The Term Structure of Corporate Bond Liquidity Spreads: Evidence from Insured Corporate Bonds

Transcription

1 The Term Structure of Corporate Bond Liquidity Spreads: Evidence from Insured Corporate Bonds Diego Leal, Bryan Stanhouse, Duane Stock November 27, 2017 Abstract Modelling the liquidity spread of corporate bonds has proven very difficult because the credit spread is composed of interactive default and liquidity components. Our research uses a special set of default free corporate bonds to isolate that part of the credit spread attributable to the liquidity spread. We find that the term structure of liquidity spreads changes dramatically from being positively sloped in periods of financial stress to being negatively sloped in periods of relative economic tranquility. Key Words: term structure, liquidity premium, corporate bonds JEL classification:g00, G12, G19 The authors are at the Price College of Business, Division of Finance, 205A Adams Hall, University of Oklahoma, Norman, OK 73019; Tel Their contact s are dleal@ou.edu, bstanhouse@ou.edu, and dstock@ou.edu respectively. Duane Stock is the corresponding author. 1

2 1. Introduction The liquidity of anything that can be traded is a very important dimension of its value. Ceteris paribus, anything that is more liquid tends to have more value than something that is relatively less liquid. The finance literature that describes and models liquidity has grown tremendously in recent decades. This growth accelerated with the market wide (aggregate) liquidity shocks of the 2008 financial crisis. As given by Kyle (1985), the basic dimensions of liquidity may be described as trading cost, depth, and resiliency. Respectively, these are commonly measured by such measures as bid-ask spreads, the Amihud (2002) measure, and changes in dealer inventory. Acharya and Pedersen (2005) model the impact of liquidity upon equity valuation by developing a liquidity-adjusted capital asset pricing model where equity returns depend on expected liquidity and covariance with market returns and market liquidity. They find that negative shocks to liquidity reduce valuation and thus give low contemporaneous returns on equities. More recent liquidity research has expanded to instruments beyond equities where databases on government bonds and the TRACE database have greatly expanded the ability to examine both government and corporate bond liquidity. For example, the liquidity of default free U.S. Treasury bonds has been analyzed by, among others, Amihud and Mendelson (1991) and, more recently, by Fontaine and Garcia (2012) and Musto, Nini and Schwarz (2016). Driessen, Nijman, and Simon (2017) analyze differential pricing and liquidity of German short and long term sovereign bonds. With respect to corporate bonds, for example, Bao, Pan, and Wang (2011) examined the liquidity of corporate bonds where they use the Roll (1984) measure in preference to bid-ask spread. It is noteworthy that they find the liquidity component of yield spread can sometimes be greater than the default spread component. Bao and Pan (2013) find that empirical 2

3 volatilities of corporate bond returns are higher than implied by the Merton (1974) model and attribute this finding to inadequate modelling of liquidity. More recently, Bongaerts, de Jong, and Driessen (2017) analyze corporate bond liquidity as a function of both asset-specific characteristics and systematic liquidity shocks. While the growing list of bond market liquidity questions answered by recent research is impressive, it is curious that research concerning the term structure of the liquidity spread for corporate bonds is very scant. The need for such research is clear given that risk free rates and default risk premiums have been clearly shown to be dependent upon maturity. Our results may be particularly useful to policy makers attempting to analyze the risk and liquidity of corporate bonds issued by banks. For clarity of terminology, we note that recent literature has defined credit spread as a function of both the default spread and the liquidity spread. The purpose of our research is to document and analyze the term structure of liquidity spreads (TSLS) for corporate debt instruments. More specifically, what determines the shape of corporate bond TSLS? Is the shape of the term structure usually positive, usually negative, usually concave, or usually convex? Or, does the slope systematically change with underlying financial and macroeconomic conditions? A unique data base of corporate bonds that have no default risk allows us to answer these questions. These corporate bonds were issued by banks and were fully insured with the full faith and credit of the U.S. Treasury so that the yield spread of these unique corporate bonds above those of U.S. Treasury bonds was solely due to any difference in liquidity. We present several interesting hypotheses regarding the determinants and shape of the TSLS. Term structures of (total) required yields for corporate bonds are naturally built upon the term structures of the different dimensions of required yield. That is, the required yield for a 3

