Counterparty Credit Risk in the Municipal Bond ...

Counterparty Credit Risk in the Municipal Bond Market

San-Lin Chung Professor of Finance Department of Finance College of Management National Taiwan University 85, Section 4, Roosevelt Road, Taipei 106, Taiwan, R.O.C. Tel: 886-2-33661084 E-mail: [email protected] Chen-Wei Kao Research Associate Department of Finance College of Management National Chung Hsing University 250 Kuo Kuang Rd., Taichung 402, Taiwan, R.O.C. TEL: 886-4-22855308 E-mail: [email protected] Chunchi Wu M&T Chair in Banking and Finance Department of Finance and Managerial Economics School of Management State University of New York at Buffalo Buffalo, New York 14260-4000 Tel: 716-645-0448 Email: [email protected] and Chung-Ying Yeh Associate Professor of Finance Department of Finance College of Management National Chung Hsing University 250 Kuo Kuang Rd., Taichung 402, Taiwan, R.O.C. TEL: 886-4-22855308 E-mail: [email protected]

I. Introduction A growing body of evidence shows that counterparty risk has emerged as an increasingly important factor driving the financial market (see, for example, Jorion and Zhang, 2007, 2009; Duffie and Zhu, 2011; Arora, Gandhi, and Longstaff, 2012; and Gorton and Metrick, 2012).

Counterparty risk is the risk that the default of a firm’s counterparty affects its own default probability. In a narrow sense, this refers to the situation that a firm’s default risk is affected by the fate of its direct counterparty. However, in a broader scope, a firm’s default risk is exposed to systemic risk propagated by a chain of counterparty reactions. When firms are interconnected, a single large default can trigger a cascade of defaults. This cascading effect can be quite severe when the market is in stress, leading to a widespread increase in default risk of firms and their cost of capital. The importance of counterparty risk is evidenced by prominent events such as the Asian and Russian financial crises and more recently, the downfall of Bear Stearns and Lehman Brothers during the subprime crisis. Whether or not counterparty risk is priced in the securities market is an important issue in asset pricing. A number of studies have investigated this issue (see, among others, Duffie and Huang, 1996; Jarrow and Yu, 2001; Hull and White, 2001; Brigo and Pallavicini, 2006; Kraft and Steffensen, 2007; Yu, 2007; Segoviano and Singh, 2008; Arora, Gandhi, and Longstaff, 2012; Gorton and Metrick, 2012). Most of these studies have focused on the effect of counterparty risk on yield spreads or derivatives pricing. Empirical evidence regarding the importance of counterparty risk is mixed. While some studies have documented a significant counterparty risk effect, others have found that this effect is trivial (see Hull and White, 2001; Kraft and Steffensen, 2007; Arora, Gandhi, and Longstaff, 2012; Gorton and Metrick, 2012). Despite the extensive literature on counterparty risk, there has been little research on the effect of this risk in the municipal bond market. The traditional literature on municipal bonds has 1

focused on the effects of taxes, ratings and bond characteristics on pricing. 1 More recent research has been devoted to the study of municipal bond market structure and its effect on the cost of trading, pricing of new issues, and price discovery (see Harris and Piwowar, 2006; Green, 2007; Green, Hollifield, and Schurhoff, 2007a, 2007b; Green, Li, and Schurhoff, 2010). In this paper, we focus on the effect of insurer-related counterparty risk on the pricing of municipal bonds. The insured municipal bond can be viewed as a portfolio of an uninsured municipal bond and insurance provided by a monoline insurer. The insurance component resembles the credit default swap of corporate bonds. Hence, the insurer credit risk is analogous to the counterparty risk in the credit default swap (CDS) market. Because of this similarity, we refer to the insurer’s credit risk simply as the insurer-specific counterparty risk. Besides this risk, a default by an insurer can trigger chain reactions of other firms in the insurance and financial markets. We refer to this marketwide counterparty risk as systemic risk. There has been considerable interest in understanding the role of counterparty risk in the pricing of credit default swaps (Segoviano and Singh, 2008; Stulz, 2010; Pu, Wang and Wu, 2011; Arora, Gandhi, and Longstaff, 2012), bonds (Jarrow and Yu, 2001; Krishnamurthy, 2010), repurchase agreements and asset-backed securities (Gorton and Metrick, 2012). As the insurer-related counterparty risk is similar by nature to counterparty risk in credit markets, our findings provide relevant policy implications for regulating financial markets. While the CDS contract and municipal bond insurance share some common features in a default insurance contract,2 there are notable institutional and structural differences between the two. For instance, CDS insurers provide collateral while insurers in the municipal bond market

1

See Livingston (1982), Arak and Guentner (1983), Kidwell and Koch (1983), Skelton (1983), Stock and Schrems (1984), Poterba (1986, 1989), Kochin and Parks (1988), Stock (1994), among others. 2 For example, the insured event (default), the insurance premium, the limit on the covered loss (notional amount) and risk sharing are similar. 2

do not. CDS contracts can be easily traded but bond insurance contracts cannot. Credit risk in CDSs can be transferred or swapped many times among many parties but this is much harder for bond insurance contracts. The total notional amount of CDS can be much larger than the amount of risk insured and CDS trading can result in a chain of swaps which amplifies counterparty risk as these risks may not net out. Due to these subtle differences, the effect of insurer-related counterparty risk in the bond insurance business will likely differ from that in the credit derivatives market. As an example, an increase in insurers’ default risk can affect not only default risk but also liquidity of insured bonds as insurers perform the functions of both credit and liquidity enhancements. In this paper, we examine the effect of insurer-related counterparty risk on municipal bond pricing. 3 The counterparty risk that we investigate in this paper includes the effects of both insurer-specific risk and systemic counterparty risk. The former is associated with the effect of insurer-specific credit quality while the latter reflects the effect of contagion transmitted through the counterparty chain. Recent studies have found that the effect of systemic counterparty risk can be substantial, especially in times of stress (see Krishnamurthy, 2010; Gorton and Metrick, 2012). The systemic risk effect is potentially more important in bond insurance business because monoline insurers are subject to the same regulations of capital and risk assessment and undertake similar strategies which create high correlation among them. Understanding how credit risk of insurers affects the effectiveness of bond insurance and the soundness of the insurance market is important for investors and regulators of municipal bonds whose market size is now close to 4 trillion (USD). Privately sold bond insurance is the primary form of credit enhancement for municipal bonds. A large proportion of municipal bonds are

3

Our focus on the effect of counterparty risk differentiates our study from other studies on the benefit of insurance (e.g., Bergstresser et al., 2010; Wickoff, 2011). 3

insured at the time of issuance but the insurer’s financial condition changes over time. Bond insurance can enhance ratings and liquidity if insurers are financially sound. Past studies have suggested that insurance adds value (see, for example, Thakor, 1982; Nanda and Singh, 2004; Pirinsky and Wang, 2011). However, these findings are largely based on the premise that bond insurers are default free, an assumption which has been called into question lately. We examine the effect of counterparty risk on the pricing of municipal bonds using a comprehensive data set provided by the Municipal Securities Rulemaking Board (MSRB) that consists of transaction prices of bonds, and the CDS data provided by Markit for the insurers selling credit protection for municipal bonds. CDS contracts written for bond insurers offer a protection to the counterparty in the event of insurer default. Hence, the CDS price is an excellent measure of the insurer-related counterparty risk. Our paper represents the first effort to use this important information for the insurer’s credit risk to study the effect of counterparty risk in the municipal bond market. Our sample period is from July 2004 to January 2011, which encompasses the whole subprime crisis period, making it particularly suitable for exploring the effect of counterparty risk on municipal bond pricing in both normal and crisis times. Our paper documents several unique findings that contribute to the literature. First, we find that counterparty risk is important for the pricing of municipal bonds. The effect of this risk is significant even in the normal period and amplifies during the subprime crisis. More importantly, the counterparty risk effect contains both insurer-specific and systemic components. Empirical results show that the effect of systemic risk is significant over and beyond the effect of the insurer-specific counterparty risk. The size of counterparty risk premiums is of economic significance and much larger than that estimated for the CDS and repo markets. Second, the importance of counterparty risk varies across bonds of different characteristics.

4

Counterparty risk premiums are higher for speculative-grade and illiquid municipal bonds. As insurance is more beneficial for these bonds, their yields are more sensitive to unexpected changes in insurer-specific counterparty risk. The insurer-specific risk is also more important for bond issued in states with severe budget deficits. On the other hand, yields of municipal bonds held by institutions such as mutual funds, exchange traded funds (ETF) and property and causality insurers, are less sensitive to the insurer-related counterparty risk. Third, the significance of counterparty credit risk effect is robust to different controls for the effects of illiquidity, bond and issuer characteristics, insurer fixed effects and bid-ask bounce in empirical estimation. The effect is also robust to alternative measures of insurer-specific and systemic counterparty risks, and marketwide liquidity. Besides the counterparty risk premium, we find that bond yields contain a sizable liquidity component, which increases substantially during the financial crisis. Lastly, we find that systemic counterparty risk affects the ratio of municipal to Treasury bond yields. The relative yield increases significantly during the financial crisis, which can be partly attributed to the flight-to-quality and flight-to-liquidity effects as investors favor Treasury bonds. Results strongly suggest that counterparty risk and other nontax factors can significantly affect the yield spread between taxable and tax-exempt bonds. These effects should be taken in account when estimating the marginal tax rate from the municipal and Treasury bond yields. There is a vast literature on the determinants of municipal bond yields (see, for example, Trzcinka, 1982; Kidwell and Trzcinka, 1982; Yawitz, Maloney, and Ederington, 1985; Buser and Hess, 1986; Green, 1993; Chalmers, 1998; Neis, 2006; Wang, Wu, and Zhang, 2008; Ang, Bhansali, and Xing, 2010; Longstaff, 2011). To our knowledge, this paper is the first to document that counterparty risk has both insurer-specific and systemic effects on the yield of

5

municipal bonds. Our paper expands the literature on the issue of counterparty risk. Empirical findings regarding the importance of counterparty risk effect have varied across markets (see Jorion and Zhang 2007, 2009; Arora, Gandhi, and Longstaff, 2012; Gorton and Metrick, 2012). We find that the magnitude of counterparty risk effect in the municipal bond market is much larger than that in other markets. Arora et al. (2012) find that the effect of counterparty risk on the CDS premium is negligible in the crisis period: a one-percentage increase in counterparty risk affects the CDS spread by only 0.002 percentage point. Gorton and Metrick (2012) finds that a one-percentage increases in counterparty risk leads to a larger amount of 0.6 to 1.3 percentage increase in repo rates of various securitized bonds during the crisis period. By contrast, we find that a one-percentage increase in insurers’ counterparty risk leads to a 2.29 percentage increase in municipal bond yields during the crisis periods. This effect is much larger than those reported by for other markets. A plausible cause for this large effect is that unlike repo and CDS markets, there is no collateral or reserve posted by insurers when they provide insurance against issuer defaults. As bond insurance is largely guaranteed by insurers’ reputation, rather than tangible assets, its protection for issuers is fragile. Our finding that the counterparty risk effect is much larger in the municipal market provides important policy implications for the Congress and the regulatory agencies who have a great deal of interest in protecting municipal bond investments and lowering the borrowing cost of municipalities. As one example, regulatory agencies may have to require collateralization of insurance liabilities by insurers to mitigate counterparty risk and ensure the soundness of the bond insurance system. The remainder of this paper is organized as follows. Section II describes the municipal bond insurance market and the nature of counterparty risk associated with bond insurers. Section III discusses the data and liquidity and counterparty risk measures. Section IV examines the effects

6

of counterparty credit risk and other factors on the pricing of insured bonds. Section V conducts additional tests and Section VI examines the relation between counterparty risk and the ratio of municipal to Treasury bond yields. Finally, Section VII summarizes our main findings and concludes the paper. II. The Municipal Bond Insurance Market A. Municipal bond insurance States and local governments and other public agencies raise money from the municipal bond market to finance public services and infrastructure. At times, these issuers may seek external credit enhancement in order to gain better access to the credit market. Bond insurance is a common form of credit enhancement for municipal bonds. In the US, municipal bonds are typically insured at the time of issuance to enhance security and liquidity. Municipal bond insurance is a third-party guarantee of timely payments of interest and principal in the event that the municipal bond issuer fails to fulfill the obligations. In return, the issuer pays a premium to the insurer in exchange for credit protection. The bond insurer is not required to accelerate payments in the event of issuer default. The premium is a fraction of the undiscounted sum of coupons and principal, and tends to be higher for revenue bonds than for general obligation bonds. Similar to other securities, municipal bonds can be issued through a competitive or negotiated offering. In the former, underwriters submit the bid which includes insurance cost, and the underwriter with the lowest bid gets the deal. In the latter, municipalities work with underwriters to decide when to issue, what the bond yield will be, and whether the bond will be insured. In either case, the issue of insurance is determined when a municipality decides to issue the bond. The rationale for the issuer to insure the bond is to boost its rating and lower borrowing cost. For

