, this potential intervention is referred to as an implicit government guarantee. We propose a new approach of assessing and estimating the implicit government guarantee and analyze whether it is reflected in the CDS spreads. We define the implicit government guarantee for a given company as the probability that the government will bail it out in case of a default. Although the company’s size affects the likelihood of government intervention, we find that financial industry membership is a more important factor. Furthermore, we find that the implicit government guarantee is priced into the CDS spreads. The government guarantee for large companies reduces the CDS spread by 16.11 bps and for small companies only by 3.73 bps. Similarly, for the financial industry, we find that the government guarantee reduces the CDS spread by 76.29 bps and for the nonfinancial industry only by 7.50 bps.


GEORGES TSAFACK
is a visiting professor of finance at the University of Rhode Island in Kingston, RI, and vice president of senior quantitative analysts at State Street Corporation in Boston, MA. gtsafack@suffolk.edu F ailure of some financial and nonfinancial firms may come at a very high cost to society and have spillover effects across all sectors of the economy. To avoid crisis propagation, the government is likely to step in and rescue certain firms deemed "Too Big," "Too Important," or "Too Interconnected" to fail. Since companies do not pay for the possibility of being bailed out by the government, which does not clearly indicate whether it will intervene, it can be considered an implicit government guarantee. The implicit government guarantee may vary from one firm to another depending on the characteristics of the firm, such as the firm size, the sector, and the connection with the overall economy. Government propensity to intervene also changes across time.
One of the side effects of the implicit government guarantee to the firm is that it may lead to a distorted perception of the company's risk of default by investors. The expectation that the government will intervene to protect the firm from failure biases investors' expectations about a company's risk of default downward. A broadly used indicator of the level of a company's perceived default risk is the credit default swap (CDS) spread. The CDS is the contract that protects the CDS buyer against the default of the referenced company. The CDS spread is the premium paid by the CDS buyer to the CDS seller for such protection. Since CDS spreads can be affected by the implicit government guarantee, they may not fully ref lect the underlying default risk of the firm. This has certain implications both from the regulators' and the investors' perspectives.
The contribution of this article is twofold. First, we propose a new way of estimating the implicit government guarantee. The implicit government guarantee remains a public-policy concern because it may involve transfer of resources from the government to bailed-out companies and, as the financial crises of 2007-2009 showed, the costs to taxpayers and society in general can be very high. Therefore, estimating the implicit government guarantee continues to be an important matter. Second, we explore the relationship between the CDS spreads and the implicit government guarantee. Our findings in this area have important implications, for example, for the estimation of default probability and the amount of regulatory capital.
The recent global f inancial crisis sparked a particular interest in estimating the value of the implicit government guarantee, and a number of papers attempted to measure it using different approaches. One group of papers (see, for example, Baker and McArthur [2009], Li et al. [2010] and Noss F ALL 2015 and Sowerbutts [2012]) relates the implicit government guarantee to the cost of funding. They argue that, in the presence of an implicit government guarantee, firms enjoy a reduced cost of funding, and a reduction in the cost of funding ref lects the size of the implicit government guarantee. The actual strategy used for computing the government subsidy varies depending on the study.
For example, Baker and McArthur [2009] use the difference in the funding costs between small and large U.S. banks before and after the Troubled Asset Relief Program (TARP) as an estimate for the subsidy. The main problem with this approach is that it makes an implicit assumption that only large financial institutions receive government support. Haldane [2010] and Ueda and di Mauro [2012] estimate the value of the government subsidy to financial institutions based on the expectations of government support embedded in the company's credit ratings. Credit-rating companies publish individual and support credit ratings. Individual ratings assess a company's strength on a stand-alone basis, whereas support ratings incorporate the probability that the company will receive government support. The implicit government guarantee is estimated as the difference between a bank's cost of funding implied by the support credit rating and the cost of funding implied by the individual credit rating. The general criticism of the rating-based approach is that it is subject to the credit rating agency's judgment regarding a company's creditworthiness; however, credit rating agencies have been known to make mistakes in the past, for example, in rating structured securities.
Another group of papers (see, for example, Gapen [2009], Lucas andMcDonald [2009], andOxera [2011]) attempts to measure the implicit government guarantee by using a contingent claims analysis. They represent the value of the implicit government guarantee as a put option on a firm's assets, with the strike price equal to the firms' default barrier. The firm defaults when the value of its assets falls below some threshold (e.g., promised payment on the debt) at some future time. If at the maturity of the option the firm's assets value is above the default barrier, then the option is not exercised. However, if the firm's asset value falls below the threshold, then the option is exercised, and its payoff is equal to the difference between the strike (the default barrier) and the value of the firm's assets. The implicit government guarantee is estimated as the expected value of the put option payoff.
The contingent claims approach requires modeling the dynamics of a firm's future assets' values. For example, Gapen [2009] uses the Black-Scholes-Merton option pricing model (see Black and Scholes [1973] and Merton [1973]) to compute the value of the implicit government guarantee to Fannie Mae and Freddie Mac. The shortcoming of the Black-Scholes-Merton model is that it assumes that the firm's (log) asset values are normally distributed, which precludes the possibility of sudden changes in the firm's asset values. Both Lucas and McDonald [2009] and Oxera [2011] extend the Black-Scholes-Merton model to incorporate the possibility of jumps in asset prices and investigate a wider range of parameter values. The main problem with the contingent claims approach is that it is very sensitive to the underlying assumptions, and the model tends to get very complex as more realistic assumptions are made.
In this article we propose a different methodology for estimating the implicit government guarantee. We define the implicit government guarantee as the probability that the government will bail out a firm facing default. To estimate the probability of government intervention we use the Logit model, which we apply to a set of 1,209 bankrupt and bailed-out companies between 2000 and 2010. Then, for a sample of companies with publicly available CDS spreads, we construct a government guarantee variable and investigate its relationship with the CDS spreads. Since the government guarantee reduces the risk of a company's default, we expect the CDS spreads to be lower when the probability of government intervention is high-that is, we expect to find a negative relationship between the CDS spreads and the government guarantee variable.
Our definition of the implicit government guarantee differs from previous studies mainly in that it is simpler and more intuitive, and it provides a clear interpretation. For instance, we can define the full government guarantee as a probability of one and no government guarantee as a probability of zero. By focusing on the value of the government guarantee, other studies make it strongly dependent on the company's financial health. Companies in a high-default-risk situation will see the value of their contingent claims increase even if the behavior of the government does not change.
Our empirical analysis shows that, although the company's size affects the likelihood of government intervention, financial industry membership is a more important determinant. Furthermore, we find that the FALL 2015 implicit government guarantee is indeed priced into the CDS spreads, and the relationship is negative. The government guarantee for the large companies reduces the CDS spreads by about 16.11 bps and for the small companies by only about 3.73 bps. Similarly, for the finance industry we find that the government guarantee reduces the CDS spreads by about 76.29 bps and for the non-finance industry by only about 7.5 bps.
We also provide some practical implications of the relationship between the government guarantee and the CSD spreads, from both the investors' and the regulators' perspectives. As CDS spreads are often used in the finance industry to estimate the probability of default (PD) and the amount of regulatory capital, we suggest that some adjustments should be used to account for the fact that the risk levels in the CDS spreads are based on the expectation of potential government intervention. In fact, the PD implied from the CDS spreads may be lower than the actual PD without government intervention. Therefore, we believe that a PD model should control for such a possibility.