4 corporate bond of a specific maturity is a function of the risk free rate for that maturity, the default premium for that specific maturity, and the liquidity premium for that specific maturity where default and liquidity are interactive. The literature on default-free U.S. Treasury term structure is massive where one example is Estrella and Hardouvelis (1991) where their research demonstrates that a positively sloped term structure of risk free rates is associated with an expanding economy. More recently, Bansal, Connolly, and Stivers (2014) study the relation between stock and bond returns as related to changes in the slope of the term structure. There is also an extensive literature concerning default risk premium term structure. Theoretical work by Merton (1974) develops an option based theory of default risk premia where the shape of the term structure varies according to the credit rating of the firm; lower quality firms tend to have negatively sloped default premium term structures whereas higher quality firms tend to have positively sloped default premium term structures. In further theoretical work by Longstaff and Schwartz (1995) the shape of the default premium term structure of a particular curve is complex and typically humped wherein the slope changes from positive to negative. Empirical work by Helwege and Turner (1999) on default premia term structure tends to show an upward sloping term structure of default premiums. Given the obvious volume and importance of research on the above term structures, it is similarly important to model the TSLS for corporate bonds. The problem is that it is very difficult to cleanly isolate spreads due to default from spreads due to liquidity because liquidity risk and default risk are interdependent. In this context, first consider the theoretical work of He and Xiong (2012). They maintain that a decline in liquidity results in an increase in both the liquidity premium and default premium of a corporate bond due to rollover risk. To illustrate their theory, assume a decline in liquidity just before an outstanding bond matures. The firm will 4

5 normally rollover the maturing debt and just issue a new bond to replace it. However, equity holder appetite for rolling over the debt is limited; they will only rollover if they perceive the value of their equity is positive after the potential rollover. He and Milbradt (2014) maintain that bargaining with bond dealers determines endogenous liquidity which, in turn, depends on the fundamental value of the firm and bond maturity. Consistent with He and Xiong (2012), a default-liquidity loop occurs because corporate default decisions interact with liquidity. Although the research by He and Xiong (2012), He and Milbradt (2014), and others represent significant advancements in modeling bond market liquidity spreads, they do not address the TSLS. Ericcson and Renault (2006) recognize that liquidity and default are related and suggest a theoretical model for cases where severe financial distress has occurred and there is negotiation between debt and equity holders. Their theoretical TSLS is negatively sloped. Feldhutter (2012) analyzes the theoretical difference in bond prices paid by small traders and large traders in order to identify liquidity crises. He assumes certain parameter values to develop a TSLS explained by expected selling pressure and, alternatively, a TSLS explained by search costs and occasional selling pressure. The shapes of the theoretical TSLS curves are sometimes positively sloped and sometimes negatively sloped depending on which of two economic situations holds. Feldhutter (2012) does not conduct an empirical estimation of liquidity term structure and how the shape may change over time. Also, he does not consider the impact of macroeconomic stress factors such as VIX and Fed funds futures. In contrast to the above attempts to develop a theoretical model of TSLS, Dick-Nielsen, Feldhutter, and Lando (2012) make a brief empirical attempt to explain TSLS but cannot explain 5

6 how it behaves. That is, they find the TSLS tends to be positively sloped when theory suggested by Amihud and Mendelson (1991), Ericsson and Renault (2006) and Feldhutter (2012) suggest a negative slope. They end their very brief term structure analysis by saying the decomposition of liquidity into individual components across maturity is outside the scope of their research. Our research better controls for default risk and, also, provides explanations for why the term structure is positively sloped under some economic conditions but negatively sloped under other economic conditions. Section 2 of this paper contains our hypotheses. Then, sections 3 and 4 describe our data and methodology. The results of testing the hypotheses are given in section 5. Section 6 summarizes our major finding and concludes our research. 2. Hypotheses We present interesting hypotheses related to our purpose. Although there are major differences, our hypotheses follow a path generally consistent with Bongaerts, de Jong, and Driessen (2017). That is, as they do, we maintain that bond market liquidity premia are compensation for both trading costs of an asset and, also, exposure of asset returns to variation in systematic liquidity. Numerous prior studies of bond market liquidity have found evidence indicating that trading costs (frequently proxied by the bid-ask spread) and market depth (frequently proxied by the Amihud measure) are dimensions of liquidity that are priced in the non-default component of a bond s spread over U.S. Treasuries. (See Longstaff, Mithal, and Neis (2005), Dick-Nielsen, Feldhutter, and Lando (2012), and Black, Stock, Yadav (2016)). One interesting follow-up empirical question is whether the impact of these liquidity measures upon the non-default spread differs with time to maturity. More specifically, does the impact of a liquidity measure upon the 6

7 liquidity premium differ depending on the underlying economic conditions and time to maturity for the specific bond? Hypothesis 1: Liquidity measures have a substantially differential impact upon liquidity spreads and the slope of the TSLS in different economic environments. Longstaff (2004) analyzes the flight-to-liquidity phenomenon regarding Refcorp bonds that were issued in the aftermath of the savings and loan crisis of the 1980 s. In general, he finds that the non-default component of these agency bonds can be mostly attributed to several consumer sentiment measures. Although Longstaff (2004) does not discuss how the market sentiment measures might impact the liquidity spread differently in alternative maturities, his results suggest that the impact is not homogenous across time to maturity. Also, Black, Stock, and Yadav (2016) conclude that the market fear factor has a positive and significant impact on determining the non-default spread of corporate bonds. These two papers however, do not address an important empirical question; namely, is the impact of market sentiment/fear factor on the non-defaultable spread different for different maturities? It is quite logical that the impact of financial instability on the non-default spread would not be uniform across the term structure. Assume that two investors at different ends of the maturity spectrum are impacted by a liquidity shock during a period of high financial uncertainty. The classic flight-to-liquidity argument proposed by Longstaff (2004) would suggest that investors would bid up the price of more liquid short term Treasury bonds, thus widening the spread. Assuming a positively sloped term structure, an enhancement of this interpretation would be that the investor holding bonds near the short-end of the term structure will likely be less concerned about the eventuality of a financial shock because the proceeds of their bond will be available relatively soon. This view is similar to theory given by Gehde-Trapp, Schuster, and 7