7

the municipality to purchase the insurance, the interest saving must exceed the cost of insurance. Rating agencies determine the credit rating of the bond. If the bond receives a low rating, the issuer may consider purchasing insurance from a monoline insurer. Both rating agencies and bond insurers are heavily regulated. Regulators thus play an important role in the municipal bond issuance process. Traditionally, municipal bond issuers appear to be rated more harshly than corporate bond issuers. This argument is supported by empirical evidence that municipal bonds with the same rating as corporate bonds have lower default risk. A more stringent rating standard for municipal issuers may have increased the demand for bond insurance to boost their ratings. As ratings are important for determining credit risk and cost of borrowing, regulators have monitored rating agencies and bond insurers very closely to ensure their integrity. The problems of rating agencies and bond insurers in the subprime debacle contribute to counterparty risk in the municipal bond market. Municipal bond insurance used to be provided by top-rated bond insurance companies until recently. The insurer’s guarantee is unconditional and irrevocable and covers 100% of interest and principal of the issue in the event of a bond default. The insurer typically collects the premium up front to provide lifetime insurance for the bond. However, only a small portion of the premium is recognized each year as taxable income. The income is offset by losses occurred and adjustments in anticipation of losses, with the remaining premium recognized as unearned premium reserves. The payment made by the insurer in the event of a bond default has the same tax status as that of the payment made by the issuer. When a bond is redeemed early by the issuer, the insurer is often able to immediately earn the entire unearned premium minus any credit given to the issuer for the premium due on the newly issued bond. Bond insurers are restricted by regulation to the business of issuing financial guarantees on

8

bonds, making them “monoline insurers”. Privately sold municipal bond insurance was initiated in 1971 by the American Municipal Bond Assurance Corporation (Ambac). From 1971 to 2007, the business of municipal bond insurance expanded rapidly. In 1980, only 3% of bond issues were insured. This ratio rose to about 60% in 2007, but then retreated to 50% in January 2011. These figures do not include insurance for seasoned bonds purchased independently by investors. The rapid growth in bond insurance business is linked to several developments in the municipal bond market. First of all, a number of publicized municipal default events and rating downgrades have changed market participants’ perceptions of the likelihood of issuer defaults. In addition, credit uncertainty and information asymmetries, partly due to an increase in the issuance amount of revenue bonds and recent state fiscal strains, have contributed to the demand for bond insurance. Bond insurers typically provide independent credit risk assessment on municipal issuers which is important for investors who are unable or unwilling to incur substantial expenses to conduct their own analysis. This information service adds to the popularity of bond insurance. Bond insurance provides a number of benefits for a municipal borrower. By reducing credit risk and enhancing liquidity, the insurance makes municipal bonds more attractive to investors and thus lowers the issuer’s borrowing costs. Investors are willing to accept the lower yield in exchange for security and higher liquidity. 4 Kidwell, Sorensen, and Wachowicz (1987) find that bond insurance lowers the net cost of borrowing and improves market efficiency. Braswell, Nosari, and Browning (1982) find that insurance provides a positive but modest net benefit. Pirinsky and Wang (2011) find that differences in state taxes give rise to an asymmetric tax exemption of municipal bonds, which can cause market segmentation and higher yields but also

4

By providing a backup guarantee to the debt issued by a lower rated borrower, bond insurers can reduce bond yields. Bond insurers in effect are selling a higher credit rating to the municipal bond issuer. 9

increases the popularity of bond insurance, thereby reducing the borrowing costs. Bond insurance can mitigate the asymmetric information problem as insurers acquire more information and provide their own credit risk assessment. Thakor (1982) shows that insurance can alleviate the problem of information asymmetries between issuers and investors because the bond insurer acts as the “third-party” information producer to generate information about the issuer’s credit quality. Insurers evaluate issuers’ ability to fulfill their obligations before making a decision about whether or not to offer insurance. As a result, they often provide more information about the quality of the issuers (see Bergstresser et al., 2010). This is an important advantage of bond insurance because information asymmetry is perceived to be high in the municipal bond market due to lack of transparency. Nanda and Singh (2004) show that bond insurance produces both tax arbitrage and capital loss effects. The former arises from preserving the tax-status of the payments received by investors from the insurer in the event of default. This feature enhances the bond value. The latter results from the fact that investors no longer receive tax loss benefits upon default by the issuer, which reduces the bond value. The tradeoff of the two effects determines the net value of insurance. While insurance offers a number of benefits, the soundness of the bond insurance system critically hinges on the insurer’s financial health. When the insurer’s credit quality is in doubt, the insured bond will no longer be default free. The insurer can suddenly suffer a loss when the securities it insures default unexpectedly and if the loss is sufficiently large, the insurer may experience financial distress. Further, if financial deterioration is widespread, it can cause a contagious effect and destabilize the financial system. B. Municipal bond insurers and counterparty credit risk The municipal bond insurance market has gone through dramatic changes in the past decades.

10

After the first private guarantee was issued by the Ambac in 1971, the Municipal Bond Insurance Association (MBIA), the Financial Guaranty Insurance Company (FGIC) and the Financial Security Assurance Inc. (FSA, now AGO) joined the municipal bond insurance business. Subsequently, the bond insurance business became more competitive and the insurance premium declined as more providers entered into the market, e.g., ACA Financial Guaranty Co., XL Capital, CIFG Assurance North America Inc., and some reinsurers, like Radian, ACE Guaranty Re, and AXA Re Finance. Initially, the primary business of the municipal bond insurer was to insure municipalities and states against default. Historically, the default rate of municipal bonds has been much lower than that of corporate bonds, and so monoline insurers’ profits from insurance premiums were relatively stable and risk exposure was low. As competition became higher among insurers, they began to offer new products. These include municipal swaps, guaranteed investment contracts (GICs), asset management and government services. They have also launched initiatives in nonUS markets and provided guarantees for foreign institutions. Around the mid-1990s, municipal bond insurers began to get involved with mortgage-based CDOs by selling protection on CDO tranches through CDS contracts. Backing CDOs by CDSs is attractive because a low-rated monoline insurer is not restricted to guarantee the securities with a credit rating lower than its own. It can therefore compete with AAA-rated monoline insurers to back top-rated CDOs while maintaining less capital. Selling CDS protection to CDO tranches was the driving force for the rapid growth of bond insurers before the subprime crisis. Insuring CDOs poses a significant challenge for evaluating default risk of insurers because the liability with swaps becomes contingent and hard to estimate precisely. In comparison with the traditional business, chasing higher profits by insuring CDOs

11

is inherently risky. While states and local governments can raise taxes to meet obligations or refinance their debts, the designers of CDOs don’t have these options. The accumulation of contingent liability has exposed municipal bond insurers to substantial risk. For example, by 2007, ACA had guaranteed 26.6 billion of CDOs backed by subprime mortgages alone while the entire equity capital of monoline insurers was only about 34 billion at that time. The subprime crisis had a tremendous impact on the bond insurance business. Ambac was first downgraded on January 18, 2008 by Fitch and then on June 19, 2008 by Moody's. Ambac's stock price fell sharply and eventually filed for Chapter 11 on November 8, 2010. The event has a significant impact on the insurance market. The substantial losses experienced by most bond insurers associated with subprime mortgages threatened their survival. Counterparty credit risk magnified in the wake of insurers’ downfall. There are only a few insurers that survive and back municipal bond issuance after the financial crisis. Despite the increasing concern about counterparty risk in financial markets, there has been little research regarding how it affects the municipal bond pricing and whether it exerts a systemic impact on this market. Importantly, as insurers play an important role in enhancing liquidity for municipal bonds, the downfall of monoline insurers affects the liquidity in this market. However, there is no quantitative assessment of this effect. These issues are of tremendous importance for practitioners, municipal bond issuers and policy makers. In this paper, we address these issues. III. The Data A. Municipal bond transaction data The data for municipal bonds are obtained from the Municipal Securities Rulemaking Board (MSRB) database. The MSRB database contains municipal bond transactions between dealers

12

and customers or among dealers themselves. The data include CUSIP, security description, issue date, issuer, coupon, maturity date, trade date, time and par volume of trades, transaction prices, and yields for each municipal bond. The prices (yield) in this study are associated with actual transactions. The initial sample contains 1,035,910 municipal bonds identified by the CUSIP with a total of 17,626,469 transactions over the period from July 2004 to January 2011. Additional information on other characteristics of municipal bonds collected from the Bloomberg system includes the bond rating, issue size and type (general obligation, revenue, certificates, etc.), embedded options (e.g., callable, puttable, sinking funds), issue prices and yields, the tax status, whether a bond is insured, and the name of the insurer, if insured. We match the MSRB data with Bloomberg’s bond characteristic and the rating information provided by rating agencies. We employ S&P ratings but our results are robust to the use of ratings provided by other agencies. Ratings are updated over time. We exclude bonds with unknown ratings, embedded options, variable rates or irregular coupons. We also eliminate transactions occurring less than six months after the bonds are issued to avoid the aftermarket effects of newly issued bonds (see Green et al., 2007b), and transactions recorded with apparent pricing errors or missing prices. The matched data sample includes 128,016 bonds with a total of 2,369,595 transactions, which consists of 66,097 insured bonds with 1,440,054 transactions and 61,919 uninsured bonds with 929,541 transactions. Panel A of Table 1 reports the summary statistics for municipal bonds in the matched sample by issuing states with most transactions, bond type, S&P ratings, bond insurance, primary insurers, trading volume (par), and maturity at trade. We report proportions of transactions as a whole (all bonds) as well as transactions for insured and uninsured bonds separately in each category. Trades are led by bonds issued in California (CA, 18%), New York (NY, 10%), and

13

Texas (TX, 7%), followed by New Jersey (NJ), Florida (FL), Illinois (IL), Puerto Rico (PR), Massachusetts (MA), Pennsylvania (PA), and Michigan (MI). Issues in these 10 states account for 60% of total transactions over the sample period. Of the entire sample, 53% are revenue bonds and 41% are general obligation (GO) bonds. 5 In terms of credit ratings, 13% are AAA rated bonds, 75% are other A-rated (A- and above) bonds, and the remaining 12% go to BBB and speculative-grade bonds. For the insured bonds, trades are led by California (22%), New York (9%) and Florida (6%). Of the total insured bond transactions, 53% are for revenue bonds and 38% are for general obligation bonds, and A-rated (AAA to A-) bonds account for 84%. For the uninsured bonds, trades are led by New York (13%), followed by California (11%) and Texas (10%). By bond type, 51% (46%) of total transactions are for revenue (general obligation) bonds and by credit rating, 28% are for AAA bonds, 67% are for AA and A bonds, and 5% are for other bonds. The insured bonds account for about 61% of total transactions. Names of insurers and their tickers are listed at the bottom of Panel A. The leading insurers (by ticker) in terms of market share are MBIA (30%), AGO (26%), FGIC (18%), and ABK (17%). XL-CAPASS, RDN, and CIFGNA account for 8% of bond trades and BRK accounts for only 0.5%, which is due to its short life in the market. The median par amount traded of the whole sample is $30,000, and the 5 and 95 percentiles are $5,000 and $600,000. For insured (uninsured) bond transactions, the corresponding statistics are $30,000, and $5,000 and $500,000 ($40,000, $9,000 and $1,000,000), respectively. Of all transactions, 80% are for bonds with maturities less than ten years and 20% are over ten years. Insured and uninsured bonds have a similar maturity distribution. Panel B of Table 1 reports mean and standard deviation (in parentheses) for bond yields. On 5

The remainder includes tax revenue bonds, certificates of participation and others. 14

average, the yields for revenue bonds are higher than for general obligation bonds. As expected, bond yields increase as the rating decreases and maturity increases. Standard deviation of yields is much higher for speculative-grade bonds. As our main objective is to investigate the direct effect of the insurer-related counterparty risk on municipal bond yields, we focus on the data of insured bonds in empirical investigation. Our sample includes bonds with a sufficient dispersion of credit ratings and maturities to represent the whole universe of the insured bond market. B. CDS spreads, recovery rates, and probabilities of default for bond insurers The CDS spread reflects the market’s perception of the reference entity’s default risk. We extract the risk-neutral probability of default (PD) from the CDS of the insurer offering financial guarantees for municipal bonds as a measure of insurer-specific counterparty risk. Risk-neutral PDs are derived from the single-name CDS spreads and recovery rates collected from the Markit database. The implied probability of default for bond insurer 𝑗 at date 𝑡 is 𝑃𝐷𝑗,𝑡 = 1 − exp(−𝜆𝑗,𝑡 𝜏),

(1)

where 𝜆𝑗,𝑡 = 𝐶𝐷𝑆𝑗,𝑡 /(1 − 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦𝑗,𝑡 ) is default intensity and τ is time to maturity. λ can be viewed as the expected value of default intensity over the CDS contract period. The implied probability is a forward-looking counterparty risk measure as it captures the expected future default probability of the insurer. 6 Daily spreads and recovery rates of the five-year CDSs offering the credit protection on insurers are used to extract the default probability for eight municipal bond insurers whose data are available over our sample period. Table 2 provides summary statistics for CDS spreads, recovery rates, and estimates of riskneutral PDs for municipal bond insurers. N in the last column is the number of days that Markit’s 6

