The Spillover Effect of Municipal Bond Insurers on Uninsured Municipal Bonds

Transcription

1 The Spillover Effect of Municipal Bond Insurers on Uninsured Municipal Bonds January 8, 2017 Abstract This paper examines the adverse spillover effect of the municipal bond insurance company on uninsured and insured municipal bonds. While previous literatures on bond insurance limit the discussion in the field of insured bonds, we argue that the collapse of insurance companies could lead to concerns about uninsured bonds by weakening the paying ability of bond issuers. Using a municipal bond panel data, we find that the deterioration of bond insurers can significantly lead to higher yields for not only the insured bond but also the uninsured bond. In addition, this spillover may come from both directly and indirectly related insurers. Further investigation on bond liquidity provides evidence that the rising risk of insurance companies could cause the decline in liquidity during the financial crisis. JEL Classification: G01, G12 Keywords: Municipal bond insurance; uninsured municipal bond; spillover effect; CDS spread; liquidity.

2 1 Introduction Almost all the states in the U.S. have both outstanding insured and uninsured municipal bonds at the same time. Although often treated as two distinct groups in the literature, many insured and uninsured municipal bonds are actually subject to the same government s financial condition if they have a common issuer and share similarities if belong to the same series. 1 Based on the link between uninsured and insured bonds, our aim of this paper is to investigate whether the collapse of the insurance companies during the financial crisis spreads to the whole market of municipal bond, including not only insured bonds but also uninsured bonds. Our intuition is that in normal times if the default happens, municipalities might at least rely on insurers to pay off insured bonds, leaving them other resources to tackle obligations on uninsured bonds. However, if insurance companies also get into trouble, it would be like adding insult to injury. Not only this will put municipalities in the exposure of insurers compromised paying ability but may also further force them to bear heavier financial burden. As a result, it may raise concerns about the payment of uninsured bonds. To test our hypotheses of spillover effects, this study seeks to answer three questions. First, does the higher risk of insurance companies increase the yield of uninsured bonds? Second, what are the different roles played by directly and indirectly related insurers? Third, how does the liquidity of uninsured and insured bonds react on the risk of insurance companies? To address these questions, we first calculate probability of default (PD) from spreads of credit default swaps (CDS) as the risk measure of insurers. With the risk measure PD, we could check if higher risk of insurers increases the yield of uninsured municipal bonds. Then, we divide the market PD into two components, the PD of directly related insurers and the PD of indirectly related insurers. We estimate their impacts on the yield to see which part plays a dominant role. Finally, in order to study the liquidity question, we try to estimate whether a higher risk of insurers decreases the liquidity of both uninsured and insured bonds. 1 There are issuers which purchase insurances for bonds with longer maturities but don t so for bonds with shorter maturities even if they belong to the same series. For example, counties of Ottawa and Allegan in state of Michigan issued a series of general obligation bonds for school buildings and site that dated in These bonds share the same cusip number in MSRB but only bonds that mature during , 2016, 2019, 2022 and 2025 are insured. Other than that, all the other characteristics of these insured and uninsured bonds are almost alike. 1

3 Overall, our empirical results strongly support the existence of the spillover effect. First of all, we identify a significant positive relationship between the default risk of insurance companies and the uninsured bond yield. We find that 1 percent increment of the PD increases the yield of uninsured bonds by 0.8 basis points (bps) in normal times and by 2.5 bps in the financial crisis. We also notice that the impact on uninsured bonds is about one fourth of the one on insured bonds in normal periods and is about two fifths during the crisis. Second, from the prospective of involved insurers, our results show that the spillover effect comes from both directly related insurers and indirectly related insurers. The impact from directly related insurers is about 1.5 times larger than the impact from indirectly related insurers. Third, the evidence from the liquidity study shows that the higher risk of insurance companies drives down the liquidity of both uninsured and insured bonds. This study connects to previous literature in several ways. First of all, previous studies have mainly focused on the advantages and disadvantages of insurances to insured bonds (e.g. Thakor (1982), Nanda and Singh (2004), Cole and Officer (1981), Kidwell, Sorensen, and Wachowicz (1987), and Chung, Kao, Wu, and Yeh (2015)). This paper is the first one to examine the spillover effect from insurers to uninsured bonds. In addition, our study extends the literature by providing a further understanding of the magnitude and the sources of the spillover effect. Third, recent papers such as Bergstresser and Shenai (2010), Ang, Bhansali, and Xing (2014), and Namvar, Ye, and Yu (2015) point out that municipal bonds experienced a liquidity declining during the financial crisis. Our results suggest that the spillover effect from the insurance companies might be a possible explanation. The rest of this paper is organized as follows. In the second section, we provide an introduction of the insurance industry and briefly review the relevant literature. In the third section, the data is described. The forth section presents the definition of key measures. Section five provides the empirical models and our estimation results. Section six contains our conclusion. 2 Background and Literature Review 2.1 Introduction of Municipal Bond Insurance Municipal bond insurance is a contract between the muni issuer and the insurance company. Before the bond insurance, issuers or underwriters of the bond have the option 2