8 Uhrig-Homburg (2016). Therefore, all-else equal, the investor holding shorter term bonds may well accept a smaller spread. This analysis implies that the liquidity spreads for short-term maturities should be less sensitive to a high VIX as compared to long-term maturities; this behavior leads to a positively sloped TSLP in periods of stress. Note that this interpretation is consistent with the notions of Longstaff (2004). Recent papers that study liquidity of corporate bonds also typically conclude that monetary policy is an important determinant of liquidity. Longstaff (2004) presents the following line of reasoning for including monetary policy: if the amount of Treasury bonds available in the market is reduced, then investors will be more willing to pay a higher premium to hold the remaining Treasury bonds. Also, we note that Lin, Wang, and Wu (2011) show that liquidity measures spike when the Federal Reserve Board announces different interest rate targets. Longstaff (2004) suggests that the impact of monetary policy is greater at the short-end of the term structure than the long end. In the time period that we study, this effect would largely depend on the segment of the term structure that is being targeted by Federal Reserve policy. For example, Longstaff provides the following reasoning: if the Federal Reserve is more active at the short-end of the term structure, then we should expect a higher non-default (liquidity) component at the short end versus the long end. At the same time, we realize that there is potential for a spill-over effect as described by Gelde-Trapp, Schuster, and Uhrig-Homburg (2016) and Goyenko, Subrahmanyam, and Ukhov (2011). That is, improvement in short maturity liquidity could spill-over to longer maturities. Given the above, we suggest hypothesis 2 as follows. Hypothesis 2: Macroeconomic variables representing financial stress, monetary policy, the term structure of risk free U. S. Treasury yields, and market-wide liquidity have a different economic on the TSLS under alternative economic conditions. 8

9 The literature that attempts to identify alternative shapes of TSLS is very scant both theoretically and empirically. However, there are some papers that provide guidance regarding the dynamics of liquidity spreads at the long end versus at the short end. For example, Ericsson and Renault (2006) find that liquidity spreads are generally decreasing with time to maturity, a result that is consistent with the empirical findings of Amihud and Mendelson (1991). Feldhutter (2012) also finds a negative slope under some conditions, but, alternatively, finds an upward sloping structure when investors expect an aggregate shock to the market. Finally, the nondefault component plots from Longstaff (2004) imply that the short end of the TSLS follows a different dynamic than the long-end, suggesting changes in the slope of the TSLS over time. Of course, the term structure of Treasuries as well as the term structure of corporate bonds is known to change under different conditions; therefore, one plausible explanation for the varying results obtained in the above literature is that the shapes of the TSLS might differ substantially in alternative economic epochs. This motivates hypothesis 3. Hypothesis 3a: The shape of the TSLS changes over time dependent upon varying economic conditions. Hypothesis 3b is strongly related to hypothesis 3a and utilizes Feldhutter (2012) theory to explain alternative slopes with the varying macroeconomic variables and economic conditions discussed above. We refer to the below determination of differential term structure slopes as the Feldhutter hypothesis. The TSLS premia during a financially stressed period is dominated by the effects of expected selling pressure and the term structure is therefore positively sloped. As in Feldhutter (2012), investors tend to become more conscious of funding liquidity shocks when there is a wide-spread, market-wide expectation of an aggregate liquidity shock. In Feldhutter s (2012) 9

10 words, investors become low investors where funding liquidity shocks represent positive holding costs. In this environment, there is an expectation that selling pressure will continue for an extended period of time and a longer maturity bond has a greater potential for being exposed to a shock because it has longer maturity. In fact, Feldhutter s (2012) model for a two-period bond has twice the shock exposure as a one period bond. The compensation for exposure to shocks (yield spread) thus grows with maturity. In contrast, as in Feldhutter (2012), non-stress periods are not characterized as experiencing broad market-wide liquidity shocks and thus search costs and occasional selling pressure effects determine the shape of the term structure. The intuition is that a shorter maturity bond trader has fewer trading opportunities during the life of the bond and may well suffer from a lack of attractive conversion opportunities. On the other hand, a long maturity trader has a longer period in which to trade and has time to look for additional counterparties with which to trade. These circumstances create a negatively sloped liquidity term structure. We note that Amihud and Mendelson (1991) and Ericsson and Renault (2006) also suggest negative term structures but do not analyze term structures under stress versus non-stress conditions. Hypothesis 3b: The slopes of TSLS are consistent with the Feldhutter (2012) theories of how expected selling pressure and occasional selling pressures impact the term structures of liquidity spreads. 3. Data Description To perform our analysis, we gathered data for three different types of bonds. The first type of bond is insured corporate bonds (ICB) which were issued by numerous banks in 2008 and These bonds were insured by the U.S. Treasury and were backed by the full faith and credit of the U.S. Treasury; thus these corporate bonds had no default risk. These bonds were 10