λ is an unbiased measure of the expected default intensity if the underlying true default intensity is independent or non-stochastic (see Longstaff et al., 2005, p. 2221). PD is a risk-neutral measure as it contains the physical PD and the risk premium. 15

quotes are available. Average CDS spreads vary considerably across municipal bond insurers. Berkshire Hathaway (BRK) has the smallest average spread of 91.04 basis points, whereas CIFGNA has the largest average spread of 3,709.66 basis points. The average spread across all insurers is 1,255.94 basis points over our sample period. Average recovery rates range from a low of 31.33% for Assured Guaranty (AGO) to a high of 39.91% for XL-CAPASS, with an overall average of 35.87%. Mean PD values vary considerably across insurers: BRK has the lowest average PD value of 1.49% and CIFGNA has the highest average value of 35.30%. There are substantial temporal variations in CDS spreads and PDs over the sample period. For example, the five-year CDS spread for Ambac had a low of 11 basis points and a high of 270% right before it filed for Chapter 11. The astonishingly high CDS spreads highlight the severity of counterparty credit risk during the crisis. The median value is much smaller than the mean of the CDS spread or PD, indicating high skewness in both distributions. Figure 1 plots the time-series of PDs for municipal bond insurers included in the sample. As shown, variations in PDs across municipal bond insurers are substantial. With the exception of Berkshire Hathaway, PDs increased dramatically after July 2007. Evidently, municipal bond insurers were severely affected by the subprime crisis. IV. Empirical Analyses To assess the importance of counterparty credit risk, we regress the insured municipal bond yield on the insurer’s risk-neutral PD and the liquidity factor with various controls that include bond characteristic and tax-related variables using panel regressions. For each bond at date t, we have the bond yield associated with each transaction and the PD value of the insurer for the bond. Given the data structure, we estimate the following panel regression: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛿1 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑠 + 𝜖𝑖,𝑗,𝑡

(2)

16

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 where 𝑦𝑖,𝑗,𝑡 is the yield on municipal bond 𝑖 with insurer 𝑗 at date 𝑡; 𝛼𝑙 is the fixed effect

parameter specific to state 𝑙; and 𝑃𝐷𝑗,𝑡−1 is the risk-neutral probability of default for insurer 𝑗 at t-1.7 As insurers’ credit risk is important intuitively, the slope coefficient of PD, 𝛿1 , should be positive, suggesting that an increase in the insurer’s default risk raises the bond yield. 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 denotes the liquidity measure at the end of the previous day 𝑡 − 1. The municipal bond market is much less liquid than the equity, foreign exchange or Treasury bond markets. As such, liquidity can be an important factor in municipal bond pricing (see Longstaff, 2011). We use a number of variables as controls in estimating the effect of counterparty risk and liquidity. These include the coupon rate, maturity, the Treasury bond yield (with the same maturity as bond i at date 𝑡), bond ratings and a tax dummy variable that controls for the tax status of the municipal bond. These are variables commonly used in the literature to explain municipal bond yields (see Green, 1993; Wang et al., 2008). Coupon rates and maturity are used as controls for bond characteristics. The slope of Treasury bond yields captures the marginal income tax effect.8 The bond rating is used to control the effect of the bond’s own default risk. We refer to the bond’s own default risk as the bond-specific default risk. We include the bond rating to capture this default risk effect. By design, in a regression with both the insurer’s default risk and the bond rating, the former should explain the variations of bond yields due to changes in the insurer’s credit quality while the latter captures the effect of the bond default risk left unexplained by the former. The rating becomes a more important measure of bond-specific default risk when the insurer’s default risk increases significantly. Finally, we add a tax dummy variable to capture the differential tax effect. This tax dummy variable takes value one when a 7

We have also used PD at time t as an explanatory variable in the regression. Unreported results show that our results are almost unchanged by using this variable. A potential problem of using PD at time t is that the CDS price used to construct PD is the close daily price, which is not available for traders during the day. 8 An investor with a marginal income tax rate τp would require a Treasury yield of y/(1- τp) in a simple textbook case with no default. 17

municipal bond is federally taxable and zero, otherwise. The effects of counterparty risk and liquidity are expected to be stronger around the subprime crisis when the default risk of insurers heightens and market liquidity dries up. To capture these effects, we include two dummy variables in the regression: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛿1 𝑃𝐷𝑗,𝑡−1 + 𝛿2 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1

+𝛾2 𝐼𝑙𝑖𝑞𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑠 + 𝜖𝑖,𝑗,𝑡

(3)

where 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 is an interactive dummy variable with value one for the crisis period, which is set to begin in July 2007 and end in June 2009, and zero otherwise. The definition of the crisis period is in line with that in Friewald, Jankowitsch, and Subrahmanyam (2012) and Dick-Nielsen, Feldhutter, and Lando (2012). With this specification, the slope coefficient of PD, 𝛿1 , represents the effect of the counterparty risk during the normal period and that of the slope dummy variable, 𝛿2 , captures the incremental effect during the crisis period. Thus, the total effect of insurer default risk on the bond yield during the crisis period is the sum of 𝛿1 and 𝛿2 . Similarly, the liquidity dummy variable 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 has value one for the illiquid period and zero, otherwise.9 The coefficient of the liquidity factor, 𝛾1 , is expected to be negative, as a bond with higher liquidity will have a lower yield. When liquidity becomes a greater concern in times of stress (see Longstaff, 2004, 2010; Dick-Nielsen et al., 2012; Friewald et al., 2012), its effect is expected to be stronger when market liquidity dries up and so 𝛾2 should be significantly negative. The regressions in (2) and (3) serve as the baseline models in our tests for the effect of counterparty risk. Since panel data are used in the regression, the disturbance terms likely

9

The illiquid period is defined somewhat differently to include the periods from July 2008 to December 2008 and after September 2010, where the former captures the precipitation in market illiquidity shortly before the collapse of Lehman Brothers and the latter captures the impact of recent state fiscal deficits after the crisis. This definition of the illiquid period is based on the time-series pattern of liquidity in Figure 2, which better captures the effect of illiquidity in the municipal bond market. 18

involve serial correlations for an individual bond, and contemporaneous and cross-serial correlations among bonds. The yield models are estimated by panel regressions in which standard errors are triple-clustered to account for the effects of serial correlation, cross-sectional dependence, and the cross-serial dependence, and heteroskedasticity in the residuals (see the Appendix for detailed description). A. The liquidity measures We construct the liquidity measures of Amihud (2002) and Pastor-Stambaugh (2003). The procedure is described in the Appendix. We add a negative sign to the Amihud illiquidity measure to make it easier to compare with the Pastor-Stambaugh liquidity measure and to interpret regression results. The converted Amihud index becomes a liquidity measure. Figure 2 plots the time series of the Amihud and Pastor-Stambaugh liquidity measures. As shown, the liquidity of the municipal bond market deteriorated rapidly after Standard and Poor’s downgraded monoline insurers Ambac and MBIA in June 2008 and hit a trough near the bankruptcy of Lehmann Brothers. It gradually recovered after that but declined again in 2010. The latest move can be attributed to the fiscal crisis of local governments that had an adverse impact on the municipal bond market.10 B. Regression results Panel A of Table 3 shows results of panel regressions of insured bond yields against counterparty risk, liquidity and other control variables with different model specifications. The panel regression is estimated with a state-specific fixed effect using the pooled data.

11

In

regression (I), we first consider only the risk-neutral probability of default (PD) of the underlying insurer as a direct counterparty risk variable and use different liquidity measures. Results show 10

See the article “A Seer on Banks Raises a Furor on Bonds” (New York Times, February 7, 2011), for the discussion of deteriorated state finances and possible calamity (fiscal cliff) in the municipal bond market. 11 For brevity, the estimates of the state-specific fixed effect parameter 𝛼𝑙 are omitted. 19

that the coefficient of PD is 1.070 (1.125) and significant at the one percent level when using the Amihud (Pastor-Stambaugh) measure as the liquidity factor. The result strongly suggests that counterparty credit risk of the insurer is priced. The point estimate of the PD coefficient indicates that an increase of ten percent in default probability of the insurer leads to an increase of about 11 basis points in the bond yield. The impact of counterparty risk is of economic significance. For example, a one-standard-derivation increase in the PD of MBIA (17.04%) results in an 18 basis-point increase in bond yields. The coefficients of tax dummy, coupon rates, maturity, and Treasury yields are all of the predicted sign and significant at the one percent level, and the adjusted 𝑅2 is 0.59. The effect of the counterparty credit risk increases substantially during the subprime crisis period, which reflects higher market uncertainty and risk aversion. In regression II with the crisis dummy variable, the coefficient of insurer counterparty risk is 0.556 (0.465) during the normal period in the regressions using the Amihud (Pastor-Stambaugh) measure, and increases by 1.734 (1.816) during the crisis period, both significant at the one percent level. This implies that a one percentage point increase in the counterparty risk leads to 2.29 percent increase during the crisis period. Counterparty risk explains a significant portion of yield variations across bonds. A onestandard-deviation increase in the cross-sectional mean of PD accounts for 7.6% (7.5%) of one standard deviation of municipal bond yields (10 bps) during the normal period and an increment of 23.5% (23.4%) during the subprime crisis period (31 bps) when using the Amihud (PastorStambaugh) liquidity measure. Liquidity is another important pricing factor for municipal bonds. Results show a significant liquidity component in the municipal bond yield regardless of which liquidity measure is used. In addition, the effect of illiquidity heightens when market liquidity dries up. For example, the

20

coefficient of the Amihud (Pastor-Stambaugh) liquidity factor is -0.477 (-.193) during the normal period and has an increment of -3.680 (-1.664) during the illiquid period. The Amihud liquidity measure appears to have greater explanatory power as indicated by higher adjusted R2 values. The coefficients of tax dummy, coupon rates, maturity, and Treasury yields are all of the predicted sign and significant at the one percent level. The coefficient of the rating is positive and highly significant in all regressions. The rating captures the effect of the bond default risk beyond the effect of PD. Results show a significant bond-specific default risk effect on yields after controlling for the effect of insurer’s risk. In summary, the municipal bond yield contains counterparty risk and liquidity premia, which increase significantly during the crisis and illiquid periods. The effect of counterparty risk on municipal bond pricing remains highly significant after accounting for the effects of illiquidity and other bond characteristics. Since our results are robust to different liquidity measures, we focus on the Amihud measure in the remaining analysis. C. Systemic counterparty risk Besides the insurer-specific counterparty risk effect, there is likely a systemic counterparty risk effect associated with contagion. When a major firm defaults, it affects other firms in a similar business as well. The failure of a large financial institution or dealer can trigger a cascade of defaults, as in the case of Lehman Brothers, which can disrupt markets, undermine investors’ confidence and increase the risk premium of municipal bonds. We next assess the importance of the systemic counterparty risk effect for municipal bond pricing. Following Gorton and Metrick (2012), we use the spread between the three-month Libor and overnight index swap (OIS) rates, Libor-OIS, as a proxy for the systemic counterparty risk

21

factor.12 The spread between Libor and OIS reflects the credit risk of financial intermediaries. By including Libor-OIS in the regression, we estimate the systemic component of the counterparty risk effect. The slope of Libor-OIS reflects the exposure to systemic counterparty risk. Panel A of Table 3 (Regression III) shows a positive effect of systemic counterparty risk on the municipal bond yield, consistent with economic intuition. The coefficients of Libor-OIS are significant at the one percent level. On average, a ten percent increase in the Libor-OIS spread raises the municipal bond yield by 5 basis points. This magnitude of systemic counterparty risk effect is of economic significance. The insurer-specific counterparty risk (PD) remains highly significant, even after controlling for the effect of systemic counterparty risk. The coefficient of PD is 0.763. When allowing for the regime change, the coefficient of PD is 0.611 during the normal period and increases by 0.925 during the crisis period. All of these coefficients are significant at the one percent level. Taylor (2009) uses the Libor-repo spread as a measure of systemic counterparty risk factor.13 For comparative purposes, we also estimate the panel regressions using this alternative measure. For brevity, we only report the coefficient estimates and standard errors for the Libor-Repo spread in parentheses below those for the Libor-OIS spread as other coefficient estimates are little affected. As shown, the Libor-repo spread is also highly significant and its coefficient is very close to that of the Libor-OIS spread. D. Counterparty risk effects across bonds with different liquidity and risk A key incentive for insuring municipal bonds is to enhance liquidity and security of municipal bonds. As the benefit of insurance is larger for illiquid and low-quality bonds, municipal bond issues with a poorer rating and lower liquidity are more likely to gain from insurance. However, 12