ESTIMATION OF THE IMPLICIT GOVERNMENT GUARANTEE
We present the methodology used to estimate the implicit government guarantee before describing the dataset we use in this step.

Methodology
Government guarantee is a concept frequently used to describe government intervention, but measuring it is a difficult issue. As the government makes no explicit commitment to rescue a firm in a default situation, the ex ante assessment of this guarantee is challenging. We define the government guarantee as the probability that the government will step in and rescue a company in distress. To predict the probability of government intervention we use the Logit model, which provides a way to describe a relationship between several independent variables and a binary dependant variable, expressed as a probability. As suggested by the literature and to keep the model parsimonious, we use company size and a dummy variable indicating whether the firm belongs to the finance industry as explanatory variables. We have also experimented with a few other explanatory variables and different models specifications (see Exhibit 1) and chose the more parsimonious model, model 2.
To predict the probability of government intervention we fit the data to the following Logistic function:

E X H I B I T 1 Logit Regression of the Variable "Dum_Bailout" for the Estimation of the Probability of Government Intervention (Government Guarantee) Using the Sample of Bailout and Bankrupt Firms over the Last Decade (2000-2010)
Note: Absolute value of t-statistics in brackets. *significant at 10%; **significant at 5%; ***significant at 1%.
where π g = the probability that the government will step in and rescue the distressed company (government guarantee); lasset = the natural logarithm of the total assets measured via their accounting value; Dum_Finance = the dummy variable indicating whether the company belongs to the financial industry.
After we estimate this logistic equation, the resulting values are used to construct a government guarantee variable for each of the companies that we use in our subsequent research.