11 part of the debt guarantee program (DGP) meant to stabilize the banking system. The debt guarantee limit was restricted to 125% of the face value of senior unsecured debt that was outstanding as of September 30, 2008 and scheduled to reach maturity on or before June 30, The last day to issue debt under the DGP was October 31, 2009 and the debt guarantee expired either at maturity or on December 31, 2012, whichever came first. Bond price data for these insured corporate bonds were gathered from the Trade Reporting and Compliance Engine (TRACE), which provides comprehensive coverage of bond trades. For these insured bonds, we also gathered information such as bond maturity, issuance dates, coupon rates and other issuance characteristics from Mergent FISD. The second type of bond used was U.S. Treasury bonds which are commonly assumed free of default risk. To compute the spread of our insured corporate bonds (ICB) over equal maturity Treasury bonds (TB), we use the H-15, which publishes data on U.S. Treasury yields, for fixed maturities, on a daily basis. A Hermitian cubic interpolation is used if the maturity of the ICB does not exactly match the H-15 data 1. Our results are robust to alternative interpolation specifications such as the linear interpolation as done by (Dick-Nielsen et al. (2012)). We use GOVPX to compute bid ask spreads of Treasury bonds. Liquidity spreads are the difference in yield between ICBs and U.S. Treasury bonds of equal maturity. The third type of bond utilized was all U.S. corporate bonds other than the insured bonds. These other corporate bonds were used to represent market wide liquidity of the corporate bond market. TRACE is used to gather prices and yields for these bonds. To remove errors, cancellations, corrections, and reversals in the TRACE data, we filter the intraday transaction data according to the procedure described in Dick-Nielsen (2009). Finally, to eliminate extreme 1 We utilize a Hermitian cubic procedure in our interpolation as done by the Treasury in the H

12 outliers, the data is further treated with the median filter described in Edwards, Harris, and Piwowar (2007). In addition to bond price data for the above types of bonds, we use a battery of variables to represent financial and macroeconomic conditions such as the VIX, U.S. Treasury term structure slope, and the 30-day Fed funds futures price. 2 Liquidity Measures In order to thoroughly examine the impact of liquidity measures, we compute four measures of liquidity: bid-ask spread, the Amihud measure, the Imputed Roundtrip Trades (Roundtrip measure), and the interquartile range. The results for the impact of the liquidity measure upon liquidity spreads are very similar for all liquidity measures where we report the results using the Amihud measure. Figure 1 shows the strong correlation among the liquidity measures over the time period of our research. 3 To proxy for the bid-ask spread we follow Hong and Warga (2000) and Black, Stock, and Yadav (2016) and aggregate for each bond in each day, the price (p) of the Buys minus the price of the Sells, weighted by the volume size of each trade (q). We then divide this by the midpoint price between the buy and the sell in each trade: 2 The Fed funds futures data is drawn from and 3 As bond market liquidity analysis has progressed, there has been debate concerning the best measure(s) of bond market liquidity, how they may or may not move together, and how bond market liquidity behaves in times of stress versus non-stress times. Dick-Nielsen, Feldhutter, and Lando (2012) compute a liquidity measure that is a composite of different measures and, furthermore, analyze the liquidity component (versus the default component) of corporate bond yields both before and after the financial crisis. Schestag, Schuster, and Uhrig-Homburg (2016) compute and evaluate a long list of alternative liquidity measures and find that the most commonly used measures are very strongly correlated and move together over time. 12

13 bbbbbb aaaaaa = NN 1 pp qq qqbb NN 1 pp qq + qqbb NN 1 pp qq qqss NN 1 pp qq qqss We next calculate the Amihud liquidity measure for all corporate bonds following the definition in Dick-Nielsen et al. (2012). We aggregate the absolute value of the returns per trade and we divide by the trade volume. The Amihud measure is designed to capture the depth dimension of liquidity, i.e. the price impact of transactions adjusted transaction size: NN AA = 100 NN aaaaaa(rr tt rr tt 1 ) vvvvvvvvvvvv / where r t = log (p t ) is the return of the bond for the transaction t, vol is the volume traded in transaction t, and N is the number of trades in one day. 4 Also, following Feldhutter (2012), we compute the imputed roundtrip measure which captures pre-arranged trades. Bonds sometimes trade two or three times within a short window. This can be interpreted as a dealer prearranging the transaction and collecting the spread. Similar to Dick-Nielsen et al. (2012), we define the roundtrip measure as the spread between the maximum price and the minimum price in such a roundtrip transaction. We also only consider roundtrip transactions where exactly two or three trades occur nearly simultaneously: RRRRRRRRRRRRRRRRRR = pp MM pp mm pp MM where pp mm is the lowest price in the pre-arranged deal and pp MM is the highest price in the prearranged deal. 4 The denominator of the Amihud measure is scaled as in previous studies such as Black, Stock, and Yadav (2016). 13