Libor is the London interbank lending rate and OIS is an effective federal fund rate. The Libor-OIS spread is directly related to cost of funding for financial intermediaries, which increases with systemic counterparty risk. 13 The Libor-Repo spread is the difference between three-month Libor and repo rates. 22

when the financial health of insurers deteriorates, the impact on these bonds will also be larger as these bonds count on insurers for providing liquidity. Thus, the yields of bonds with lower liquidity and quality are expected to be more sensitive to the credit risk of insurers. D.1 Counterparty risk effect for illiquid bonds To see if the impact of counterparty credit risk is larger for illiquid bonds, we include an interactive dummy variable 𝐼𝑖𝑙𝑙𝑖𝑞𝑢𝑖𝑑 𝑏𝑜𝑛𝑑 × 𝑃𝐷 as an additional regressor in the yield regression. The dummy variable takes value one if a bond has an Amihud individual bond liquidity measure below the overall average. Moreover, we further control for the effects of newly issued bond (onthe-run) and bond type (revenue versus GO). Municipal bond yields differ by bond type, e.g., off-the-run bonds have higher yields than on-the-run bonds as the latter are more liquid. Similarly, revenue bonds typically have higher yields than general obligations bonds as the latter have broader income support. Investors have higher risk exposure to hold off-the-run and revenue bonds and, therefore, demand more compensation. Panel B of Table 3 (Regressions I & II) reports the results of regressions. Results show a significant incremental effect of counterparty risk for illiquid bonds at the one percent level. Results strongly suggest that there is an interactive effect of the insurer’s default risk and liquidity on the yield of municipal bonds. In addition, the coefficient of 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 is negative and that of 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 is positive, consistent with the hypotheses that new bonds have lower yields and revenue bonds are riskier and so have higher yields. D.2 Counterparty risk effect for low-quality bonds The counterparty risk effect should be stronger for low-quality bonds. Further, this risk effect may increase during the crisis period due to the flight-to-quality effect. To test these hypotheses, we include a dummy variable to capture the interactive effect of bond quality and PD, and permit

23

a differential effect during the crisis period in the yield regression:14 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖

+𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 + 𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 ) × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡

(6)

and 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖

+𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 + 𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 ) × 𝑃𝐷𝑗,𝑡−1 + (𝛿2 + 𝜑2 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 ) × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡

(7)

where 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 is the dummy variable that has value one for the municipal bond with a speculative-grade rating and zero otherwise. The slope of PD, 𝛿1 , measures the effect of the counterparty credit risk on investment-grade bond yields and that of the interactive term, 𝜑1 , contains the incremental effect for speculative-grade bonds. In (7), 𝛿2 and 𝛿2 + 𝜑2 capture the incremental effect of counterparty credit risk for investment- and speculative-grade bonds during the crisis period. Thus, during the crisis period, the insurer’s default risk effect for investmentgrade bonds is the sum of 𝛿1 and 𝛿2 and that for the speculative-grade bonds is the sum of 𝛿1 , 𝛿2 , 𝜑1 , and 𝜑2 . Panel B of Table 3 (Regressions III and IV) shows that counterparty credit risk is indeed more important for low-quality municipal bonds. The coefficient of the interactive variable 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝑃𝐷 is 1.391, which is significant at the one percent level. Consistent with our hypothesis, results show that speculative-grade bond yields are much more susceptible to insurer default risk. The sensitivity also increases for speculative-grade bonds during the financial crisis 14

For brevity, we do not report the insurer fixed effect here but our results are robust to the control for the insurer fixed effect. 24

(see last line) but falls short of significance at the five percent level. One possible reason is that the dummy variables of liquidity and PD have already picked up most of the flight-to-liquidity and flight-to-quality effects over the crisis period. V. Robustness checks A. CDS spreads as an alternative measure of the insurer’s default risk In the analysis above, we use the risk-neutral default probability implied by the CDS spread as a measure of the insurer’s default risk. This reduced-form approach supposedly provides a less biased estimate of default risk (see Longstaff et al., 2005). An alternative way is to use the insurer’s CDS spread directly as a measure of counterparty credit risk. This approach provides a model-independent measure of counterparty risk. The CDS spread reflects the market perception of insurer default probability. Duffie and Liu (2001) indicate that this measure can be biased. However, given the efficiency of the CDS market, CDS spreads can still be quite informative about the perceived credit risk of the insurers selling the bond insurance. Using the CDS spread as an alternative measure of the insurer’s default risk allows us to check if the estimate of the counterparty risk effect based on the risk-neutral probability measure is reasonable. Panel A of Table 4 reports the results of panel regressions using the insurer’s CDS spread as a measure of counterparty credit risk. Here we replace PD with the CDS spread for the insurer at day t-1, while controlling for the effect of systemic counterparty risk as in Panel A of Table 3. As shown, the coefficient of the CDS spread is significantly positive. Results confirm that counterparty risk is important for the pricing of insured municipal bonds. When the dummy variable is introduced to capture the effect of the financial crisis, the coefficient is significantly positive. The CDS coefficient is 0.291 during the normal period and increases by 0.735 during the crisis period. Results again show that counterparty risk becomes

25

much more important during the crisis period. In short, using the CDS spread as a proxy for the insurer credit risk confirms that the insurerspecific counterparty risk is important in the municipal bond pricing and that the size of this counterparty risk premium increases substantially during the crisis period. Moreover, the effects of systemic counterparty risk and illiquidity remain almost intact, suggesting that our results are robust to different credit risk measures for monoline insurers. B. Alternative measures of systemic counterparty risk Libor-OIS reflects the credit risk of financial intermediaries as a whole, which may not tie very closely to monoline insurers. An alternative systemic counterparty risk for monoline insurers is their aggregate PD measure. We next replace Libor-OIS by this alternative measure in the regression as a robustness check. Panel B of Table 4 reports the results. Results show a similar pattern when we use the aggregate PD as an alternative systemic counterparty risk measure. Thus, our results are robust to different systemic counterparty risk measures. C. Controls for the fixed effects of insurers Municipal bond insurers are heterogeneous and bond yields may reflect this heterogeneity. Insurers differ in many ways such as management quality, financial health, business model and reputation. To capture the fixed effects related to insurer characteristics, we include dummy variables for individual insurers in yield regressions. We introduce seven insurer dummy variables using MBIA as the benchmark and control the firm and time fixed effects in the regression.15 The coefficients of these dummy variables represent the insurer-specific effects on bond yields relative to MBIA. The insurer-specific fixed effect may become more important in times of stress and this effect is captured by including the interactive dummy variables in the

15

MBIA is chosen as the benchmark due to the completeness of its data and its large market share in the municipal bond insurance business. 26

regression. Specifically, we estimate the following panel regressions: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖

+𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 + 𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + 𝛿1 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + ∑7𝑘=1 𝜂𝑘 𝐼𝑘 + 𝜖𝑖,𝑗,𝑡 , (8)

and 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖

+𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 + 𝛽8 𝐼𝑟𝑒𝑣𝑒𝑢𝑒 + 𝛿1 𝑃𝐷𝑗,𝑡−1 + 𝛿2 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + ∑7𝑘=1 𝜂𝑘 𝐼𝑘 + ∑7𝑘=1 𝜁𝑘 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐼𝑘 + 𝜖𝑖,𝑗,𝑡

(9)

where 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 takes value one for on-the-run bonds (with age less than one year) and zero otherwise, 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 has value one for revenue bonds and zero for general obligation bonds, and where 𝐼𝑘 is the dummy variable for insurer 𝑘. Table 5 (Regression I and II) reports panel regression results. Results continue to show that counterparty risk is priced and this risk becomes more important during the crisis period even after controlling for the effect of bond type and insurer fixed effects in the regression. The coefficients associated with bond characteristics are all significant at the one percent level. There is a dispersion of insurer fixed effects which are mostly significant. This dispersion may reflect that the pools of bonds insured vary in their composition across the insurers. Results show that the yields of municipal bonds insured by ABK, BRK, CIGFNA, AGO, and RDN are higher than those insured by MBIA (the benchmark), and the yields of bonds insured by FGIC and XLCAPASS are lower than those insured by MBIA. Furthermore, most of the insurer dummy coefficients are significantly positive during the crisis period, indicating that insurer fixed effects widen relative to MBIA.

27

D. The bid-ask bounce effect Our results are based on transaction yields which are potentially subject to microstructure noise. To see if results are sensitive to the bid-ask bounce, we run the regression using midpoints (midyields) as the dependent variable instead. We obtain the midpoints transaction prices following the procedure as in Green, Li and Schurhoff (2010). That is, if there are multiple buy and sell transactions on a given day, we take the midpoint of the highest sell and lowest buy prices (yields), and if there is only one sell or buy transaction, we use the average yield on all interdealer transactions as the midpoint yield for that particular day. 16 The right side of Table 5 (Regressions III and IV) reports the results using the midpoints as the dependent variable. As shown, the results are insensitive to the bid-ask bounce. In fact, the estimation of the counterparty risk effect becomes even more precise. All key explanatory variables are significant at least at the five percent level and the magnitude of the coefficient is in line with the regressions using transaction yields. Thus, the bid-ask bounce does not appear to be a serious concern. Overall, our results are robust to different counterparty default risk measures and to controls for insurer characteristics and bid-ask bounce in the empirical estimation. There is clear evidence that counterparty risk is important in the municipal bond pricing. 17 E. Is counterparty risk more important for troubled states? A number of states have experienced severe financial difficulty since the onset of the subprime crisis. For example, the total shortfalls in percentage of general funds are 65% and 52.8% for

16

This procedure reduces the sample size due to the treatment on multiple transactions and requirements for interdealer trades but as our sample size is very large, this has little impact on estimation efficiency. 17 The estimate for the pricing effect is robust to further controls for potential endogeneity, individual-specific liquidity, lagged bond yields and uses of different rating measures by the Moody’s or Fitch. These results are available upon request. 28

Arizona and California and over 40% for Illinois and Nevada in 2010.18 Bond insurance can enhance liquidity and credit quality and lower the cost of borrowing, and these benefits are potentially more important for issuers in states with financial difficulty. When the financial health of municipal bond insurers deteriorates, the issuers in troubled states are likely to suffer more. Thus, yields of municipal bonds issued in these states are expected to be more sensitive to insurers’ credit risk than those issued in other states. To test this hypothesis, we include an interactive dummy variable in regressions, 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 , which has value one for municipal bonds issued in troubled states and zero otherwise. The troubled states are defined as those states with a deficit (in percentage of general funds) above the mean (29%) across all states in 2010. The slope coefficient of 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 × 𝑃𝐷 captures the differential effect of counterparty risk for bond issues from the troubled states. Regressions I and II of Table 6 report the results that include the troubled state dummy variable. Consistent with the hypothesis, bonds issued by the troubled states are more sensitive to the insurer’s default risk. The coefficient estimates of the interactive term 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 × 𝑃𝐷 are 0.518 and 0.529 with and without the crisis dummies for liquidity and counterparty risk effects, all significant at the one percent level. Results strongly support the hypothesis that counterparty risk is more important for bonds issued in the troubled states. Based on the point estimate, on average a 10% increase in the insurer’s default risk adds about six basis points to the cost of debt for the issuers in these states. F. Is the counterparty risk effect less important for institutional investors? Institutional investors may be able to hedge bond insurance risk better than retail investors because they have more financial resources or better skills to perform this function. To

18

See the report of the Center on Budget and Policy Priorities, June 27, 2012. 29

investigate this possibility, we include an interactive dummy variable 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 × 𝑃𝐷 in the regressions for institutional trades, which takes value one if the par amount traded is above $100,000 and zero otherwise. 19 Regressions III and IV of Table 6 report the results that include this effect. The coefficient of the interactive institutional dummy variable is negative and significant at the one percent level for all regressions, indicating that the effect of counterparty credit risk is significantly lower for institutional investors. VI. The effect of counterparty risk and the ratio of municipal to Treasury yields The standard textbook version of the relation between the taxable Treasury bond yield (yT) and tax-exempt municipal bond yield (yM) is yM = (1-τp) yT. Using this naïve formula, one could back out an implied marginal investor’s income tax rate τp. This simple formula obviously ignores liquidity, default risk and other factors, which can affect yields of municipal bonds (see Green, 1993; Ang, Bhansali, and Xing, 2010; Longstaff, 2011).20 Longstaff (2011) estimates the implied marginal tax rate from municipal bond yields using a more general model and a unique data set that contains short-term (1-week) municipal bond yields. He finds that the marginal tax rate depends on macroeconomic factors. In addition, credit risk and illiquidity (nondefault component) are important factors for municipal bond yields. Our analysis above shows that counterparty risk is important in the pricing of municipal bonds. This finding suggests that the ratio of municipal to Treasury bond yields should be affected by counterparty risk. As a risk factor, counterparty risk can directly affect the risk premium of municipal bonds and hence the relative yields of municipal and Treasury bonds. Moreover,