4 to pay a premium to the insurance company to have the bond insured. The amount of premium normally depends on the credit quality of the issuer. Once the issuer defaults, meaning that it cannot pay either interests or principal of the bond in a timely manner, the insurer have the obligation to deliver those payments to investors. Not only functions as a way to lower the default risk, insurances grant insured bonds with the enhanced rating that as high as ratings of insurance companies. While many institutions and investors on the market consider only bonds in the investment grade, little known and smaller issuers count on insurances to make their bonds more appealing. During the 45 years of history, monoline insurances companies experienced their waxed and waned. Ever since the first municipal bond insurance took effective in 1971, as shown in Figure 1 by 2006, insurances once dominated the municipal bond market with nearly sixty percent of newly issued bonds are insured. However, in addition to municipal bond insurance, insurers were also involved deeply in collateralized debt obligations. During the financial crisis, this led to substantial loss in revenue and rating downgrades for monoline insurance companies, compounding problems for municipal bond issuers. 2 Ambac, the earliest insurer of municipal bonds, filed for Chapter 11 bankruptcy in November Once an insurance company loss investment grade rating, muni issuers might just lose credit accordingly. According to Standard & Poor s (2012), after the financial crisis, the proportion of new issued municipal bonds that came with insurance drops to 5%. 2.2 Municipal Bond Insurance Literature There are two strands in the existing literature on the municipal bond insurance. The first strand focuses on discussing the benefit of insurances so as to explain the rationality behind the existence of insurances. The advantage has been verified from various angles such as Cole and Officer (1981) and Quigley and Rubinfeld (1991) from the perspective of interest cost saving; Thakor (1982) from signaling effect; Kidwell, Sorensen, and Wachowicz (1987) from the net benefit of insurance after accounting for the insurance premium and Nanda and Singh (2004) from the tax benefit. 2 For example, prior to 2007, there are seven insurance companies who are Aaa rated by Moody s. At the end of 2008, their ratings were as follows. Ambac: Baa1. MBIA: Baa1. FGIC: B1. XLCA: B2. CIFG: Ba2. Only AGC and FSA still had ratings above the investment grade, with Aa2 and Aa3 respectively. 3

5 The collapse of the monoline insurers in the financial crisis inspires another strand of literature which pays more attention to the risk associated with insurance companies. These studies argue that although the municipal bond insurance has long been considered as a shield to prevent the default, insurers are actually not as safe as they were expected and their fragility could exert negative effects on the insured bond. For example, Bergstresser and Shenai (2010) find that the yield of insured bonds is actually higher than that of uninsured bonds after Ambac was downgraded, the yield inversion" phenomena. Although they didn t give any specific reason for the inversion, they point out that the liquidity of insured bonds decreased a lot after 2008 and it might be a cause. Namvar, Ye, and Yu (2015) confirm the existence of the yield inversion". With a reduced-form model, they indicate that the financial crisis, the liquidity factor accounts for a larger proportion in the yield of the insured bonds than that of the uninsured bond. To further explain why the insurance might be the detriment to insured bonds, Brune and Liu (2011) study the yield of insured bonds before and after the rating downgrade of major insures. They find the rating downgrade not only increases the yield of their own insured bonds, but also the yield of bonds covered by other insurers. Chung et al. (2015) point out that the counter-party risk of bond insurers significantly affects the yield of insured bonds. Overall, previous studies have focused on either the benefit of bond insurance or the adverse effect from the insurance market on insured bonds. In contrast, in this study the focus is on the natural linkage between the insured bond and the uninsured bond. In particular, we argue that uninsured bonds are not immune from the fall of insurers as the collapse of insurance industry. We also try to link the decrease in liquidity in the financial crisis to the risk of monoline insurers. 3 Data This analysis utilizes bond-level panel data. We match and merge three data resources as our data: (1) The MSRB database; (2) Markit CDS dataset; and (3) Bloomberg. They are described as follows. The municipal bond transactions data comes from Municipal Securities Rulemaking Board (MSRB). The following information on each transaction was collected: the trade date/time, the settlement date, the CUSIP-9 number for the security, the maturity date, the 4

6 coupon, the transaction price, the bond yield, the trade amount and the trade type. The original MSRB data is from June 1st, 2004 to January 1st, 2011, containing 61,953,024 observations of transactions for different bonds. Filter rules were applied to clean and construct our dataset. First, we delete data with missing information, such as the issuer, the trade date, the maturity date, and the yield. Then we delete observations with abnormal behaviors such as negative days to maturity or more than one maturity date for the same bond. We also keep only non-callable bonds.ăăsince we aim to use a panel data, the time series characteristic requires each bond to have some certain time length. Thus, we require each bond to have at least 5 daily observations to be included in our sample. Finally, for every bond, we combine all its daily transactions into a daily average. The Markit dataset provides us with daily composite CDS spread which is the average across all the quotes from 13 CDS dealers. The data includes CDS spreads on maturities from 6 months to 30 years. It also contains other information on the reference entities, such as the firm name, the credit rating, the maturity, the recovery rate, the ticker and the currency denomination. We utilize the CDS spread data of eight major municipal insurance companies. The eight monoline insurance companies were Assured Guaranty (AGO), Ambac (ABK), Berkshire Hathaway (BRK), Financial Guaranty Insurance Company (FGIC), CIFG Assurance (CIFG), MBIA (MBIA), Radian Group (RDN) and XL Capital Assurance Inc. (XL-CAPASS). Because of the liquidity concern, we use the spread and recovery rate of the five year single name CDS to construct our risk measures. Bloomberg provides us additional information on other characteristics of municipal bonds. Specifically, we collect the issue size, the issue date, the issue state, the bond type, the insurance company name, and bond ratings. We merge all three data sets according to the eight-digit cusip number and the date of trade. Table I provides a detailed statistics summary of our sample. As Panel (a) shows, the final dataset contained 1,743,746 observations from 138,600 bonds in the United States, daily from June 2004 to January This includes 63,038 uninsured bonds from 9,767 issuers, and 75,562 insured bonds from 13,215 issuers. In terms of bond characteristics, insured and uninsured bonds are quite similar in yields and maturity. But uninsured bonds have shorter bond ages, larger issue sizes and trade sizes. These characteristics are controlled in our regressions. Panel (b) of Table I reports the bond number of different bond subgroups. We find insured and uninsured bonds have close distribution among different rating categories and issuer types. 5