14 Finally, we calculate the daily interquartile range as another proxy for the daily bid-ask. We calculate the interquartile range as the 75th percentile of a bond-day price minus the 25th percentile divided by the median of the bond price in that day: IIIIII = pp 0.75 pp 0.25 pp 0.50 We also include the volatility of liquidity measures, which Dick-Nielsen, Feldhutter, and Lando (2012) have shown to be able to explain part of the liquidity spread. We calculate the volatility of each measure by calculating the standard deviation over 20 day windows. We choose 20 day windows as a compromise between sample size and explanatory power of the variable. Our results are also robust to windows of different sizes 5. Finally, using TRACE, we also compute the above liquidity measures for the full sample of corporate bonds between 2008 and 2012 as proxies for market-wide liquidity. To remove errors due to cancellations, corrections, and reversals in the TRACE data, we filter the intraday transaction data according to the procedure described in Dick-Nielsen (2009). Finally, to eliminate extreme outliers, the data is further treated with the median filter described in Edwards, Harris, and Piwowar (2007). We also include the bid-ask spread for U.S. Treasury bonds from GOVPX and CRSP as a proxy for overall liquidity in the market and our results are robust to using either. Table 1 displays detailed information regarding means and standard deviations of liquidity measures. For statistical analysis that follows, we use the Amihud measure where, again, these statistical results are very similar if the above alternative liquidity measures are used. 5 We also calculated the volatility of the liquidity measures by using 1-month and 3-month rolling windows. Larger windows mean we have to drop more observations from our regressions. 14

15 4. Methodology Epoch Selection A fundamental part of our analysis is to appropriately select epochs of the time period 2008 to 2012 for which underlying economic conditions were clearly different. We choose these epochs based on significant changes of GDP, VIX, and Fed funds rates futures prices. By identifying variations in the price of the Fed funds rate futures price (10% upwards or downwards), we believe we can identify periods of relative economic stress. Thus, our period of stress is from October 2008 to November 2009 and the non- stress period is November 2009 to December Figure 2 provides plots of VIX and Fed funds futures. These periods are very similar to the stress and non-stress periods used in Acharya, Amihud, and Bharath (2013) and, also, NBER defined periods of economic contractions and expansions. Figure 3 contains raw liquidity premium spreads (ICB yields less Treasury yields of equal maturity) plotted against maturity for the different epochs. The plots are averages of all bond spreads with the same time to maturity. These spreads are aggregated by maturity buckets of one-week length to avoid noise and high dispersion in the data. The first panel provides preliminary evidence of a positive slope for the early (stress) part of the data while the second panel clearly suggests a negative slope for later (non-stress) observations. Appendices A and B use alternative epochs where the main results are similar to Figure 3 and other results we report below. Maturity portfolio selection To test whether periods of stress and non- stress have a differential impact on the TSLS, we aggregate bonds into maturity buckets. We chose two buckets short and long in order to parsimoniously describe the slopes of the TSLS without sacrificing sample size in each of the 15

16 buckets. We alternatively used three buckets short, medium, and long in addition to using different epochs where the results are always similar. See Appendices A and B for this robustness analysis. We now allocate our daily bond observations into the two buckets according to the following procedure. If the time to maturity is below the 50 th percentile for that epoch, the observation is categorized as short-term, and if it is above the 50 th percentile, it is categorized as long-term. To test hypotheses about liquidity spreads, we proceed as follows. For each epoch, and each maturity portfolio (see epoch and maturity portfolio selection above), we run the following specification of the liquidity spread (LS) where the liquidity measure is one of our four liquidity measures. The liquidity spread is the yield on the insured corporate bond less the yield on the equal maturity U.S. Treasury. In the interest of parsimony, we only report Amihud measure results which are very similar to the results for all alternative liquidity measures. VIX is the wellknown volatility index, Fed funds futures is the futures contract price, Treasury slope is the yield of a 6 month Treasury less the yield of a 3 month Treasury, TTM is time to maturity, market liquidity is the liquidity measure for all corporate bonds in TRACE, volatility of liquidity is the standard deviation of the liquidity measure for the bond over a 20-day rolling window, and e it represents the error term. LLSS ii,tt = αα + ββ 1 (LLLLLLLLLLLLLLLLLL MMMMMMMMMMMMMM) ii,tt + ββ 2 (VVVVVV) tt + ββ 3 (FFFFFF FFFFFFFFFFFFFF PPPPPPPPPP) tt + ββ 4 (TTTTTTTTTT ssssssssss, 6mm 3mm) tt + ββ 5 (TTTTTT) ii,tt + ββ 6 (MMMMMMMMMMMM LLLLLLLLLLLLLLLLLL) tt + (VVVVllllllllllllllll oooo LLLLLLLLLLLLLLLLLL) ii,tt + ee ii,tt 16