The threshold to identify an institutional trade is close to the 75th percentile of par amount traded. This criterion is similar to that used by Ang, Bhansali, and Xing (2010). 20 Empirical findings show that the ratios of municipal bond yields to Treasury yields imply marginal tax rates which are smaller than expected and that this problem increases with maturity. This phenomenon is dubbed the “muni-bond puzzle”. Green (1993) shows that tax-trading strategies generating offsetting losses can cause this phenomenon, as the tax-trading benefit increases with maturity and pulls down the yield curve of taxable bonds at the long end. 19

30

counterparty risk can affect economic performance. Counterparty risk may trigger a cascade of defaults that disrupt the function of the financial system and cause economic recession as evidenced by the subprime crisis. Lower income in the recession will be associated with a lower marginal income tax rate given the progressive US tax rate structure. Thus, counterparty risk is likely to be negatively related to the marginal investor’s income tax rate or positively related to the ratio of municipal to Treasury bond yields. To see whether marketwide counterparty credit risk can explain time variations in the ratio of municipal to Treasury bond yields, we regress the yield ratio on the systemic counterparty risk measure and macroeconomic variables with controls. Besides the Libor-OIS spread, we use the average PD across municipal bond insurers as an alternative measure of systemic counterparty risk and estimate the following regression: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦

𝑦𝑡

= 𝛼𝑙 + 𝛽1 𝑆&𝑃500 𝑅𝑒𝑡𝑢𝑟𝑛𝑡−1 + 𝛽2 𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙 𝑖𝑛𝑐𝑜𝑚𝑒 𝐺𝑟𝑜𝑤𝑡ℎ𝑡−1 +𝛽3 ∆𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑚𝑒𝑛𝑡𝑡−1 + 𝛽4 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 + 𝛽5 𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑝𝑎𝑟𝑡𝑦𝑡−1 + 𝛽6 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 +𝛽7 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽8 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 + 𝛽9 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡

(10)

The dependent variable is the monthly (t) average ratio of municipal to Treasury bond yields with the same maturity. Aggregate variables in the regression model include monthly S&P 500 index returns, the monthly growth of per capita personal disposable income, the monthly change in the national unemployment rate and the marketwide liquidity index at t-1.21 We control for the effects of the rating and institutional trading. Counterparty is the systemic counterparty risk variable which is either the monthly average (risk-neutral) probability of default PD across municipal bond insurers or 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 in month t-1. The interactive variable 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 ×

21

The data for the S&P 500 index, personal income, and the national unemployment rate are obtained from the website of the Federal Reserve at St. Louis. 31

𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 captures the flight-to-liquidity effect whereas the interactive variable 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 captures the flight-to-quality effect. During the financial crisis, investors abandon risky securities in favor of safe liquid securities. Since US Treasuries are viewed as a safe haven, investors may reduce their municipal bond holdings and increase their Treasury holdings. This can increase the ratio of municipal to Treasury bond yields. Table 7 reports the results of panel regressions. The coefficient of counterparty risk is positive and significant at the one percent level regardless of whether we use the aggregate PD or 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 as the systemic counterparty risk measure. Results show that counterparty risk significantly affects the ratio of municipal to Treasury bond yields. The institutional dummy is significantly negative. The coefficients of the S&P 500 return and the growth of personal income are significantly negative whereas that of changes in unemployment rates is significantly positive. The sign of these coefficients is consistent with the hypothesis that the marginal investor’s income tax rate is procyclical. The two dummy interactive variables for bond credit quality and liquidity are significant. The coefficient of the interactive dummy variable 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 captures the flight-toquality effect. The positive coefficient of this variable supports the flight-to-quality hypothesis that investors abandon risky municipal bonds in favor of Treasury bonds in times of stress. As investors sell risky municipal bonds and buy Treasury bonds, municipal bond prices decrease and Treasury bond prices increase, leading to a higher yield ratio. Furthermore, the coefficient of 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 is significantly negative, suggesting that the ratio of municipal to Treasury bond yields increases as market liquidity precipitates. This finding is consistent with the flight-to-liquidity hypothesis that investors prefer liquid Treasury bonds to illiquid municipal bonds when market liquidity dries up. When investors chase liquidity, municipal bond prices fall

32

and Treasury bond prices rise, and the ratio of municipal to Treasury bond yields increases. In summary, there is strong evidence that counterparty credit risk is positively related to the ratio of municipal to Treasury bond yields. Municipal bond investors require a higher premium when counterparty risk increases. Also, high counterparty risk is associated with poor financial market performance and economic recession. This may explain why higher systemic counterparty risk is accompanied by a higher ratio of municipal to Treasury yields, which implies a lower marginal income tax rate. Furthermore, we find that the ratio of municipal to Treasury yields increases significantly during the financial crisis. This pattern is attributable to the buying and selling pressure in the municipal and Treasury markets associated with the flightto-liquidity and flight-to-quality effects. VII. Conclusions In this paper we investigate whether counterparty credit risk associated with monoline insurers is an important determinant of municipal bond yields. We document evidence of significant counterparty credit risk effect in the municipal bond market. The effect of counterparty risk is of economic significance and is much larger than that reported for the CDS and repo markets. This effect is robust to various controls for the liquidity measures, bond characteristics, insurers’ fixed effects, and bid-ask bounce in panel regressions. More importantly, the evidence suggests that there is a systemic effect of counterparty risk on the pricing of municipal bonds. The systemic counterparty risk effect accounts for a sizable proportion of the total counterparty risk effect. The effect of counterparty credit risk varies by municipal bond characteristics, issuer origin and market conditions. The effect is greater for illiquid bonds and speculative-grade bonds, and issues from states with more severe fiscal problems. There is an interactive effect of insurance default risk and illiquidity. Both counterparty risk and illiquidity effects are much stronger

33

during the crisis period, more so for speculative-grade municipal bonds. Additionally, we find that counterparty risk is positively correlated with the ratio of municipal to Treasury bond yields. High counterparty risk is typically accompanied by economic downturns, which in turn imply a lower marginal investor’s income tax rate. Furthermore, the ratio of municipal bond yields to Treasury yields increases significantly during the financial crisis, which can be attributed to the flight-to-liquidity and flight-to-quality effects in times of heightened market uncertainty. Our results have important implications for the modeling of municipal bonds. We find that counterparty risk is an important pricing factor for municipal bonds. This finding contrasts with previous findings for the credit derivatives market that the counterparty risk effect is trivial, and suggests that the importance of counterparty risk hinges on institutional differences, i.e. collateralization and tradability of financial contracts. In addition, liquidity is a key factor for the municipal bond pricing. The effects of liquidity and counterparty credit risk amplify during the subprime crisis when monoline insurers got into trouble. This finding suggests that liquidity enhancement is important for municipal bond issues and the downfall of insurers has an adverse effect on liquidity of municipal bonds and increases their liquidity premium. Our findings suggest that these risk factors should be incorporated in the term structure model of municipal bonds in order to explain the municipal bond price behavior more satisfactorily.

34

Appendix A. Liquidity measures To capture the effect of the liquidity factor, we utilize two marketwide liquidity measures: Amihud (2002) and Pastor and Stambaugh (2003). The Amihud (2002) illiquidity measure is based on the price impact of trades. The illiquidity for an individual bond at time t can be measured by |𝑟

1

𝐷𝑎𝑦𝑠 𝐼𝐿𝐿𝐼𝑄𝑖𝑡 = 𝐷𝑎𝑦𝑠 ∑𝑑=1 𝑖𝑡 𝑉𝑜𝑙𝑖,𝑑,𝑡 𝑖𝑡

|

𝑖,𝑑,𝑡

where 𝑟𝑖,𝑑,𝑡 is the return for bond 𝑖 on day 𝑑 within a one-month rolling window (𝑡 − 30, 𝑡), 𝑉𝑜𝑙𝑖,𝑑,𝑡 is the respective daily volume in dollars, and 𝐷𝑎𝑦𝑠𝑖𝑡 is the number of days for which transaction data are available for bond 𝑖. This liquidity measure is first calculated day-by-day for individual municipal bonds using a one-month rolling window and then aggregated across all bonds (including both insured and uninsured bonds) to obtain a marketwide illiquidity index, 𝑁

𝑡 𝐼𝐿𝐿𝐼𝑄𝑀𝑡 = (1⁄𝑁𝑡 ) ∑𝑖=1 𝐼𝐿𝐿𝐼𝑄𝑖𝑡 where 𝑁𝑡 is the number of municipal bonds at time t.22 A high

value of ILLIQ indicates low liquidity. To construct the Pastor-Stambaugh (2003) measure, we estimate the following regression: 𝑒 𝑒 ) × 𝑉𝑜𝑙𝑖,𝑗,𝑡 + 𝑢𝑖,𝑗,𝑡 , 𝑟𝑖,𝑗,𝑡+1 = 𝜌0 + 𝜌1 𝑟𝑖,𝑗,𝑡 + 𝜋𝑖,𝑡 sign(𝑟𝑖,𝑗,𝑡 𝑒 where 𝑟𝑖,𝑗,𝑡 = 𝑟𝑖,𝑗,𝑡 − 𝑟𝑚,𝑡 is the return of municipal bond 𝑖 with issuer 𝑗 at date 𝑡, 𝑟𝑖,𝑗,𝑡 , in excess 𝑒 of the equally weighted municipal bond market return 𝑟𝑚,𝑡 ; sign(𝑟𝑖,𝑗,𝑡 ) is the signed indicator 𝑒 𝑒 which takes value of 1 if 𝑟𝑖,𝑗,𝑡 is positive, and -1 if 𝑟𝑖,𝑗,𝑡 is negative; and 𝑉𝑜𝑙𝑖,𝑗,𝑡 is the par volume

(in 10,000 dollars) for municipal bond 𝑖. The coefficient estimate 𝜋𝑖,𝑡 measures the liquidity of bond 𝑖 and is expected to have a negative sign. The regression is estimated for individual bonds We winsorize individual 𝐼𝐿𝐿𝐼𝑄𝑖𝑡 data using the 5th and 95th percentile of the distribution to mitigate the impact of outliers in constructing the aggregate liquidity measure. 22

35

daily using a one-month rolling window based on the returns and daily volume data for all bond transactions (insured and uninsured bonds) in the market. Following this, we aggregate individual 𝜋𝑖,𝑡 to obtain a marketwide liquidity level for the municipal bond market 𝜋𝑀𝑡 .23 Liquidity risk is measured by the sensitivity of bond returns to innovations in market liquidity. We obtain liquidity innovations for both measures from the residuals of level regressions using the methods suggested by Pastor and Stambaugh (2003) and Acharya and Pedersen (2005), respectively. B. Adjustment for heteroskedasticity and serial correlations across bonds and over time This section outlines the procedure of adjusting for the effects of serial and cross correlations and heteroskedasticity in the residual terms to obtain a consistent estimate of standard errors. The panel regression can be expressed as 𝑦𝑖,𝑡 = 𝑿′𝑖,𝑡 𝜷 + 𝜀𝑖,𝑡 ,

where 𝑦𝑖,𝑡 is the dependent variable (bond yields), Xi,t is the vector of explanatory variables, εi,t is the error term, and 𝜷 is the coefficient vector. Suppose that the data sample involves N bonds (𝑖 = 1, … , 𝑁) observed over the period 𝑡 = 1, … , 𝑇. The correlation structure of the error term 𝜀𝑖,𝑡 is 𝐸(𝜀𝑖,𝑡 𝜀𝑖,𝑘 ) ≠ 0, 𝐸(𝜀𝑖,𝑡 𝜀𝑗,𝑡 ) ≠ 0 and 𝐸(𝜀𝑖,𝑡 𝜀𝑗,𝑘 ) ≠ 0 for all 𝑡 ≠ 𝑘 and 𝑖 ≠ 𝑗. We propose a triple-clustered variance-covariance estimator that accounts for the autocovariances in the residuals of an individual bond, contemporaneous covariances between the residuals of different bonds, and cross-serial covariances between the residuals of different bonds. The resulting variance-covariance matrix is an extension of Thompson’s (2011) doubleclustered variance-covariance matrix. The extended two-dimension clustered variancecovariance representation can be written as 23

We require a minimum of ten return observations per rolling month window in running the regression in (5). We include both insured and uninsured bonds in the regression to obtain a broad base liquidity index. 36

𝑉̂𝑏𝑜𝑛𝑑&𝑡𝑖𝑚𝑒 = 𝑉̂𝑏𝑜𝑛𝑑 + 𝑉̂𝑡𝑖𝑚𝑒 − 𝑉̂𝑊ℎ𝑖𝑡𝑒 + 𝑉̂𝐶 ,

where 𝑉̂𝑏𝑜𝑛𝑑 = 𝑯−1 ∑𝑖 𝒄̂𝑖 𝒄̂′𝑖 𝑯−1 , 𝑉̂𝑡𝑖𝑚𝑒 = 𝑯−1 ∑𝑡 𝒔̂𝑡 𝒔̂′𝑡 𝑯−1 , ̂ 𝑖,𝑡 𝒖 ̂ ′𝑖,𝑡 𝑯−1 , 𝑉̂𝑊ℎ𝑖𝑡𝑒 = 𝑯−1 ∑𝑡 ∑𝑖 𝒖 𝑙 𝑙 ̂ 𝑖,𝑡 𝒖 ̂ ′𝑖,𝑡−𝑙 + ∑𝐿𝑙=1 ∑𝑡 (1 − ) 𝒖 ̂ 𝑖,𝑡 𝒖 ̂ ′𝑖,𝑡+𝑙 ] 𝑯−1 , 𝑉̂𝐶 = 𝑯−1 ∑𝑖 [∑𝐿𝑙=1 ∑𝑡 (1 − 𝐿) 𝒖 𝐿