7 4 Definition of Key Measures 4.1 Default Risk Measures We use the probability of default implied from the CDS spread of insurers as a proxy for their default risks. Thus, PD is forward-looking and reflects the market expectation of the future default probabilities. The PD of one particular bond insurer i at day t is calculated by using the following formula. PD i,t = 1 e λ i,t T i,t (1) where λ i,t = CDS Spread i,t /(1 Recovery Rate i,t ). T i,t denotes the term to maturity. After we calculate the daily PD for each individual insurance company, we average them to get the market PD. Thus, the market PD at day t is calculated as follows. PD m,t = 1 N t N t i=1 P D i,t (2) where N t is the total number of individual PDs at day t. We use PD m,t as a daily proxy for the default risk of the whole bond insurance industry at day t. we use PDs for most of our regressions, we use CDS spreads as a alternative measure for robust check. 4.2 Liquidity Measures Liquidity is also an important factor affecting the municipal bond yield. 3 We follow Green, Hollifield, and Schürhoff (2007) and use the dealer s markup as our primary liquidity measure. The markup measures the spread of dealeră s purchase and sell price of one transaction. The intuition is that more liquid bonds should have a smaller purchase and sell price difference. To construct the markup measure, we match the purchase and sell transaction pairs based on three matching criteria. We first match the bond purchase and sell transactions if the purchase and sale are of the same amount and occurred on the same day. 3 For example, Wang, Wu, and Zhang (2008) finds that the liquidity premium accounts for about 6 to 20 % of the yield of bonds with A or AA rating. Ang, Bhansali, and Xing (2014) estimates that the liquidity premium is doubled during the financial crisis and drives most of the variations of municipal bond yields. 6

8 We denote these matches as the "immediate match group", following the terminology of Green, Hollifield, and Schürhoff (2007). Then we match each purchase transaction with several consecutive sell transactions if the sum of the consecutive sell amounts is equal to the purchase amount. We denote this group as the "round-trip group". Finally, we match the remaining purchase and sells based on the first-in-first-out (FIFO) principle, i.e., the consecutive sells are matched with the purchases until the purchase amount is met. We denote them as the "FIFO group". We do the matches for all the recorded transactions over the whole sample period. Then for matched pair i, we calculate the markup using the following formula, Markup i = Volume-weighted Average Sell Price i Purchase Price i Purchase Price i (3) Finally, on each day, we equally average all calculated markups for each bond to get the daily markup of that bond. In addition to the markup, we also calculate the Amihud illiquidity measure (AMH Illiquidity) as well as the Pastor and Stambaugh illiquidity measure (PS Illiquidity). Although these two measures are designed for the equity market, they have also been examined in the municipal bond market. 4 Proposed by Amihud (2002), the Amihud illiquidity measure is based on intuition is that a large amount of trading should affect the price of an illiquid asset more than the price of a liquid asset. Thus a larger value of Amihud illiquidity measure indicates that the bond is more illiquid. For each bond i at day t, we calculate the measure as follows, Amihud Illiquidity i,t = 1 N i,t N i,t n=1 Price n,t Price n 1,t Price n 1,t Trade Volume n,t (4) where N i,t is the total number of transactions of bond i at day t, Price n,t is the transaction price of nth trade, Price n 1,t is the transaction price of n 1th trade, and Trade Volume n,t is the trading volume of nth trade. We use a one month rolling window to construct the individual Amihud measure for each bond on every available date. Then for each day, we formulate a market wide Amihud measure by taking the simple average of all individual Amihud measures on that day. 4 See Wang, Wu, and Zhang (2008) and Chung et al. (2015) for the applications in the municipal bond market. 7

9 Proposed by Pastor and Stambaugh (2001), the Pastor and Stambaugh illiquidity measure also reflects the fact that the price of an illiquid asset tends to be more sensitive to trade volumes than that of a liquid asset. PS measure is based on the following regression. Return Excess i,t+1 = Constant+β i,treturn i,t +γ i sign(return Excess i,t ) Trade Volume i,t +ε i,t+1 (5) where Return Excess is the difference between the bond i s return and the market return at i,t time t. sign(return Excess ) is the sign of excess return. It takes 1 if the return is positive and -1 if the return is negative. Trade Volume i,t is the trading volume of bond i at time t. γ i is the PS illiquidity measure reflects the return sensitivity to the trading volume. Larger γ i means less liquidity. We first calculate the daily γ i for each individual municipal bond on a one month rolling window. Then we use the monthly average of all individual γ i as the market PS measure. 5 Empirical Methodology and Estimation Results 5.1 Identifying the Spillover Effect from Municipal Bond Insurers to the Uninsured Municipal Bond In order to verify the existence of the spillover effect, we decompose this question into four hypotheses. We mainly focus on analyzing the relationship between the risk of insurers and the yield of municipal bonds. Our first hypothesis is described as follows: Hypothesis 1. The default risk of municipal bond insurers affects the yield of uninsured municipal bonds. To test Hypothesis 1, we regress the uninsured bond yield on the market PD of muni insurers while controlling the liquidity and bond characteristics. The regression specification is as follows: Uninsured Muni Yield i,t = Constant + β 1 PD m,t 1 + β 2 Crisis Dummy t PD m,t 1 + β 3 Illiquidity t 1 + β 4 Illiquid Dummy t Illiquidity t 1 (6) + Controls i,t + ε i,t 8