17 Here ii is one of the two epochs and tt is one of the two maturity buckets. We follow a panel regression in this specification and we include issuer fixed effects. We also cluster the standard errors at the firm level to account for serial correlation in the covariates. In later analysis we, estimate a vector autoregression (VAR) system for how short (long) term spreads may persist to preserve a particular TSLS shape for stress periods versus non-stress periods. 5. Results The results from regressing liquidity spreads upon important explanatory variables related to our hypotheses are detailed in Table 2a. Our measure of bond specific liquidity is the Amihud measure (AMIHUD). We also used other measures of liquidity described above (bid-ask spread, roundtrip, and interquartile range) where all show very similar results; these alternative results are available from the authors. We include explanatory variables, not directly related to our hypotheses time to maturity (TTM), market-wide liquidity (AMIHUDMKT) and volatility of liquidity (AMIHUDVOL) as control variables because other studies such as Dick-Nielsen, Feldhutter and Lando (2012) utilize them. Our right hand side variables are characterized by large differences in their respective magnitudes. Consequently, in order to facilitate a comparison of their relative impact upon the liquidity spread, we have standardized (zero mean, standard deviation of one) our regressors. After this transformation of our data, a unit increase in any independent variable corresponds to a one standard deviation increment in that variate. We maintain that our most important result is likely the differential slope of the TSLS in a stress period (positive slope) versus a non-stress period (negative slope) as shown above and, also, more definitively, in figures and tables below. We run separate regressions for short and long-term maturity buckets in stress and in non-stress economic periods in order to test our hypotheses. One aspect of our results is that 17

18 the coefficient of determination averages 51% over our period of economic stress for short and long-term securities, while the average R 2 for short and long-term liquidity spreads in our nonstress epoch is only 15%. In addition, long-term (LT) reduced form coefficients are larger than short-term (ST) regression coefficients for six of seven variates in a periods of stress, while, in distinct contrast, the inequality is reversed for five of seven independent variables during the non-stress period. These four observations point to the possibility that market participants pay very close attention to bond specific liquidity measurements, macroeconomic variables, and monetary policy during periods of economic stress. Furthermore, investors translate the behavior of these variables into portfolio decisions. This could be especially true for long-term bond holders, since liquidating LT bonds when a financial shock occurs can be very expensive. In Table 2a, bond specific liquidity is quantified by the Amihud measurement, AMIHUD. In our stress period, a unit increase in the standard deviation of Amihud liquidity increases the short-term liquidity spread by 4.4 basis points and the long-term spread by 15.6 basis points. Both regression coefficients are statistically significant at the 1% level. Of course, Amihud liquidity is actually a measurement of illiquidity, where an increase corresponds to an increase in the absolute value of the change in the log of the security price due to the transaction at hand. The greater the AMIHUD, the greater the illiquidity; consequently, the positive effect of AMIHUD upon both ST and LT liquidity spreads is well anticipated. However, remarkably, the long-term regression coefficient on AMIHUD is nearly four times larger than the impact of AMIHUD on the short-term spread. Not only does the impact of AMIHUD increase with the time to maturity, it does so dramatically. This is emphatic support for the notion that times of stress enhance the focus of investors upon meaningful economic variables. Furthermore, changes 18

19 in AMIHUD disproportionately impact the LT yield spread since the consequences of holding LT bonds during a financial shock can be severe. We note that the Amihud measure changes markedly from the early part of the stress period to the later part of the stress period. Using the regression coefficients of AMIHUD to examine the differential change in the liquidity spread as AMIHUD changes within the stress LLLL ii period yields dd(llll ii ) = dd(aaaaaaaaaaaa). Clearly dd(llll LLLL) will be greater than dd(llss SSSS ), with dd(aammiiiiiiii ) > 0. Consequently, we have differential changes in the liquidity spread that contribute to the determination of the positively sloped term structure of the liquidity spread depicted in Figures 3, 4, and 6A. In our non-stress epoch, AMIHUD continues to have a positive impact upon the liquidity spread. Both coefficients are statistically significant with one standard deviation increase in AMIHUD increasing the ST liquidity spread by 28.6 basis points and, in contrast, increasing the LT liquidity spread by only 4.8 basis points. These coefficients detail a dramatic reversal in the relative importance of AMIHUD for short-term and long-term spreads in stress free periods. Equally notable is the fact that AMIHUD's impact upon the LT liquidity spread is one-third of the size it was during a financial crisis. Relatively free of the threat of a liquidity shock, clientele effects, as suggested by Gehde-Trapp, Schuster, and Uhrig-Homburg (2016), motivate some investors to hold long-term securities with little need for a liquidity premium. Meanwhile, enhanced spreads are enjoyed by ST bond holders as compensation for incurring the repeated search costs of owning short-term bonds. In summary, the AMIHUD regression coefficients offer unqualified support for hypothesis 1. The impact of our liquidity measurement varies dramatically with a standard deviation increase in AMIHUD occasioning a minimum change in the LLSS SSSS of 4.4 basis points in 19