̂ 𝑖,𝑡 = 𝑿𝑖,𝑡 𝜀̂𝑖 ,𝑡 , 𝒄̂𝑖 = ∑𝑡 𝒖 ̂ 𝑖,𝑡 , 𝒔̂𝑡 = ∑𝑖 𝒖 ̂ 𝑖,𝑡 , and 𝜀̂𝑖 ,𝑡 is the estimated residual of 𝑯 = ∑𝑖,𝑡 𝑿𝑖,𝑡 𝑿′𝑖,𝑡 , 𝒖 the regression and L is the length of lags. 𝑉̂𝑏𝑜𝑛𝑑 is the variance-covariance component clustered by bonds, 𝑉̂𝑡𝑖𝑚𝑒 is the variance-covariance component clustered by time, 𝑉̂𝑊ℎ𝑖𝑡𝑒 is the White heteroskedasticity variance-covariance component, and 𝑉̂𝐶 is the cross-serial covariance component clustered by both bonds and time. The combination of the first three components 𝑉̂𝑏𝑜𝑛𝑑 + 𝑉̂𝑡𝑖𝑚𝑒 − 𝑉̂𝑊ℎ𝑖𝑡𝑒 constitutes the variance-covariance matrix proposed by Petersen (2009) and Thompson (2011), which contains the components of standard errors associated with contemporaneous residual correlations among bonds, residual correlations over time and the White heteroskedasticity. The extended variancecovariance matrix further adds the last component 𝑉̂𝐶 to capture the cross-serial correlations across bonds. The extended version is more general as it takes into account the pronounced cross-serial correlations among bonds over time. We compute the Newey-West sum for the lagged cross-serial correlation terms and aggregate them across different time intervals to obtain 𝑉̂𝐶 . The maximum lag length is set equal to six months. The remaining three components are estimated using the same procedure as in Thompson (2011). From these components, we obtain a consistent estimator of standard errors in panel regressions.

37

References Acharya, V., Pedersen, L., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77, 375-410. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time series effects. Journal of Financial Market 5, 31-56. Ang, A., Bhansali, V., Xing, Y., 2010. Taxes on tax-exempt bonds. Journal of Finance 65, 565601. Ang, A., Green, R., 2011. Lowering borrowing costs for states and municipalities through CommonMuni. Discussion paper 2011-1, The Hamilton Project. Arak, M., Guentner, K., 1983. The market for tax-exempt issues: Why are the yields so high? National Tax Journal 36, 145-161. Arora, N., Gandhi, P., Longstaff, F.A., 2012. Counterparty credit risk and the credit default swap market. Journal of Financial Economics 103, 280-293. Bergstresser, D., Cohen, R, Shenai, S. 2010. Financial guarantors and the 2007-2009 credit crisis, Working paper, Harvard Business School. Braswell, R., Nosari, E., Browning, M., 1982. The effect of private municipal bond insurance on the cost to the issuer. Financial Review 17, 240-251. Brigo, D., Pallavicini, A., 2006. Counterparty risk and contingent CDS valuation under correlation between interest rates and defaults. Working paper, Imperial College and Banca Leonardo. Buser, S.A., Hess, P.J., 1986. Empirical determinants of the relative yields on taxable and taxexempt securities. Journal of Financial Economics 17, 335-355. Chalmers, J., 1998. Default risk cannot explain the muni puzzle: Evidence from municipal bonds that are secured by U.S. Treasury obligations. Review of Financial Studies 11, 281-308. Dick-Nielsen, J., Feldhutter, P., Lando, D., 2012. Corporate bond liquidity before and after the onset of the subprime crisis. Journal of Financial Economics 103, 471-492. Duffie, D., Huang, M., 1996. Swap rates and credit quality. Journal of Finance 51, 921–949. Duffie, D., Liu, J., 2001. Floating-fixed credit spreads. Financial Analysts Journal 57, 76–87. Duffie, D., Zhu, H., 2011. Does a central clearing counterparty reduce counterparty risk? Review of Asset Pricing Studies 1, 74-95. Friewald, N., Jankowitsch, R., Subrahmanyam, M., 2012. Illiquidity or credit deterioration: A study of liquidity in the US corporate bond market during financial crises. Journal of Financial Economics 150, 18-36.

38

Gorton, G., Metrick, A., 2012. Securitized banking and the run on repo. Journal of Financial Economics 104, 425-451. Green, R., 1993. A simple model of the taxable and tax-exempt yield curves. Review of Financial Studies 6, 233-264. Green, R., 2007. Issuers, underwriter syndicates, and aftermarket transparency. Journal of Finance 62, 1529-1550. Green, R., Hollifield, B., Schurhoff, N., 2007a. Financial intermediation and costs of trading in an opaque market. Review of Financial Studies 20, 235-273. Green, R., Hollifield, B., Schurhoff, N., 2007b. Dealer intermediation and price behavior in the aftermarket for new bond issues. Journal of Financial Economics 86, 643-682. Green, R., Li, D., Schurhoff, N., 2010. Price discovery in illiquid markets: Do financial asset prices rise faster than they fall? Journal of Finance 65, 1669-1702. Harris, L., Piwowar, 2006. Secondary trading costs in the municipal bond market. Journal of Finance 61, 1361-1397. Hull, J., White, A., 2001. Valuing credit default swaps II: Modeling default correlations. Journal of Derivatives 8, 12-21. Jarrow, R., Yu, F., 2001. Counterparty risk and the pricing of defaultable securities. Journal of Finance 56, 1765-1799. Jorion, P., Zhang, G., 2007. Good and bad credit contagion: Evidence from credit default swaps. Journal of Financial Economics 84, 860-883. Jorion, P., Zhang, G., 2009. Credit contagion from counterparty risk. Journal of Finance 64, 2053-2087. Kidwell, D.S., Koch, T.W., 1983. Market segmentation and the term structure of municipal yields. Journal of Money, Credit and Banking 18, 482-494. Kidwell, D., Sorensen, E., Wachowicz, J., 1987. Estimating the signaling benefits of debt insurance: the case of municipal bonds. Journal of Financial and Quantitative Analysis 22, 299-313. Kidwell, D., Trzcinka, C., 1982. Municipal bond pricing and the New York City fiscal crisis. Journal of Finance 37, 1239-1246. Kochin, L., Parks, R., 1988. Was the tax-exempt bond market inefficient or were future expected tax rates negative? Journal of Finance 43, 913-931. Kraft, H., Steffensen, M., 2007. Bankruptcy counterparty risk and contagion. Review of Finance 11, 209-252.

39

Krishnamurthy, A., 2010. How debt markets have malfunctioned in the crisis. Journal of Economic Perspectives 24, 3-28. Liu, S.X., Wang, J., Wu, C., 2003. Effects of credit quality on the relation between tax-exempt and taxable yields. Journal of Fixed Income 13, 80-99. Livingston, M., 1982. The pricing of municipal bonds. Journal of Financial and Quantitative Analysis 17, 179-193. Longstaff, F.A., 2004. The flight-to-liquidity premium in U.S. Treasury bond prices. Journal of Business 77, 511-526. Longstaff, F.A., 2010. The subprime credit crisis and contagion in financial markets. Journal of Financial Economics 97, 436-450. Longstaff, F.A., 2011. Municipal debt and marginal tax rates: Is there a tax premium in asset prices? Journal of Finance 66, 721-751. Longstaff, F.A., Mithal, S., Neis, E., 2005. Corporate yield spreads: default risk or liquidity? New evidence from the credit default swap market. Journal of Finance, 60, 2213-2253. Nanda, V., Singh, R., 2004. Bond insurance: what is special about munis? Journal of Finance 59, 2253-2280. Neis, E., 2006. Liquidity and municipal bonds. Working paper, UCLA. Pastor, L., Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal of Political Economy 111, 642-685. Petersen, M.A., 2009. Estimating standard errors in finance panel data sets: comparing approaches. Review of Financial Studies 22, 435-480. Pirinsky, C., Wang, Q., 2011. Market segmentation and the cost of capital in a domestic market: Evidence from municipal bonds. Financial Management 40, 455-481. Poterba, J.M., 1986. Explaining the yield spread between taxable and tax-exempt bonds, in H. Rosen (ed.), Studies in State and Local Public Finance, University of Chicago Press, Chicago. Poterba, J.M., 1989. Tax reform and market for tax-exempt debt. Regional Science and Urban Economics 19, 537-562. Pu, X., Wang, J. and Wu, C., 2011. Are liquidity and counterparty risk priced in the credit default swap market? Journal of Fixed Income 20, 59-79. Segoviano, M., Singh, M., 2008. Counterparty risk in the over-the-counter derivatives market. Working paper 08/258, International Monetary Fund. Skelton, J.L., 1983. Relative risk in municipal and corporate debt. Journal of Finance 38, 625634. 40

Stock, D., Schrems, E., 1984. Municipal bond demand premiums and bond price volatility: A note. Journal of Finance 39, 535-539. Stock, D., 1994. Term structure effects on default risk premia and the relationship of defaultrisky tax-exempt yields to risk-free taxable yields: A note. Journal of Banking and Finance 18, 1185-1203. Stulz, R.M., 2010, Credit default swaps and the credit crisis, Journal of Economic Perspectives 24, 73–92. Taylor, J., 2009. The financial crisis and the policy responses: an empirical analysis of what went wrong. NBER working paper No. 14631. Thakor, A., 1982. An exploration of competitive signalling equilibria with "third party" information production: the case of debt insurance. Journal of Finance 37, 717-739. Thompson, S.B., 2011. Simple formulas for standard errors that cluster by firm and time. Journal of Financial Economics 99, 1-10. Trzcinka, C., 1982. The pricing of tax-exempt bonds and the Miller Hypothesis. Journal of Finance 37, 907-923. Wang, J., Wu, C., Zhang, F., 2008. Liquidity, default, taxes, and yields on municipal bonds. Journal of Banking and Finance 32, 1133-1149. Wilkoff, S., 2011. The effect of insurance on municipal bond yields. Working paper, University of California, Berkeley. Yawitz, J.B., Maloney, K.J., Ederington, L.H., 1985. Taxes, default risk, and yield spreads. Journal of Finance 30, 1127-1140. Yu, F., 2007. Correlated defaults in intensity-based models. Mathematical Finance 17, 155-173.

41

Table 1 Summary statistics for municipal bond data This table reports summary statistics of municipal bonds. The data sample includes 128,016 bonds with a total of 2,369,595 transactions over the period from July 2004 to January 2011, in which there are 66,097 insured bonds with a total of 1,440,054 transactions and 61,919 uninsured bonds with a total of 929,541 transactions. Panel A reports the distribution of municipal bonds by issuing state, bond type, proportion of insured bonds, credit rating, par volume and maturity. The rows of all bonds, insured bonds, and uninsured bonds report proportions of transactions in these categories. For the par amount traded, we report the percentiles of the distribution. Panel B reports mean and standard deviation of municipal bond yields by bond type, rating and maturity for the whole sample, and insured and uninsured bonds, respectively. Panel A States of issues with most transactions All bonds

CA 17.61% CA 22.03% NY 13.27%

Insured bonds Uninsured bonds

NY 10.49% NY 8.70% CA 10.78%

TX 7.13% FL 6.36% TX 10.15%

NJ 4.96% PR 5.60% MA 4.98%

FL 4.93% NJ 5.44% NJ 4.22%

IL 4.55% IL 5.23% VA 4.11%

PR 4.04% TX 5.18% IL 3.50%

MA 3.65% PA 4.37% OH 3.47%

PA 3.55% MI 3.74% MD 3.37%

MI 3.09% MA 2.78% NC 3.27%

Type of Bonds Revenue 52.54% 53.23% 51.47%

All bonds Insured bonds Uninsured bonds

GO 41.40% 38.47% 45.92%

Certificate 3.45% 4.58% 1.69%

Tax 1.67% 2.41% 0.53%

Special 0.76% 1.06% 0.29%

Warrants 0.19% 0.25% 0.10%

S&P credit rating All bonds Insured bonds Uninsured bonds

AAA

AA+,AA,AA-

A+,A,A-

BBB+,BBB,BBB-

BB+,BB,BB-,and below

13.06% 3.31% 28.12%

55.05% 58.74% 49.36%

20.10% 21.93% 17.28%

10.49% 14.43% 4.40%

1.29% 1.59% 0.84%

Insurance Insurance Company

Insured Yes

No

60.74%

39.26%

MBIA

AGO

29.96%

26.15%

FGIC

ABK

RND

18.40%

16.75%

4.71%

XLCAPASS 2.50%

CIFGNA

BRK

0.72%

0.46%

Par amount traded All bonds Insured bonds Uninsured bonds

5th% 5,000 5,000 9,000

1st Q 20,000 15,000 20,000

Mean 262,628 230,169 312,292

Median 30,000 30,000 40,000

3rd Q 100,000 80,000 100,000

95th% 600,000 500,000 1,000,000

Maturity at trade 1-2 year

All bonds 1.26% Insured bonds 1.14% Uninsured bonds 1.46% Insurer Assured Guaranty Ltd Ambac Financial Group, Inc. Berkshire Hathaway Assurance Corp CIFG Assurance North America Inc. Financial Guaranty Insurance Company Municipal Bond Insurance Association Radian Group Incorporated XL-CAPASS Capital Assurance