10 where i is the bond index, t is the time index. Uninsured Muni Yield i,t represents the yield of uninsured bond i at date t. The PD m is the probability of default of insurers. As described in the previous section, markup is used as the illiquidity measure while Amihud and PS measures are also used for robust check. We also control bond characteristics such as maturity, trading size, issue size, treasury yield, bond credit rating, state rating, bond age, return of the muni index, GO dummy and pre-refunded dummy. The detailed definitions of control variables are given in Table A.1. Coefficient β 1 measures the marginal effect of the default risk of insurers to the yield of uninsured bonds. If there exists a spillover effect, β 1 should be positive and significant. β 2 is the coefficient before the interaction term of the PD m and the financial crisis dummy. A positive β 2 suggests that the spillover effect is magnified during the financial crisis. β 3 represents the marginal effect of liquidity on municipal bond yields. We would expect β 3 to be positive and significant. We consider both OLS model and the fixed effects model. The fixed effect is on the bond issuer level. The standard errors are also clustered on this level. The estimation results for equation 6 are presented in Table II. The first three columns present the OLS results and the last three columns present the fixed effects panel data regression results. Column 4 shows our most representative result. From the table we could observe that the coefficient β 1 is positive and significant across all six specifications. From OLS models to fixed effects models, the value of β 1 ranges from to across different specifications, suggesting that 1 percentage point increment of the market average PD would increase the yield of uninsured municipal bonds by approximately 0.5 to 0.8 bps in the normal time. This result shows that even when the risk of insurers is low, the spillover effect still exists. The yield of uninsured bonds are indeed impacted by the default probability of bond insurers, although with a quite moderate magnitude. Second, we notice that β 2, the coefficient before the interactive term Crisis Dummy PD m, is also significantly positive across all six specifications. We estimate that 1 percentage point increment of the market PD would increase the yield of uninsured bonds by approximately extra 1.7 bps during the crisis period. It means that the spillover effect was actually doubled or even tripled during the crisis, implying serious concern from uninsured bond investors over the default risk of bond insurers. Third, consistent with previous liquidity studies such as Wang, Wu, and Zhang (2008), our results show a positive correlation between the liquidity factor and the municipal 9

11 bond yield. All the coefficients before illiquidity measure are significantly positive. This result is stable regardless of different measure definitions. It means that the liquidity factor contributes to the yield of uninsured bonds. A positive β 4 suggests that investors concern more about the liquidity when the overall liquidity is low. The coefficients of other control variables in general have the expected signs. Overall, these results indicate that the risks of insurance companies indeed affect the yield of uninsured municipal bonds and this correlation was magnified during the crisis period. 5.2 A Comparison of the Effects of Insurers between Uninsured Bonds and Insured Bonds The Effect of Insurers on Insured Municipal Bonds Our previous results suggest that the default risk of bond insurers spills over to the uninsured municipal bond market. Given the direct connection between the insurance and the insured municipal bond, we expect that the default risk of muni insurers also affect the insured municipal bond market. Moreover, the effect on insured bonds should be larger than the one on uninsured bonds. Thus, we propose the following two hypotheses. Hypothesis 2a. The default risk of municipal bond insurers affects the yield of insured municipal bonds. Hypothesis 2b. The default risk of municipal bond insurers should have a larger effect on insured municipal bonds than that on uninsured municipal bonds. To test Hypothesis 2a, we check the relationship between the yield of insured bonds with the PD of their insurance companies. This is similar to the test conducted in Chung et al. (2015). For each bond, we collect the PD of all its directly related insurance companies and calculate a equally-weighted average of them. We use this average as a proxy for the risk of the direct insurers. Then we estimate the following statistical model. Insured Muni Yield i,t = Constant + β 1 PD i,t 1 + β 2 Crisis Dummy t PD i,t 1 + β 3 Illiquidity t 1 + β 4 Illiquid Dummy t Illiquidity t 1 (7) + Controls i,t + ε i,t 10

12 where i is the bond index and t is time index. Insured Muni Yield i,t represents the yield of insured bond i at date t. PD i denotes the individual PD associated with the insured bond i. The control variables are the same as the ones in equation 6. We consider the fixed effect on the bond issuer level and cluster the standard errors at the same level. Table III presents the estimation results for equation 7. The first three columns present the OLS results and the last three columns present the fixed effects panel data regression results. Column 4 contains the most representative result. In general, the results of insured bonds are consistent with our expectations. We find that the coefficients of PD i and Crisis Dummy PD i are positive. The impact on the insured bond yield ranges within 0.26 to 0.63 bps during the normal period, but increases to 1.27 to 1.70 bps during the crisis. Our results show that the risk of insurance companies does influence the yield of insured bonds and that influence became larger in the crisis Comparing the Impacts on Uninsured Bonds and Insured Bonds Although we have already estimated the effect of PD on both uninsured bonds and insured bonds, the coefficients in Table II and III are not directly comparable. The reason is that we use the market PD in the uninsured bond regression but the individual PD in the insured bond regression. To compare the magnitudes of PD on different bonds, we pool both insured and uninsured bond together and regress them against the same market PD. The specification is as follows. Yield i,t = Constant + β 1 PD m,t 1 + β 2 Crisis Dummy t PD m,t 1 + β 3 Insured Dummy i PD m,t 1 + β 4 Crisis Dummy t Insured Dummy i PD m,t 1 (8) + β 5 Illiquidity t 1 + β 6 Illiquid Dummy t Illiquidity t 1 + Controls i,t + ε i,t where i is the bond index and t is the time index. Yield i,t is the yield of municipal bond i at time t. Insured Dummy i equals 1 if the bond is insured and 0 if it is uninsured. It is our intent to focus on β 3 and β 4, which measure the marginal effect of PD on insured bonds compared with the one on uninsured bonds, under the normal period and the crisis period respectively. If Hypothesis 2b is true, then both β 3 and β 4 would be positive and significant. 11