Government Guarantee Data
To estimate the implicit government guarantee we use the set of 1,209 companies. This data set includes both bankrupt and bailout companies over the period from 2000 to 2010. We use the list of bankrupt companies from the UCLA-LoPucki Bankruptcy Research Database. 1 We define the bailout companies as all firms bailed out by the government from 2000 to 2010. Any bailout in our study involves an injection of government money. The list of such companies is available from ProPublica's website. 2 We have 884 bankrupt companies; 13.57% of them are from the finance industry. Our data sample also includes 325 companies bailed out by the government; 93.54% of them are financial institutions. The correlation between the finance dummy variable and the bailout dummy variable is 75.48%, and the correlation between the assets size variable and the bailout dummy is 35.96%.

Relationship with the CDS Spread
With the implicit government guarantee, investors adjust their perception of a company's risk of default. To understand whether the implicit government guarantee affects investors' perception of the company's risk of default, we explore the relationship between the government guarantee variable constructed in the previous section and the CDS spreads. The CDS spread is a premium that must be paid by a protection buyer to the protection seller annually over the life of the contract, expressed in basis points. Since the CDS spread is a good proxy for the level of a company's default risk, we expect it to be negatively related to the level of the implicit government guarantee.

The CDS Spread Regression Specification
To relate the CDS spreads to the implicit government guarantee we use a panel regression, a method typically used to analyze multidimensional data. Since our dataset includes both cross-sectional and time series data, the panel regression is a suitable procedure. For our analysis we chose the constant coefficient panel regression model, which is an ordinary least squares (OLS) regression on pooled data. In our regression we include the government guarantee variable as well as additional firm-specific and macroeconomic control variables described in the next section: where π g,i,t-1 = the implicit government guarantee; Firm i,t-1 = the firm-specific variables; and Macro t-1 = the macroeconomic variables.
We define the CS i,t as a relative CDS spread of company i at time t. 3 The relative CDS spread is computed by taking the midpoint between the bid and the ask quotes for the firm and dividing it by the five-year T-bond rate. The main rationale for such a definition of the relative CDS spread is that the CDS spread is approximately the difference between the corporate bond yield and the risk-free rate.
Note that all the explanatory variables are lagged by one time period (i.e., one day). This is done to avoid the simultaneity problem. We first run the regression with only the government guarantee variable. Then, we add various firm-specific control variables, such as equity volatility, firm credit ratings, leverage, and various macroeconomic variables as suggested by the empirical literature.

CDS Data
Our CDS data sample consists of the U.S. companies listed on Bloomberg as of May 2010. We use daily data for the period from January 2000 through May 2010, and we focus on five-year CDS contracts. The CDS data were available for 1,421 companies in nine FALL 2015 industry segments. However, not every company offered information about all other independent variables. Out of 1,421 filings, only 363 offered insight into their historical CDS spreads as well as all other independent variables. In our analysis we used only complete listings, so our final sample consists of 363 firms. Out of these firms, about 10% come from the finance industry. Note that companies that offered limited CDS data were included into the data sample. Therefore, the resulting data set is unbalanced.