3-5 year

6-10 year

>10 year

24.36% 23.30% 25.99%

54.70% 53.32% 56.83%

19.67% 22.23% 15.72%

Ticker AGO ABK BRK CIFGNA FGIC MBIA RDN XL-CAPASS

42

Panel B. Mean and standard deviation (in parentheses) of bond yields (%) All Revenue All bonds 3.58 3.72 (1.32) (1.10) Insured 3.73 3.81 (1.21) (1.22) Uninsured 3.34 3.58 (1.44) (1.20)

General obligation 3.35 (1.10) 3.60 (1.09) 3.04 (1.11)

by rating All bonds Insured bonds Uninsured bonds

All bonds Insured Uninsured

AAA 3.02 (1.11) 3.42 (1.11) 2.95 (1.10) 1-2 year 1.88 (1.27) 1.94 (1.43) 1.81 (1.10)

AA 3.38 (1.19) 3.52 (1.16) 3.13 (1.20)

A 3.96 (1.26) 3.88 (1.13) 4.12 (1.48) by maturity 3-5 year 2.46 (1.18) 2.64 (1.22) 2.22 (1.12)

BBB 4.45 (1.22) 4.38 (1.18) 4.84 (1.34) 6-10 year 3.64 (0.89) 3.76 (1.00) 3.46 (0.78)

BB and below 4.77 (2.01) 4.36 (1.32) 6.03 (2.99) >10 year 4.93 (1.14) 4.90 (1.43) 4.98 (0.99)

43

Table 2 Summary statistics for CDS spreads, recovery rates, and PDs of municipal bond insurers This table reports summary statistics for CDS spreads (in basis points), recovery rates (in percentages), and the probabilities of default (PDs) of municipal bond insurers (in percentages). Daily CDS spread and recovery rate data are from the Markit database. The PD is estimated from the CDS spread and recovery rate of the municipal bond insurer. Specifically, the probability of default for the bond insurer 𝑗 at date 𝑡 is calculated as 𝑃𝐷𝑗,𝑡 = 1 − exp(−𝜆𝑗,𝑡 𝜏), where default intensity is given by 𝜆𝑗,𝑡 = 𝐶𝐷𝑆𝑗,𝑡 /(1 − 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦𝑗,𝑡 ). N denotes the number of days on which the Markit’s quotes are available for municipal bond insurers. The sample period is from July 2004 to January 2011. Bond Insurer ABK

AGO

BRK

CIFGNA

FGIC

MBIA

RND

XL -CAPASS All Insurers

Variable CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%) CDS spreads(bps) Recovery rates(%) PDs(%)

Mean 1861.41 34.05 17.39 1051.38 31.33 15.10 91.04 39.85 1.49 3709.66 34.04 35.30 2840.43 33.16 22.91 1413.26 33.62 15.05 737.02 37.69 9.94 290.78 39.91 4.30 1255.94 35.87 12.87

Standard Deviation 3011.58 7.47 22.69 999.71 7.71 10.64 103.56 0.71 1.68 3222.41 6.96 26.12 4250.07 9.70 28.00 1752.87 9.65 17.04 838.44 4.14 10.38 631.98 2.07 8.86 2364.48 7.35 18.71

Minimum

Median

Maximum

N

11.00 20.00 0.18 24.00 18.25 2.76 7.00 36.25 0.12 33.00 20.00 0.55 9.00 15.00 0.15 13.00 15.75 0.22 26.00 26.02 0.43 13.00 29.20 0.22 7.00 15.00 0.12

191.50 39.35 3.14 783.00 29.98 11.00 29.00 40.00 0.48 3277.00 35.00 40.08 148.00 39.17 2.44 141.50 39.57 2.33 456.00 39.67 7.32 29.00 40.00 0.47 130.00 40.00 2.18

26990.00 40.48 96.86 5242.00 42.50 56.77 527.00 42.25 8.41 9488.00 40.00 74.48 43777.00 44.17 99.52 9190.00 55.00 67.97 3807.00 45.39 40.94 3476.00 45.00 41.56 43777.00 55.00 99.52

1586

866

1646

388

1115

1646

1646

1025

9918

44

Table 3 Panel regressions of insured bond yields on the bond insurer’s risk-neutral PD, liquidity, and controls Panel A reports results for panel regressions of insured bond yields on (i) the risk-neutral default probability (PD) of the corresponding bond insurer; (ii) the liquidity factor; and (iii) control variables that include the tax status, Treasury yields, coupon rates, maturities, and S&P ratings, with the state-specific fixed effect. The sample period is from July 2004 to January 2011. We consider the following two regression specifications. I.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛿1 𝑃𝐷𝑗,𝑡−1

+𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 II.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛿1 𝑃𝐷𝑗,𝑡−1

+𝛿2𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 III.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛿1𝑃𝐷𝑗,𝑡−1 +

𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 IV.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛿1 𝑃𝐷𝑗,𝑡−1 +

𝛿2 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 is the yield on

+ 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡

where municipal bond 𝑖 at time 𝑡 insured by the insurer 𝑗; 𝛼𝑙 is the fixed effect parameter specific to state 𝑙; 𝑇𝑎𝑥𝑖 is the tax dummy variable for municipal bond 𝑖 that takes a value of one when the “Federal Tax Provision” is “Federally Taxable”, and zero otherwise; 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 is time to maturity; 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 is the coupon rate; 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 is the Treasury bond yield with the same maturity as the corresponding municipal bond; 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 is the liquidity factor proxied by the Amihud; 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 is the S&P rating for the municipal bond 𝑖 that takes value 1=AAA, 2=AA+, 3=AA, ..., etc.; 𝐿𝑖𝑏𝑜𝑟 − 𝑂𝐼𝑆(𝑅𝑒𝑝𝑜) is the difference between the three-month Libor and OIS (Repo) rates (in percentages); 𝑃𝐷𝑗,𝑡−1 is the risk-neutral default probability on the insurer 𝑗 at time 𝑡 − 1; 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 is the dummy variable that takes a value of one for the period of the subprime crisis from July 2007 to June 2009, and zero otherwise; and 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 is the dummy variable that takes a value of one for the illiquid periods from July 2008 to December 2008 and after September 2010, and zero otherwise. 𝑅̅2 is the adjusted 𝑅 2. Panel A: Regressions with counterparty risk effects Regression I Amihud Coef. Std.

Variable 𝑇𝑎𝑥 0.484 𝐶𝑜𝑢𝑝𝑜𝑛 -0.072 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 0.079 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 0.479 𝑅𝑎𝑡𝑖𝑛𝑔 0.075 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 (𝐿𝑖𝑏𝑜𝑟– 𝑅𝑒𝑝𝑜) 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 -1.605 𝑃𝐷 1.070 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷 ̅2

𝑅

0.027

Regression II

Pastor-Stambaugh Coef. Std. 0.471

0.027

Regression III

Amihud Pastor-Stambaugh Coef. Std. Coef. Std. 0.511 0.027

0.501

Coef.

Std.

0.027

0.524

Regression IV Coef.

Std.

0.027

0.525

0.026

0.005

-0.079

0.006

0.006

-0.069

0.006

-0.077 0.006

-0.075

0.006

-0.078

0.004

0.084

0.004

0.078 0.004

0.083

0.004

0.079

0.004

0.079

0.004

0.016

0.467

0.013

0.021

0.435

0.016

0.479 0.013

0.422

0.013

0.454

0.005

0.076

0.005

0.079 0.005

0.080

0.005

0.080

0.005

0.080

0.005

0.526

0.031

0.348

0.030

(0.524)

(0.032)

(0.355)

(0.031)

0.384

-0.487

0.180

-0.477 0.170

-0.193

0.086

-0.890

0.246

-0.418

0.159

0.174

1.125

0.106

0.556 0.176

0.465

0.111

0.763

0.151

0.590

0.161 0.422 0.094

0.523

-1.664

0.714

1.734 0.097

1.816

0.118

0.925

-3.680 0.574

0.611 -2.554

0.641

0.620

0.645

0.656

45

Table 3 (continued) Counterparty credit risk effects on illiquid and low-quality bonds This table reports results of panel regressions of insured bond yields for illiquid and speculative-grade bonds. Regressions I and II report the results that include an interactive dummy variable 𝐼𝑖𝑙𝑙𝑖𝑞𝑢𝑖𝑑 𝑏𝑜𝑛𝑑 × 𝑃𝐷 for illiquid bonds, which has a value of one if the bond’s Amihud index is below the average, and zero otherwise. Regressions III and IV report the results that capture the counterparty risk effect for speculative-grade bonds where 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 is the dummy variable that has a value of one for the municipal bond with a speculative-grade rating, and zero otherwise. The sample period is from July 2004 to January 2011. Panel B: Illiquid bond effects/Speculative-grade bond effects

Variable Tax 𝐶𝑜𝑢𝑝𝑜𝑛 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 (𝐿𝑖𝑏𝑜𝑟– 𝑅𝑒𝑝𝑜) 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝑃𝐷 𝐼𝑖𝑙𝑙𝑖𝑞𝑢𝑖𝑑 𝑏𝑜𝑛𝑑 × 𝑃𝐷 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝑃𝐷 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷 𝑅̅2

Regression I Coef. Std. 0.556 -0.082 0.078 0.460 0.078 0.526 (0.524) -0.286 0.084 -0.894 0.599 0.452

0.662

0.026 0.005 0.004 0.015 0.005 0.031 (0.032) 0.014 0.010 0.247 0.084 0.081

Regression II Coef. Std. 0.557 -0.083 0.077 0.472 0.078 0.348 (0.347) -0.275 0.090 -0.430 0.444 0.451

0.026 0.005 0.004 0.012 0.005 0.028 (0.030) 0.013 0.010 0.163 0.096 0.081

-2.501 0.933

0.424 0.093

0.663

Regression III Coef. Std.

Regression IV Coef. Std.

0.547 -0.083 0.078 0.463 0.038 0.536 (0.530) -0.277 0.088 -0.907 0.425

0.025 0.005 0.004 0.016 0.004 0.032 (0.033) 0.013 0.011 0.246 0.163

0.548 -0.084 0.077 0.474 0.036 0.350 (0.350) -0.266 0.094 -0.443 0.248

0.025 0.005 0.003 0.012 0.004 0.029 (0.030) 0.013 0.011 0.162 0.173

1.391

0.167

1.413 -2.484 0.981 0.108

0.170 0.421 0.093 0.101

0.661

0.673

46

Table 4 Robustness regressions Panel A reports results using CDS as an alternative measure for the insurer’s default risk. Panel B reports the results by substituting aggregate PD for Libor-OIS as a systemic counterparty risk measure. Panel A: CDS spread as the measure of insurer default risk Regression I

Regression II

Variable 𝑇𝑎𝑥

Coef.

Std.

Coef.

Std.