13 The estimation results in Table IV strongly support our hypothesis. The coefficients of the double interaction Insured Dummy PD m and the triple interaction Crisis Dummy Insured Dummy PD m are significantly positive. This suggests the impact of PD on insured bonds is larger than that on uninsured bonds in both normal and crisis periods, which supports Hypothesis 2b. In addition, comparing the coefficients of PD m with Insured Dummy PD m and Crisis Dummy PD m with Insured Dummy PD m, we find that in the normal period, the differences between the effect on uninsured bonds with the one on insured bonds are about to 1 bps (β 3 ), but in the financial crisis, the differences drop to 0.11 to 0.25 bps (β 4 ). One possible explanation might be that if in normal times the uninsured bond investors are not all that bothered about the insurers, they are much bothered in the financial crisis when many insurers got into trouble at the same time. And the small β 4 means that their worries rise sharply during the crisis that it is almost comparable to that of insured bonds. 5.3 Decomposition of the Spillover Effect In the previous sections, we analyzed the overall spillover effect on the uninsured bond. However, we still want to learn more about which group of insurers plays a primary role. In this section, we decompose the market risk of insurers into the PD of directly linked insurers (PD sel f ) and the PD of indirectly linked insurers (PD other ). To be more specific, for a municipal bond issuer, the directly linked insures are the insurance companies with which it does business. All other insurance companies are treated as indirectly linked insurers or other insurers. Our intension is to see whether directly linked insurers and indirectly linked insurers both affect the uninsured bonds. We summarize this intuition into the following hypothesis. Hypothesis 3a. The PD of directly linked insurance companies and the PD of other indirectly linked insurers both affect the yield of uninsured bonds. Hypothesis 3b. For a municipal bond issuer, the PD of directly linked insurance companies should have a larger impact on the yield of uninsured municipal bonds than the PD of other insurance companies. To test Hypothesis 3a, we first restrict our sample to those issuers who have both outstanding insured and uninsured bonds. Then we identify the directly linked insurers and 12

14 indirectly linked insurers for each issuer. To explain how PD sel f and PD other are constructed, we illustrate the definitions as follows. Let us denote the total number of insurance companies on the market as N. Suppose a municipal bond issuer employs N 1 (N 1 < N) insurance companies to insure its bonds. These N 1 insurance companies are grouped as the self related insurers and the remaining N 2 = N N 1 insurers are grouped as other insurers. Thus, the PD sel f and PD other for that issuer at time t are derived as below, N PD m,t = 1 N i=1 N 1 PD i,t = 1 PD i,t + 1 N N i=1 = N 1 N ( 1 N 1 N 1 i=1 N i=n 1 +1 PD i,t PD i,t ) + N 2 N ( 1 N 2 N i=n 1 +1 PD i,t ) (9) = N 1 N PD 1,t + N 2 N PD 2,t = PD sel f,t + PD other,t It is straightforward to see that the sum of PD sel f and PD other equals to the market PD m for each time t. There are two components affecting the value of PD sel f (PD other ), the value of individual PD i (PD j ) and the total number of the insurance companies, N 1 (N 2 ). It is quiet intuitive. In the first case, if either one of their insurers is in trouble, i.e. PD i is large, the PD 1,t will be larger. In the second case, if an issuer employs many insurance companies, i.e. N 1 is large, during the financial crisis when many insurers tend to go wrong at the same time, it may be exposed to higher risks. We calculate the PD sel f and the PD other for all the municipalities which issued both insured and uninsured bond and estimate the following regression model. Uninsured Muni Yield i,t = Constant + β 1 PD sel f,t + β 2 Crisis Dummy t PD sel f,t + β 3 PD other,t + β 4 Crisis Dummy t PD other,t + β 5 Illiquidity t 1 + β 6 Illiquid Dummy t Illiquidity t 1 (10) + Controls i,t + ε i,t 13

15 where i is the bond index and t is the time index. We consider the fixed effect on the bond issuer level. The standard errors are also clustered on this level. We expect all the coefficients with the PDs to be significantly positive and, more importantly, β 1 has a larger magnitude than β 3. Table V provides us with several interesting results. First, consistent with the spillover hypothesis Hypothesis 3a, all the coefficients of PD sel f and PD other are positive and significant. It suggests that not only the directly related insurers but the indirectly related insurers could affect the yield of uninsured bonds. Secondly, β 1 is larger than β 3 while β 2 is larger than β 4. It means that PD sel f always has larger influences than PD other, in both normal period and the crisis period. In addition, we find the difference of impacts between PD sel f and PD other over the uninsured bond becomes smaller in the financial crisis. For example, column (6) shows that in the normal period, the coefficient of PD sel f is while the coefficient of PD other is Thus, the effect of the PD from direct linked insurers is about two times as large as the effect of the PD from other insurers. During the crisis period, the extra effect of PD sel f is and the extra effect of PD other is 0.599, suggesting investors still concern more about self related insurers than indirectly related insurers. However, we could see that the difference between the coefficients of PD sel f and PD other is not as much as before crisis. This might due to the reason that over the normal period, when the default risk of insurers is quite low, investors care more about spillover risk associated with themselves. However, when the default risk of insurers attract more attention, investors become concern about the risk of the overall insurance industry, thus they assign more weights to other insurers. 5.4 The Spillover Effect on Bond Liquidity In the previous sections, we mainly focus on the relationship between insurance companies and the yield of municipal bonds. In this section, we would like to pay some attention to the bond liquidity. The reason is that while insurances are supposed to enhance the municipal bond liquidity, they may backfire when the credibility of insurers are not valid anymore. Could the risk of insurers help to explain the liquidity decline in the financial crisis? We would like to know if it is possible that investors would be reluctant to hold municipal bonds even before the real fundamentals of the issuers become impaired by the troubled insurance company. To study this question, we propose the following hypothesis. 14