Firm-Specific Variables
In our regressions we use a number of firm-specific control variables that can potentially explain the variation of the CDS spreads.
1. Equity Implied Volatility. Zhang et al. [2009] find that volatility risk alone predicts about 50% of the variation in the CDS spread levels. Furthermore, Cao et al. [2010] find that put-option implied volatility dominates historical volatility in explaining the time-series variation in CDS spreads. In our study we use the average daily implied volatility of the firm call and put options available from Bloomberg as a proxy for volatility. 4 We expect this to be positively related to the CDS spreads because higher volatility increases the probability of a firm's default. 2. Leverage. We compute the leverage ratio as a ratio of Total Liabilities to Total Assets. The data were obtained from COMPUSTAT. Since accounting data is only available at the quarterly level, we use linear interpolation to obtain daily data. Just like equity return, leverage can be used as an indicator of a firm's financial health. We expect a positive relationship between a firm's leverage and the CDS spreads. 3. Credit Ratings. Credit ratings ref lect the general credit worthiness of a company and its ability to make payments. In our regressions we use a dummy variable that takes the value of 1 if a company's credit rating is A-or higher, and 0 if it is below. The credit rating data were collected from Bloomberg. We use ratings provided by Standard & Poor's (S&P's) rating agency where available; when ratings by S&P are not available, we use ratings by Moody's. We expect a negative r elationship between the CDS spreads and the company's credit rating. 4. Liquidity Risk. Liquidity risk can be thought of as an ability to trade large quantities of securities quickly without causing significant changes in market prices. We compute the liquidity risk as the CDS bid-ask spread divided by the mid-value of the bid and ask. Bid-ask spread is the most widely used proxy for liquidity risk. A security is considered to be liquid if it has a small bid-ask spread. The literature on whether liquidity should have a positive or negative effect on CDS spreads is ambiguous. For example, Tang and Yan [2007] find that relative CDS spreads tend to increase with the bid-ask spread. Acharya and Johnson [2007] find a weak negative relationship between CDS spreads and the relative bid-ask spread. More recently, Pires et al. [2011] find that CDS premiums increase with the absolute bid-ask spreads and decrease with the relative bid-ask spreads.

Macroeconomic Variables
In our analysis we also control for four macroeconomic variables that can potentially explain the variations in the CDS spreads. All of our macroeconomic data were obtained from Bloomberg. We discuss each of these variables individually: 1. Treasury rate. In our analysis we use a series of five-year Treasury rates. The literature on whether spot interest rates should have a positive or negative effect on CDS spreads is ambiguous. Longstaff and Schwartz [1995] find that credit spreads are negatively related to interest rates because higher interest rates reduce the probability of default, which in turn reduces credit spreads. A negative relationship was also found by Collin-Dufresne et al. [2001] and Ericsson et al. [2009]. However, high interest rates can also be related to tightened monetary policy. For example, Zhang et al. [2009] find that short term interest rates have significant positive effects on CDS spreads, which they connect to changes in monetary policy. 2. Short-term interest rate. We use a six-month London Interbank Offered Rate (Libor) rate. Its effect on the CDS spreads is ambiguous due to the same reasoning as for the Treasury rate.
3. Slope of the Treasury yield curve. We compute the slope of the treasury yield curve as the difference between a 10-year Treasury rate and a 2-year Treasury rate. The slope of the yield curve is an indicator of expectation of future interest rates. The expected effect of the slope on the CDS spreads is ambiguous. The slope can be considered an indicator of overall economic health. If the term structure has a positive slope, this is considered to be an indicator of "good times." If this is the case, the relationship between the slope and the CDS spreads should be negative. A significant negative relationship between the slope of the yield curve and CDS spreads was found, for example, by Cao et al. [2010]. However, the positive slope of the yield curve can also be connected to the economic environment with rising inf lation and tightened monetary policy. In this case the relationship between the slope and the CDS spreads will be positive. A significant positive relationship between the slope of the yield curve and CDS spreads was found, for example, by Zhang et al. [2009]. 4. S&P 500 daily return. We use closing values of the S&P 500 index to compute the S&P 500 daily return. Since higher market returns are related to improved market conditions, we expect a negative relationship between index returns and CDS spreads.

Summary Statistics
Exhibit 2 presents the summary statistics of the CDS spreads and explanatory variables used in the CDS regressions. Due to missing observations, we have to deal with unbalanced panel data. The number of firms with a representative number of observations varies depending on the variable. The portion of the finance companies in our CDS data sample is about 10%, and about 39% of the firms have a credit rating of A-or higher. The average company size is small, with about $16,800 million in total assets, on average. The average CDS spread is 152.16 basis points with a large standard deviation. The mean leverage for all companies is about 66%, and average equity volatility is about 38%.

EMPIRICAL ANALYSIS
The empirical analysis follows the steps defined previously. We investigate the implicit government guarantee results first, and then analyze its relation with CDS spreads.