0.512

0.026

0.512

0.026

𝐶𝑜𝑢𝑝𝑜𝑛

-0.077

0.005

-0.077

0.005

𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦

0.083

0.004

0.082

0.004

𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦

0.423

0.015

0.434

0.012

𝑅𝑎𝑡𝑖𝑛𝑔

0.084

0.005

0.083

0.005

𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆

0.555

0.029

0.420

0.027

(𝐿𝑖𝑏𝑜𝑟– 𝑅𝑒𝑝𝑜)

(0.552)

(0.030)

(0.419)

(0.028)

𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑

-0.906

0.252

-0.493

0.168

𝐶𝐷𝑆

0.399

0.042

0.291

0.072

𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑

-2.159

0.377

𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐶𝐷𝑆

0.735

0.098

𝑅̅2

0.640

0.649

Panel B: Regressions using aggregate PD of insurers as a systemic counterparty risk measure

𝑇𝑎𝑥

Regression III Coef. Std. 0.493 0.027

Regression IV Coef. Std. 0.502 0.026

𝐶𝑜𝑢𝑝𝑜𝑛

-0.076

0.005

-0.078

0.006

𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦

0.068

0.004

0.070

0.004

𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦

0.566

0.016

0.552

0.013

𝑅𝑎𝑡𝑖𝑛𝑔

0.086

0.005

0.084

0.005

𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑃𝐷

9.427

0.031

6.661

0.030

𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑

-0.773

0.246

-0.204

0.159

𝑃𝐷

0.399

0.151

0.410

0.161

𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑

-3.258

0.422

𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷

0.793

0.094

Variable

𝑅̅2

0.642

0.654

47

Table 5 Panel regressions of municipal bond yields with insurer fixed effects This table reports results for panel regressions of insured bond yields with controls for coupon rates, maturities, ratings, bond type, insurer fixed effect, and state-specific fixed effect. 𝐼𝑘 is the fixed effect dummy variable for the bond insurer 𝑘, 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 is the dummy variable for new bonds that takes a value of one when bond age is less than twelve months, and zero otherwise; 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 is the dummy variable that takes a value of one for revenue bonds, and zero for general obligations bonds. Other variables and the tickers for insurers are as defined in Tables 1 and 3. Regressions I and II use actual transaction yields. Regressions III and IV are based on yields at midpoints of transactions each day. 𝑅̅2 is the adjusted 𝑅2. The sample period is from July 2004 to January 2011. Transaction yields Regression I Regression II Variable 𝑇𝑎𝑥 𝐶𝑜𝑢𝑝𝑜𝑛 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 (𝐿𝑖𝑏𝑜𝑟– 𝑅𝑒𝑝𝑜) 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝑃𝐷 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷 𝐴𝐵𝐾 𝐵𝑅𝐾 𝐶𝐼𝐹𝐺𝑁𝐴 𝐹𝐺𝐼𝐶 𝐴𝐺𝑂 𝑅𝐷𝑁 𝑋𝐿 − 𝐶𝐴𝑃𝐴𝑆𝑆 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐴𝐵𝐾 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐵𝑅𝐾 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐶𝐼𝐹𝐺𝑁𝐴 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐹𝐺𝐼𝐶 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝐴𝐺𝑂 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑅𝐷𝑁 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑋𝐿 − 𝐶𝐴𝑃𝐴𝑆𝑆 ̅2

𝑅

Coef. 0.537 -0.082

Std. 0.026 0.005

Coef. 0.531 -0.083

Std. 0.026 0.005

0.074 0.506 0.081 0.516 (0.515) -0.287 0.088 -0.882 0.909

0.004 0.018 0.005 0.032 (0.033) 0.013 0.010 0.237 0.376

0.070 0.557 0.081 0.298 (0.315) -0.255 0.089 -0.382 1.005

0.004 0.017 0.005 0.029 (0.028) 0.013 0.010 0.140 0.388

-2.870

Midpoint yields Regression III Regression IV Coef.

Std.

Coef.

Std.

0.893 -0.095 0.061 0.483

0.052 0.008 0.005 0.026

0.881 -0.097 0.056 0.552

0.052 0.007 0.005 0.024

0.083 0.498 -0.250 0.060 -1.049

0.007 0.033 0.022 0.018 0.290

0.084 0.293 -0.211 0.064 -0.500

0.007 0.030 0.022 0.018 0.172

1.151

0.092

1.301 -3.060

0.099 0.448

0.451

0.818

0.094

0.023 0.308 0.296

0.017 0.065 0.042

-0.083 0.403 0.056

0.019 0.073 0.067

0.020 0.317 0.288

0.018 0.067 0.043

0.874 -0.076 0.424 0.119

0.098 0.020 0.077 0.083

-0.085 0.122 0.770 -0.133

0.020 0.020 0.063 0.046

-0.197 0.166 0.657 -0.277

0.021 0.028 0.083 0.050

-0.088 0.131 0.780 -0.146

0.021 0.021 0.064 0.047

-0.177 0.189 0.667 -0.261

0.022 0.030 0.080 0.052

0.323

0.023

0.270

0.024

0.055

0.062

-0.078

0.070

0.132

0.070

0.049

0.081

0.053

0.026

0.018

0.027

-0.006

0.027

-0.081

0.029

0.357

0.099

0.322

0.103

0.270

0.042

0.194

0.043

0.655

0.671

0.646

0.663

48

Table 6 The effect of counterparty credit risk for troubled states and institutional holdings This table reports results for panel regressions that include the troubled state effect and the institutional holding effect. The sample period is from July 2004 to January 2011. We estimate the following models: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 +

I.

𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 ) × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 II.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 +

𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 ) × 𝑃𝐷𝑗,𝑡−1 + 𝛿2 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 III.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 +

𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 ) × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 IV.

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 = 𝛼𝑙 + 𝛽1 𝑇𝑎𝑥𝑖 + 𝛽2 𝐶𝑜𝑢𝑝𝑜𝑛𝑖 + 𝛽3 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖,𝑡 + 𝛽4 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦𝑡 + 𝛽5 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽6 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆𝑡 + 𝛽7 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 +

𝛽8 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + (𝛿1 + 𝜑1 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 ) × 𝑃𝐷𝑗,𝑡−1 + 𝛿2 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷𝑗,𝑡−1 + 𝛾1 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛾2 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 where 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 is the dummy variable that takes a value of one for the municipal bonds issued by states with above average budget shortfall rates, and zero otherwise. 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 is dummy variable for an institution trade that takes a value of one if the par amount traded is above $ 100,000, and zero otherwise. The remaining variables are as defined in Tables 3. The liquidity factor is based on the Amihud liquidity measure. 𝑅̅2 is the adjusted 𝑅2.

Regression I Variable Tax 𝐶𝑜𝑢𝑝𝑜𝑛 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑅𝑎𝑡𝑖𝑛𝑔 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 (𝐿𝑖𝑏𝑜𝑟– 𝑅𝑒𝑝𝑜) 𝐼𝑛𝑒𝑤𝑏𝑜𝑛𝑑 𝐼𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝑃𝐷 𝐼𝑡𝑟𝑜𝑢𝑏𝑙𝑒𝑑𝑠𝑡𝑎𝑡𝑒𝑠 × 𝑃𝐷 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 × 𝑃𝐷 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 × 𝑃𝐷 𝑅̅2

Regression II

Coef. 0.561 -0.082 0.084 0.454 0.095 0.528 (0.524)

Std. 0.029 0.006 0.004 0.016 0.005 0.031 (0.032)

Coef. 0.562 -0.082 0.083 0.466 0.095 0.349 (0.351)

Std. 0.029 0.006 0.004 0.013 0.005 0.029 (0.030)

-0.299 0.088

0.014 0.011

-0.288 0.095

0.014 0.011

-0.903 0.506

0.248 0.170

-0.439 0.342

0.164 0.179

0.518

0.148

0.529

0.147

-2.494

0.441

0.948

0.076

0.641

0.653

Regression III Coef.

Std.

Regression IV Coef.

Std.

0.557

0.026

0.557

0.026

-0.080 0.080 0.462 0.078 0.526 (0.524)

0.005 0.004 0.015 0.005 0.031 (0.032)

-0.081 0.078 0.474 0.078 0.348 (0.351)

0.005 0.004 0.012 0.005 0.028 (0.030)

-0.282 0.091 -0.898 0.804

0.014 0.010 0.247 0.091

-0.271 0.097 -0.433 0.650

0.014 0.010 0.163 0.103

-0.407

0.042

-0.409

0.041

-2.505

0.423

0.932

0.093

0.650

0.662

49

Table 7 Panel regressions of the ratio of municipal to Treasury bond yields This table reports results for panel regressions of the ratio of municipal bond yields to Treasury bond yields with the same maturity. We estimate the following regression: 𝑖𝑛𝑠𝑢𝑟𝑒𝑑 𝑦𝑖,𝑗,𝑡 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦

𝑦𝑡

= 𝛼𝑙 + 𝛽1 𝑆&𝑃500 𝑅𝑒𝑡𝑢𝑟𝑛𝑡−1 + 𝛽2 𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙 𝑖𝑛𝑐𝑜𝑚𝑒 𝐺𝑟𝑜𝑤𝑡ℎ𝑡−1 + 𝛽3 ∆𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑚𝑒𝑛𝑡𝑡−1 + 𝛽4 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 + 𝛽5 𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑝𝑎𝑟𝑡𝑦𝑡−1 + 𝛽6 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝛽7 𝑅𝑎𝑡𝑖𝑛𝑔𝑖 + 𝛽8 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 + 𝛽9 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 + 𝜖𝑖,𝑗,𝑡 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦

𝑖𝑛𝑠𝑢𝑟𝑒𝑑 where 𝑦𝑖,𝑗,𝑡 /𝑦𝑡 is the monthly average ratio of insured municipal bond yields to Treasury bond yields in month 𝑡 ; 𝑆&𝑃500 𝑅𝑒𝑡𝑢𝑟𝑛𝑡−1 is the monthly return on the S&P 500 index in month 𝑡 − 1; 𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙 𝑖𝑛𝑐𝑜𝑚𝑒 𝐺𝑟𝑜𝑤𝑡ℎ𝑡−1 is the monthly growth of personal income; ∆𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑚𝑒𝑛𝑡𝑡−1 is the monthly change in the national unemployment rate; 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 is the dummy variable for an institution trade that takes a value of one if the par amount traded is above $ 100,000 and zero otherwise; 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡−1 is the monthly liquidity factor proxied by the Amihud measure; the systemic counterparty risk measure (𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑝𝑎𝑟𝑡𝑦) can be either

𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑃𝐷 which is the monthly averaged risk-neutral default probability across municipal bond insurers or 𝐿𝑖𝑏𝑜𝑟– 𝑂𝐼𝑆 which is the difference between the three-month Libor and OIS rates; 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 is the dummy variable that takes a value one for the municipal bonds with a speculative-grade rating (below BBB), and zero otherwise; 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 is the dummy variable which has a value of one for the subprime crisis period, and zero otherwise; and 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 is the dummy variable which has a value of one during the illiquid period, and zero otherwise. 𝑅̅2 is the adjusted 𝑅2. The sample period is from July 2004 to January 2011.

Variable 𝑆&𝑃500 𝑅𝑒𝑡𝑢𝑟𝑛 𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙 𝐼𝑛𝑐𝑜𝑚𝑒 𝐺𝑟𝑜𝑤𝑡ℎ 𝐼𝑖𝑛𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 ∆𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑚𝑒𝑛𝑡 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑃𝐷 𝐿𝑖𝑏𝑜𝑟 − 𝑂𝐼𝑆 𝑅𝑎𝑡𝑖𝑛𝑔 𝐼𝑠𝑝𝑒𝑐𝑢𝑙𝑎𝑡𝑖𝑣𝑒 × 𝐼𝑠𝑢𝑏𝑝𝑟𝑖𝑚𝑒 𝐼𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 × 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦: 𝐴𝑚𝑖ℎ𝑢𝑑 𝑅̅ 2

Regression I Coef. Std.

Regression II Coef. Std.

-0.435 -0.037 -0.076 0.983 -0.736 1.222

0.164 0.005 0.004 0.319 0.164 0.248

-0.552 -0.077 -0.083 1.649 -0.848

0.161 0.006 0.004 0.302 0.227

0.018

0.002

0.051 0.006

0.022 0.002

0.343

0.019

0.461

0.021

-0.809

0.288

-1.177

0.361

0.298

0.259

50

Figure 1. Probabilities of default for municipal bond insurers This figure plots the time-series of PDs for eight municipal bond insurance companies: ABK, AGO, BRK, CIFGNA, FGIC, MBIA, RDN, and XL-CAPASS. The risk-neutral default probabilities of the corresponding bond insurers are obtained from the CDS spreads and recovery rates for municipal bond insurers. The sample period is from July 2004 to January 2011 with missing values for some insurers.

1.0

ABK

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0 2004/7

1.0

2006/7

2008/7

2010/7

BRK

0.0 2004/7

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0 2004/7

1.0

2006/7

2008/7

2010/7

FGIC

0.0 2004/7

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0 2004/7

1.0

2006/7

2008/7

2010/7

RDN

0.4

0.4

0.2

0.2

2010/7

2006/7

2008/7

0.0 2004/7

2010/7

MBIA

XL-CapAss

0.6

2010/7

CIFGNA

1.0

0.6

2008/7

2008/7

2006/7

0.8

2006/7

2006/7

0.0 2004/7

0.8

0.0 2004/7

AGO

2006/7

2008/7

2008/7

2010/7

2010/7

51

Figure 2. The time series of aggregate liquidity measures This figure plots the time series of aggregate liquidity for the municipal bond market. The upper and lower panels display the Amihud and Pastor-Stambaugh liquidity innovations, respectively. The sample period is from July 2004 to January 2011 and the liquidity measures are constructed from the sample including both insured and uninsured municipal bonds. The Amihud illiquidity innovations are converted to liquidity innovations by adding a negative sign. 0.2

0

-0.2

-0.4 2004 2005 2006 2007 2008 2009 2010 The Amihud liquidity measure

0.2

0.0

-0.2 2004 2005 2006 2007 2008 2009 2010 The Pastor-Stambaugh liquidity measure