16 Hypothesis 4. The default risk of the municipal bond insurers can affect the liquidity of both insured and uninsured municipal bonds. To test Hypothesis 4, we estimate the relationship between bond liquidity and the market PD using the following regression. Liquidity i,t = Constant + β 1 PD m,t 1 + β 2 Crisis Dummy t PD m,t 1 + Controls i,t + ε i,t (11) where the i is the bond index and t is the time index. The markup measure is used as Liquidity i,t, the left hand side variable. If the market PD does affect the muni liquidity, then the coefficients of PD m,t 1 and Crisis Dummy t PD m,t 1 should be both positive. We set the fixed effect on the issuer level and cluster the standard errors on the same level. The estimation result is presented in Table VI. The first two column show how the market PD influences the liquidity of uninsured bonds and the next two columns show the influences to insured bonds. First of all, the coefficients of PD are around 0.8 and significant in all four regressions. This suggests that even during the normal times, insurance companies still has impacts on the liquidity of the uninsured and insured bonds. Second, the coefficients of the cross products Crisis Dummy PD m are also positive across the four regressions. In terms of magnitude, we find the impact of PD on the liquidity is about doubled during the crisis period. Thus, Table VI provides evidence for the hypothesis that the market PD affects bond liquidity and it could be a reason for drawing down the bond liquidity over the financial crisis. 5.5 Robustness Check with Alternative Default Risk Measure For the robustness check, we used the five-year CDS spread of the insurance company in place of the probability of default in all of the previous regressions. The results with the CDS spread are consistent with those using the PD. First, Table A.2 shows that the market CDS spread of the insurers positively affects the uninsured bond yield, i.e., 1 percent increase in the spread increase the uninsured yield by around 0.3 bps in the normal period and about 1.6 bps in the crisis period. Second, Table A.3 shows that the individual CDS spread of the insurers also positively affects the insured bond yield. Third, in terms of magnitudes, Table A.4 implies the market CDS spread has a larger impact on the insured bond yield than the uninsured bond yield in the financial crisis. Moreover, we construct 15

17 the CDS Spread sel f and CDS Spread other in the same spirit of equation 9 and use them to decompose the spillover effect. Table A.5 shows that with their CDS spreads, the directly linked insurers still have a larger impact on the uninsured bond yield than the indirectly linked insurers. Finally, Table A.6 confirms the positive relationship between the CDS spread of insurers and the municipal bond liquidity. In sum, all our previous conclusions hold for the alternative default risk measures. 6 Conclusion This paper examines the spillover effect from municipal bond insurance companies to the uninsured municipal bond. We first identify that the probability of default of insurance companies significantly affects the uninsured municipal bond yield, in both before and during the financial crisis. Through comparison, we also observe that the risk from insurers exerts a larger influence on insured bonds than on uninsured bonds but that difference becomes much smaller over the crisis period. These findings together imply that uninsured bonds and insured bonds should not be treated as unrelated. Moreover, we find that, for bond issuers, spillover may not only comes from their directly linked insurance companies, but could also from other insurance companies. In addition, we propose a reason why the liquidity decrease during the financial crisis. Our investigation of the liquidity shows that the liquidity of both insured and uninsured bonds were greatly drawn down by higher risks of insurance companies. 16

18 References Amihud, Y Illiquidity and stock returns: cross-section and time-series effects. Journal of financial markets 5: Ang, A., V. Bhansali, and Y. Xing The muni bond spread: Credit, liquidity, and tax. Columbia Business School Research Paper. Bergstresser, D., and S. Shenai Financial guarantors and the credit crisis. Brune, C., and P. Liu The contagion effect of default risk insurer downgrades: The impact on insured municipal bonds. Journal of Economics and Business 63: Chung, S.-L., C.-W. Kao, C. Wu, and C.-Y. Yeh Counterparty credit risk in the municipal bond market. Cole, C. W., and D. T. Officer The interest cost effect of private municipal bond insurance. Journal of Risk and Insurance Green, R. C., B. Hollifield, and N. Schürhoff Financial intermediation and the costs of trading in an opaque market. Review of Financial Studies 20: Kidwell, D. S., E. H. Sorensen, and J. M. Wachowicz Estimating the signaling benefits of debt insurance: The case of municipal bonds. Journal of Financial and Quantitative Analysis 22: Namvar, E., X. Ye, and F. Yu Modeling municipal yields with (and without) bond insurance. Available at SSRN Nanda, V., and R. Singh Bond insurance: What is special about munis? The Journal of Finance 59: Pastor, L., and R. F. Stambaugh Liquidity risk and expected stock returns. Working Paper, National Bureau of Economic Research. Quigley, J. M., and D. L. Rubinfeld Private guarantees for municipal bonds: Evidence from the aftermarket. National Tax Journal Standard & Poor s The u.s. bond insurance industry is on a path to reemergence, but of a different profile. Standard & Poor s Rating Reports. 17

19 Thakor, A. V An exploration of competitive signalling equilibria with âăijthird partyâăi information production: The case of debt insurance. The Journal of Finance 37: Wang, J., C. Wu, and F. X. Zhang Liquidity, default, taxes, and yields on municipal bonds. Journal of Banking & Finance 32:

20 Table I Summary Statistics This table reports the summary statistics of our sample. Panel (a) reports the bond number, the issue number, the issuer number, the yield, the maturity, the bond age, the issue size, and the trade size. Panel (b) reports the bond number and percentage by bond ratings, bond types, and bond issuer types. For each variable, we report the corresponding statistics of the whole bond sample, the uninsured bond sample, and the insured bond sample. The sample period is from June 2004 to January Panel (a): Summary Statistics by Insurance Groups All Bonds Uninsured Bonds Insured Bonds Observations Issues Issuers Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation Yield (basis points) Maturity (months) Age (months) Issue Size (millions) Trade Size (millions)

21 Panel (b): Summary Statistics by Bond Ratings, Bond Types, and Issuer Types All Bonds Uninsured Bonds Insured Bonds Number Percentage Number Percentage Number Percentage AAA, AA+, AA, AA % % % A+, A, A % % % BBB % % % BB+, BB, BB-, B+, B, B % % % CCC % % % D % % % NR % % % G.O. Limited % % % G.O. Unlimited % % % Revenue Bonds % % % County Issuer % % % School District % % % Development Authority % % % Redevelopment Authority % % % Water & Sewer System % % % 20

22 Table II Yields of Uninsured Municipal Bond and the Market Default Probabilities of the Insurers This table presents the estimation results of how the yield of uninsured municipal bonds responses to the risks of monoline insurance companies. The yield of uninsured bonds is the dependent variable. We estimate the model with both the OLS regression and the fixed effects panel data regression. For the uninsured bond i, the panel data specification is described as follows. Uninsured Muni Yield i,t = Constant + β 1 PD m,t 1 + β 2 Crisis Dummy t PD m,t 1 + β 3 Illiquidity t 1 + β 4 Illiquid Dummy t Illiquidity t 1 + Controls i,t + α i + ε i,t Columns (1)-(3) present the OLS estimation results and columns (4)-(6) show the fixed effects estimation results. PD m,t denotes the market PD at day t, which equals to the simple average of all individual PDs at the same day. Three illiquidity measures, the markup, the Amihud Illquidity and the PS Illiquidity, are used for the robust purpose. The control variables include the bond maturity, bond trade size, bond issue size, treasury yield, bond credit rating, bond state rating, bond age, return of the muni index, GO dummy and pre-refunded dummy. The definitions of the control vairables are introduced in Table A.1. The standard errors are clustered at the individual issuer level and are reported in the parentheses. *, **, and *** denote the significance level at 10%, 5%, and 1% respectively. Data ranges from June 2004 to January Ordinary Least Squares Fixed Effects Panel Regression (1) (2) (3) (4) (5) (6) PD m (0.081 ) (0.102 ) (0.118 ) (0.064 ) (0.089 ) (0.107 ) Crisis Dummy PD m (0.085 ) (0.086 ) (0.086 ) (0.058 ) (0.057 ) (0.061 ) Markup (0.040 ) (0.042 ) Illiquid Dummy Markup (0.024 ) (0.019 ) AMH Illiquidity (0.019 ) (0.021 ) Illiquid Dummy AMH Illiquidity (0.009 ) (0.008 ) PS Illiquidity (0.129 ) (0.107 ) Illiquid Dummy PS Illiquidity (0.287 ) (0.254 ) Maturity (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) Trade Size (0.004 ) (0.004 ) (0.004 ) (0.002 ) (0.002 ) (0.002 ) Issue Size (0.009 ) (0.009 ) (0.009 ) (0.013 ) (0.013 ) (0.013 ) Treasury (0.011 ) (0.011 ) (0.010 ) (0.008 ) (0.008 ) (0.008 ) Rating (0.013 ) (0.012 ) (0.012 ) (0.022 ) (0.022 ) (0.022 ) State Rating (0.012 ) (0.012 ) (0.012 ) (0.030 ) (0.030 ) (0.030 ) Age (0.010 ) (0.010 ) (0.010 ) (0.007 ) (0.007 ) (0.007 ) Muni Index (0.001 ) (0.001 ) (0.001 ) (0.001 ) (0.001 ) (0.001 ) GO Dummy (0.029 ) (0.029 ) (0.029 ) (0.098 ) (0.100 ) (0.099 ) Pre-refunded Dummy (0.095 ) (0.096 ) (0.096 ) (0.121 ) (0.116 ) (0.121 ) Constant (0.195 ) (0.203 ) (0.194 ) (0.189 ) (0.189 ) (0.192 ) Observations Adjusted R