Implicit Government Guarantee
Consistent with the common belief, we find that both a firm's size and its finance industry membership are related positively to the implicit government guarantee (see Exhibit 1). Analyzing the size effect on the

E X H I B I T 2 Summary Statistics
FALL 2015 financial and non-financial industry, we find no evidence of a significant difference between the two (see Exhibit 1, Model 1). The best model specification is Model 2, which estimates the government guarantee based on the size variable and the dummy variable of finance industry membership; therefore, this is the specification we use in our further analysis. 5 We construct the implicit government guarantee variable for the sample of 363 firms. The average probability of a government bailout for all firms between 2000 and 2010 is 0.1155 (see Exhibit 3). However, the average government guarantee varies significantly depending on whether the firm belongs to the finance industry. We find that the average government guarantee for finance firms is 0.8279, whereas for non-finance firms it is only 0.0181.
The government guarantee also varies by credit worthiness of the company. We find that companies with higher credit ratings are slightly more likely to be bailed out by the government. The same result holds for both finance and non-finance companies. Additionally, we observe that the government guarantee depends on a company's size, with large companies being more likely to receive a government bailout (see Exhibit 4). This result holds for both finance and non-finance firms.
Exhibit 5 analyzes the evolution of the implicit government guarantee across time for all companies, and separately for finance and non-finance firms. We observe that there was a downward shift in the probability of a government bailout after the latest financial crisis. This effect is more pronounced for non-financial firms. For financial firms we observe some decrease in the implicit government guarantee in 2007-2008 and an increase in 2009. Our data sample is dominated by small non-financial firms. Many similar firms failed and were not bailed out by the government during the latest financial crisis. Most of the firms that received government subsidies were financial firms. This is consistent with the high probability of a government bailout for financial firms and the low probability for non-financial firms that we observe.
The relative stability of the bailout probability for finance companies may seem counterintuitive. In the political environment of 2007-2008, the debate about the end of "Too Big to Fail" led some investors to lower their expectations about the probability of government intervention. Furthermore, letting Lehman Brothers

E X H I B I T 4 Average Implicit Government Guarantee by Firm Size, Finance Membership, and Firm Rating E X H I B I T 3 Average Implicit Government Guarantee by Industry and Credit Ratings
collapse sent a negative signal that weakened the government guarantee. At the same time, the government passed a bailout plan to save the financial system. This somewhat mitigated the drop in probability of government intervention for financial companies, even though the overall probability decreased. This result is particularly interesting in the sense that it confirms that during the crisis the concept of "Too Big to Fail" was questioned, while, at the same time, financial companies remained more likely to be bailed out.

The CDS Spread Regressions
Our main findings from the regressions that relate the CDS spreads to the implicit government guarantee and other firm-specific and macroeconomic variables are reported in Exhibit 6. Model 1 is a base-line regression of the CDS spreads against the implicit government guarantee; Model 2 adds the firm-specific control variables to the base model; Model 3 adds macroeconomic control variables to the base model; Model 4 adds all of the control variables to the base model; and Model 5 analyzes the effects of the business cycle. Empirical results show that relative CDS spreads are strongly negatively related to the implicit government guarantee. This result holds across all model specifications, and the effect remains strong even after including all of the control variables. This means that the higher the likelihood that the government will step in and rescue the troubled company, the less the company is viewed as risky and the lower the price of the default risk associated with its bonds.
The effects of all the control variables are consistent with general intuition and expectations based on relevant literature. All firm-specific variables are highly significant in any model specification. The equity volatility coefficient is positive, which is in line with Zhang et al. [2009], who found that volatility is the main driving factor of CDS spreads. The leverage coefficient

E X H I B I T 5 Average Implicit Government Guarantee across Time for All Firms, Finance, and Non-Finance Firms
FALL 2015 is also positive, which is consistent with the Merton [1974] framework that predicts higher vulnerability of a firm when its leverage ratio increases and approaches unity. As expected, credit ratings are negatively related to CDS spreads, indicating that firms with higher credit ratings have lower CDS spreads.
Finally, we find that the liquidity coefficient is positive, demonstrating that a firm's illiquidity increases the CDS spreads. Coefficients associated with the interest rates and the slope macroeconomic variables are all negative and highly significant in all model specifications. Both the short term interest rate represented by the Libor rate and the five-year T-bond rate are negative related with the CDS spreads, which is consistent with Longstaff and Schwartz [1995], Longstaff et al. [2005], and others who found that an increase in interest rates reduces a company's default probability, which, in turn, reduces the credit spreads. The coefficient of the slope variable is also negative, which is consistent with the interpretation of the slope variable as an indicator of "good times." Finally, the S&P 500 return coefficient is negative, just as expected, but insignificant.
To relate the government guarantee to the business cycle-specifically, how government actions affect