20 stress times and, in strong contrast, having a maximum impact of 28.6 basis points upon LLSS SSSS in non-stress times. Importantly, in times of stress, AMIHUD s impact is increasing in time to maturity and, in contrast, it is falling in the time to maturity in non-stress free periods. We now address hypothesis 2 where we suggest that macroeconomic variables representing financial stress and market-wide liquidity have a different impact on TSLS under alternative economic conditions. Of course, VIX is a standard measure of financial stress. Again, we report results for the stress period first. A standard deviation increase in VIX during a period of financial stress increases the liquidity spread on ST bonds 12.9 basis points and 22.3 basis points on long-term bonds where both coefficients are statistically significant. Their positive impact is intuitive since an increase in VIX proxies an elevated level of investor anxiety which generally occasions an increase in the liquidity spread. The fact that the LT reduced form coefficient on VIX is nearly twice as large as the short-term coefficient provides further evidence that periods of economic stress motivate long-term security holders to pay close attention to and to react to macroeconomic factors. The average standardized value of VIX during our stress period was 1.32 while the average normalized value of VIX for 13 months before the crisis was A change in VIX of 1.75 standard deviations combined with our regression coefficients for LT VIX and ST VIX yields dd(llll LLLL ) = and dd(llll SSSS )= These differential changes in the liquidity spread during a period of economic stress contribute to the determination of the positively sloped term structure of the liquidity spread depicted in Figures 3, 4, and, most prominently, 6A. In our non-stress period, VIX again registers a positive and statistically significant impact upon both ST and LT liquidity premiums, and percentage changes, respectively. However, it is important to note that the relative magnitudes of VIX upon ST and LT securities is 20

21 reversed. Even more importantly, the regression coefficient of VIX upon the LT liquidity spread, in our non-stress epoch is only one seventh of its size in the earlier epoch. While the average VIX is zero over all three epochs, the VIX retreats to an average of standard deviations below the mean in the stress free interval, reassured investors return to being comfortable with holding LT bonds. They require very little in regard to liquidity premiums and they minimize the frequency of incurring search costs by owning securities with remote dates of maturity. The empirical support for hypothesis 2 is clear as an increase in VIX can change LLSS LLLL in a stress period as much as 22.3 basis points, or, in contrast, only increase the liquidity spread for ST bonds as little as 4.5 basis points in a non-stress period. Longstaff (2004) suggests that the short-term liquidity spread is less sensitive to VIX than the LLSS LLLL. In contrast, our regression results record a greater increase in the LLSS SSTT (4.5 basis points) than in the LLSS LLLL (3.4 basis points) for a standard deviation increase in VIX during a non-stress epoch. We used the Fed funds futures price (FFFP) to proxy the impact of Federal Reserve behavior upon the liquidity spread. The Fed fund futures is a popular 30-day contract whose price implicitly contains investor expectations about the future cost of overnight borrowing between banks. The sustained actions of the Federal Reserve in the Fed funds market in the stress period pushed the average FFFP 1.4 standard deviations above its pre-stress level found in the 13 months before the crisis of This escalated value of the Fed funds futures price failed to impact the ST liquidity spread in a statistically meaningful way. However, this absence of a statistically significant regression coefficient is a powerful result. It suggests a strong relationship between the ST yields on ICB bonds and Treasury bonds. Clearly if FFFP was 1.4 standard deviations above its pre-stress level, then the Treasury yield must have fallen 21