23 Table III Yields of Insured Municipal Bond and the Market Default Probabilities of the Insurers This table presents the estimation results of the insured municipal bond yields response to the risks of the corresponding insurer. The yield of the insured bond is regressed with respect to the PD of individual insurers, controlling the illiquidity measure and other bond characters. We estimate the model using both the OLS regression and the fixed effects panel data regression. For the insured bond i, the panel data specification is described as follows. Insured Muni Yield i,t = Constant + β 1 PD i,t 1 + β 2 Crisis Dummy t PD i,t 1 + β 3 Illiquidity t 1 + β 4 Illiquid Dummy t Illiquidity t 1 + Controls i,t + α i + ε i,t Columns (1)-(3) present the OLS estimation results and columns (4)-(6) show the fixed effects estimation results. Three illiquidity measures, the markup, the Amihud Illquidity and the PS Illiquidity, are used for the robust purpose. The control variables are the same as Table II. The definitions of the control vairables are introduced in Table A.1. The standard errors are clustered at the individual issuer level and are reported in the parentheses. *, **, and *** denote the significance level at 10%, 5%, and 1% respectively. Data ranges from June 2004 to January Ordinary Least Squares Fixed Effects Panel Regression (1) (2) (3) (4) (5) (6) PD i (0.074 ) (0.073 ) (0.074 ) (0.046 ) (0.052 ) (0.054 ) Crisis Dummy PD i (0.045 ) (0.050 ) (0.051 ) (0.031 ) (0.035 ) (0.035 ) Markup (0.040 ) (0.034 ) Illiquid Dummy Markup (0.018 ) (0.015 ) AMH Illiquidity (0.036 ) (0.027 ) Illiquid Dummy AMH Illiquidity (0.065 ) (0.056 ) PS Illiquidity (0.011 ) (0.008 ) Illiquid Dummy PS Illiquidity (0.030 ) (0.025 ) Maturity (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) Trade Size (0.003 ) (0.003 ) (0.003 ) (0.002 ) (0.002 ) (0.002 ) Issue Size (0.010 ) (0.010 ) (0.010 ) (0.006 ) (0.006 ) (0.006 ) Treasury (0.012 ) (0.012 ) (0.011 ) (0.011 ) (0.010 ) (0.010 ) Rating (0.045 ) (0.045 ) (0.044 ) (0.027 ) (0.026 ) (0.026 ) State Rating (0.010 ) (0.010 ) (0.010 ) (0.018 ) (0.019 ) (0.019 ) Age (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) Muni Index (0.001 ) (0.001 ) (0.001 ) (0.001 ) (0.001 ) (0.001 ) GO Dummy (0.022 ) (0.023 ) (0.023 ) (0.092 ) (0.092 ) (0.089 ) Pre-refunded Dummy (0.063 ) (0.063 ) (0.064 ) (0.136 ) (0.135 ) (0.138 ) Constant (0.278 ) (0.286 ) (0.281 ) (0.196 ) (0.201 ) (0.201 ) Observations Adjusted R

24 Table IV A Comparison of the Responce Among Two Groups in terms of Magitude This table compares the magnitude of insured bond and uninsured bond to the market average PD. Both insured and uninsured bond yields are regressed on the same market PD, the market liquidity variable, and other control variables. For the bond i, the panel data regression is specified as follows. Yield i,t = Constant + β 1 PD m,t 1 + β 2 Crisis Dummy t PD m,t 1 + β 3 Insured Dummy i PD m,t 1 + β 4 Crisis Dummy t Insured Dummy i PD m,t 1 + β 5 Illiquidity t 1 + β 6 Illiquid Dummy t Illiquidity t 1 + Controls i,t + α i + ε i,t Columns (1)-(3) present the OLS estimation results and columns (4)-(6) show the fixed effects estimation results. Three illiquidity measures, the markup, the Amihud Illquidity and the PS Illiquidity, are used for the robust purpose. The control variables are the same as Table II. The definitions of the control vairables are introduced in Table A.1. The standard errors are clustered at the individual issuer level and are reported in the parentheses. *, **, and *** denote the significance level at 10%, 5%, and 1% respectively. Data ranges from June 2004 to January OLS Fixed Effects Panel Regression (1) (2) (3) (4) (5) (6) PD m (0.067 ) (0.062 ) (0.080 ) (0.060 ) (0.070 ) (0.071 ) Crisis Dummy PD m (0.070 ) (0.061 ) (0.071 ) (0.064 ) (0.066 ) (0.065 ) Insured Dummy PD m (0.092 ) (0.083 ) (0.090 ) (0.086 ) (0.088 ) (0.084 ) Crisis Dummy Insured Dummy PD m (0.071 ) (0.068 ) (0.072 ) (0.067 ) (0.071 ) (0.069 ) Markup (0.022 ) (0.020 ) Illiquid Dummy Markup (0.013 ) (0.011 ) AMH Illiquidity (0.019 ) (0.021 ) Illiquid Dummy AMH Illiquidity (0.005 ) (0.006 ) PS Illiquidity (0.001 ) (0.000 ) Illiquid Dummy PS Illiquidity (0.001 ) (0.001 ) Crisis Dummy (0.013 ) (0.013 ) (0.014 ) (0.013 ) (0.012 ) (0.014 ) Insured Dummy (0.012 ) (0.014 ) (0.012 ) (0.015 ) (0.012 ) (0.014 ) Crisis Dummy Insured Dummy (0.013 ) (0.016 ) (0.014 ) (0.015 ) (0.014 ) (0.015 ) Maturity (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) Trade Size (0.002 ) (0.001 ) (0.002 ) (0.001 ) (0.002 ) (0.001 ) Issue Size (0.005 ) (0.007 ) (0.005 ) (0.007 ) (0.005 ) (0.007 ) Treasury (0.007 ) (0.005 ) (0.007 ) (0.004 ) (0.007 ) (0.005 ) Rating (0.009 ) (0.008 ) (0.009 ) (0.008 ) (0.009 ) (0.008 ) State Rating (0.007 ) (0.011 ) (0.007 ) (0.011 ) (0.007 ) (0.012 ) Age (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) (0.000 ) Muni Index (0.001 ) (0.000 ) (0.000 ) (0.000 ) (0.001 ) (0.000 ) GO Dummy (0.017 ) (0.061 ) (0.017 ) (0.063 ) (0.017 ) (0.062 ) Pre-refunded Dummy (0.053 ) (0.070 ) (0.053 ) (0.070 ) (0.054 ) (0.070 ) Constant (0.111 ) (0.119 ) (0.109 ) (0.115 ) (0.123 ) (0.116 ) Observations Adjusted R