E X H I B I T 6 Robust OLS Regression of Relative CDS Spread on Government Guarantee, Firm Characteristics, and Some Macro-Variables. Independent Variables are Delayed by One Lag (day)
F ALL 2015 CDS spreads during an economic crisis-we introduce a dummy variable to account for the changes after January 2007. The results in Exhibit 6 show a stronger effect of the government guarantee on CDS spreads after this date, suggesting that just before or during the crisis investors price the government guarantee more.
To analyze the industry and the size effect on CDS spreads we split our data sample into financial and nonfinancial firms, and into small and large firms. To split the dataset into large and small companies we used the cutoff value of lasset at 9.9214, which is our data set median. The average value of the lasset variable for the "small" dataset is 8.7767 and the average lasset value for the "large" data set is 11.3550. The regression results are reported in Exhibit 7. They show that the government guarantee variable is significant for all four regressions, and the rest of the control variables (except for the S&P 500 return variable) are all highly significant and have expected signs. The effect of the government guarantee is larger for the large companies.
To get the actual contribution of the government guarantee to the CDS spreads, we can multiply the regression coefficients by the average government guarantee for the data sample and then by the average five-year T-bond rate. The government guarantee for the large companies reduces the CDS spread by about 16.11 bps and for the small companies only by about 3.73 bps. Similarly, for the finance industry we obtain that the government guarantee reduces the CDS spread by about 76.29 bps and for the non-finance industry only by about 7.50 bps. This suggests that the size of a company ("Too Big to Fail") affects the CDS spreads mainly within the financial industry. As financial firms are usually more connected with the whole economy, this can be seen as the "Too Interconnected to Fail" implication.

E X H I B I T 7 Robust OLS Regression of the Relative CDS Spread on Government Guarantee, Firm Characteristics, and Some Macro-Variables. Independent Variables are Lagged by One Day
Note: Robust t statistics in parentheses. *significant at 10%; **significant at 5%; ***significant at 1%.

OTHER IMPLICATIONS OF THE IMPLICIT GOVERNMENT GUARANTEE AND ITS RELATIONSHIP WITH THE CDS SPREADS
A company's gain from government intervention goes beyond the cash it receives for its rescue. The company will have a direct benefit from its own bailout and an indirect benefit from the rescue of the system. When appropriate, government intervention eventually creates additional value for the system as a whole. For instance, Veronesi and Zingales [2010] estimate that U.S. government intervention in the financial sector, which was announced in 2008, increased the value of banks' financial claims by $131 billion at a cost to taxpayers of $25-$47 billion, with a net benefit between $84 and $107 billion. Previously, O'Hara and Shaw [1990] found that the Comptroller of the Currency's 1984 public announcement that the 11 largest banks were "Too Big to Fail" increased valuation of these banks by 1.3% on average and decreased valuation of those banks suspected not to be in that group.

Investors Perspective
Ex ante, the estimate of the dollar value of the government guarantee for a given firm should account for both direct and indirect benefits. Although the direct gain can be inferred from the amount used to bail the company out, it is difficult to estimate the indirect gain, as this includes systemic factors and the interconnection among the companies. In efficient markets the overall benefit of a government guarantee should be ref lected in the CDS spreads.
Our approach can help estimate the dollar value of an implicit government guarantee for bondholders using the relationship among the CDS spread, the probability of default, and the bond yield. 6 When the government guarantee becomes explicit (e.g., after a bailout plan announcement), the impact on the probability of default can be derived using the risk-neutral implied volatility. For instance, Veronesi and Zingales [2010] estimate that the announcement of the 2008 bailout decreased the default probability of the eight biggest U.S. financial institutions on average by more than half, with Morgan Stanley as the biggest beneficiary.
Although bondholders extract significant gain from government intervention through the reduction of the CDS spreads, this is less likely the case for shareholders, as the government maintains a share of the company at a cheap price during the process. This implies that an equity portfolio can be hedged by bond-related products to mitigate the risk in case of a bailout.
Our results show a strong relationship between the state of the economy and the impact of the government guarantee on CDS spreads. We find that after January 2007, investors strongly priced the likelihood of the government stepping in. As noted earlier, this may be due to the increase in indirect benefits, as any potential bailout would be large and involve many companies in the system. This finding is another indication in favor of appropriate diversification between equity and bonds, especially using products from the finance sector, which is more likely to be rescued in case of trouble.

Regulator Perspective
The implicit government guarantee poses a serious issue for regulators, as it may lead to a moral hazard problem associated with the management of "Too-Bigto-Fail" and "Too-Interconnected-to-Fail" companies. Although the expectation that the government will intervene has a positive impact on the financial system, as it reduces the risk of bankruptcy and increases the enterprise value, the cost is usually supported by the taxpayers.
Another implication of the relationship between the government guarantee and the CDS spread is for the regulatory capital, whose estimation is based on the assessment of the default risk. Implying the default risk of a company from the CDS spreads incorporates the implicit government guarantee. This can lead to an underestimation of the actual probability of default (without government intervention). As regulators should protect both Wall Street and Main Street, having an estimate of the risk of default without government intervention at the expense of taxpayers is more appropriate. Therefore, the probability of default implied from the CDS spreads should be adjusted to account for potential government intervention. Although the actual steps for such adjustment are beyond the scope of this article, we provide some insights for this exercise.

CONCLUSION
After providing a formal intuitive definition of the implicit government guarantee, we use a simple and well-elaborated approach to estimate it. Unlike other papers that assess the implicit government guarantee in terms of its value, we define it as the likelihood of the government to step in and rescue a troubled company. Using a unique sample of data on bailout and bankrupt companies, we estimate a logistic function to characterize the implicit government guarantee for any company in relation to its size and finance industry membership. In the second step we relate the CDS spreads to the implicit government guarantee, and control with the traditional variables.
Empirical results show that a company's size is secondary in the government's decision to bail it out; the main decisive factor is whether the firm belongs to the finance industry. Although companies with high ratings are more likely to be rescued, their advantage over low-rated companies is very small. We also find that the implicit government guarantee is priced in CDS spreads, especially of financial companies, and therefore, a firm's probability of default implied by CDS spreads may be biased.
An important implication of our research is related to the regulatory capital which, when implied from CDS spreads, should be adjusted to account for the implicit government guarantee. How to perform such an adjustment and how to relate this new measure of the government guarantee to the actual value of the bailout with its relation to the business cycle are challenging issues that will be addressed in our future research. ENDNOTES 1 A sample of bankrupt companies' data can be found on the website: http://lopucki.law.ucla.edu/. A full list can be obtained by emailing the website author.
2 For the list of government bailout companies, follow the link: http://www.propublica.org/special/governmentbailouts. Here, bailouts are defined by specific programs (e.g., TARP) through which the government provides financial help to prevent companies from defaulting. 3 We use the relative CDS spread instead of the absolute spread to control for the risk-free rate over which the spread is implicitly based. Although the absolute CDS spread should provide a good estimate of the risk level across firms at a given point in time, from a time series perspective the level of the risk-free rate may affect the spread, as investors tend to make a tradeoff between corporate bonds and treasuries. For the same corporate risk level, investors will require a larger spread to switch to corporate bonds when the Treasury rate is larger. For instance, let's suppose that for a given company on Day 1 the risk-free rate is 0.2% and the CDS spread is 1%, whereas on Day 2 the risk-free rate is 5%. Assuming that the underlying risk level for that company remains the same for these two days, an investor who on Day 1 was indifferent between the 0.2% interest rate on Treasury and the 1.2% yield on corporate bonds will more likely prefer the 5% interest rate on the Treasury to the 6% yield on the corporate bond. This will push the yield higher, and the spread (which follows the difference from the Treasury rate) will increase. The relative CDS spread is a way to adjust for this time-varying effect of the risk-free rate, while remaining equivalent to the absolute CDS spread in cross-section. One may think of a linear adjustment and assume that the Treasury rate as a regressand is sufficient; however, we believe that a proportional adjustment is more appropriate. 4 Bloomberg uses closest to at-the-money options for computing implied volatility. 5 The choice of Model 2 is justified by its parsimony. Although Model 1 has a slightly higher pseudo-R 2 , a test comparing both models shows that the difference is not significant enough to justify the inclusion of the additional variable. Moreover, the size and the finance membership variables display significant relation, as evident from their respective t-statistics. 6 For details about the link among the CDS spread, the probability of default, and the bond yield, see Hull [2010].