22 dramatically due to Federal Reserve policy behavior. However, ST ICB yields matched the deterioration of government yields and left the ST liquidity spread unaffected by FFFP in the stress period. This remarkable interdependence between the two yields establishes the existence of market forces which preserve the short-term liquidity spread in the stress period despite aggressive monetary policy. The reduction in the anticipated Fed funds futures rate did occasion a statistically significant change in the long-term liquidity spread of -7.0 basis points. Under the threat of a forced conversion of LT assets, changes in monetary policy influence investor behavior. In the non-stress time period, Table 2a documents a significant positive relationship between FFFP and the liquidity spread of LT bonds. A one standard deviation increase in the Fed funds futures price increases the long-term liquidity spread by 1.3 basis points. As in the stress period, a change in FFFP occasions no statistically significant impact upon the ST liquidity spread. Again, we argue that an insignificant regression coefficient documents the strength of market forces to preserve the existing short-term premium regardless of Federal Reserve operations. According to hypothesis 2, monetary policy will impact segments of the term structure differently and the effect(s) will change over the business cycle. Our research analyzes shortterm monetary policy, by the Federal Reserve, in terms of its impact upon the Fed funds futures price. Surprisingly, the FFFP has no statistically significant impact upon the short-term liquidity in either epoch. This result is in contrast to Longstaff s (2004) conjecture that the greater the Federal Reserve activity at the short end of the maturity spectrum, the greater the spread. In agreement with hypothesis 2, our empirical results do establish the FFFP as having a statistically meaningful impact at the long end of the term structure of the liquidity spread and that the 22

23 direction of that effect depends on business conditions. That is, the sign is different (negative) under stress. It is often held that the slope of the Treasury term structure proxies the expected change in risk-free yields. While we have no prior notions as to the impact of the slope of Treasury term structure upon the liquidity spread, Table 2a documents the regressor s impact with reduced form coefficients of 2.7 basis points on the short-term and 3.9 basis points on the long-term liquidity spread. The estimates are statistically significant and increasing in the TTM (time to maturity). It is possible that an increase in the slope of the Treasury term structure reflects inflationary expectations or contractionary monetary policy. Either scenario, of course, engenders the kind of investor anxiety that must be offset with a higher liquidity premium. These regression results confirm the positively sloped term structure of the liquidity spread. For the 13 months before the crisis, the standardized slope of the term structure of treasury securities averaged standard deviations above the zero mean garnered over the pre-stress, stress, and stress-free periods. The average normalized value of TREASLP for the stress period was so that the differential change in TREASLP was [ ] = Combining dd(tttttttttttttt) > 0 with estimates for the marginal impact of the treasury slope upon the liquidity spread for ST and LT securities occasions a dd(llss ii ) that is increasing in the time to maturity and contributes to the determination of the positively sloped term structure of the liquidity spread in a period of stress. In the non-stress period, our regression analysis documents no meaningful relationship between the treasury slope and short-term liquidity premiums. However, the impact of the slope of treasury term structure upon LT liquidity spreads is positive and statistically significant. Consistent with our earlier analysis, the regressor s impact upon the spread in a period of calm is 23

24 proportionately much less than its impact upon the LT premium in a crisis, 2.7 basis points and 3.9 basis points, respectively. As the threat of a forced asset conversion diminishes, LT bond owners become less sensitive to meaningful independent variables and become marginally more passive. Figures 6A and 6B dramatically depict the deterioration in the liquidity spread of LT securities as we move from a period of financial stress to a period of relative economic tranquility. The standardized slope of the Treasury term structure fell from to standard deviations below the mean, moving from the first to the second epoch where dd(tttttttttttttt) = [ ]. Consequently, the liquidity spread on LT bonds fell by dd(llss LLLL ) = (0.027)( ) = or -2.7 basis points. Clearly the behavior of dd(llss LLLL ) = SS LLLL dd(tttttttttttttt) contributes significantly to the transition of the term structure of the liquidity spread from the configuration of Figure 4 to the negatively sloped Figure 5. Hypothesis 3 maintains that the shape of the term structure of the liquidity spread changes from a positive to a negative slope reflecting changing business conditions 6. We establish our support for this notion by utilizing Figures 6A and 6B. To generate these figures, we first collected the estimated daily values of the liquidity spread according to their time to maturity. These estimated daily values, for each of the two economic scenarios, are the product of right hand side variables and their respective parameter estimates at the time of the transaction. However, a complication arises because, on average for each day of a transaction, more than a dozen estimated spreads are recorded for the same time to maturity. Consequently, in order to summarize those estimated values of the liquidity spread relative to variations in the 6 In contrast, note that hypothesis 2 concerns the complex impact of macroeconomic variables which can, in turn, impact the slope of the liquidity term structure. 24

25 time to maturity, we minimized the sum of the squared deviations of those computed values from a mean computed value at each TTM. Clearly the Figures 6A and 6B admit to a non-linear possibility. The positively sloped term structure of liquidity premiums in Figure 6A (stress period) is not a surprise. Three sets of the regression coefficients were statistically significant in the determination of both the ST and LT liquidity spreads in this epoch. The impact of the regressor is greater upon the LT liquidity premiums than the short-term liquidity spread in all three sets of stress period estimates. As the economy transitioned from our pre-stress period to epoch 1, all three independent variables recorded an increase in their average standardized value 7. These changes taken in conjunction with the difference in the size of short-term and long-term regression coefficients created the positively sloped term structure depicted in Figure 6A. The economic stress associated with period 1 reflects, and creates, independent variables which resulted in the configuration of liquidity premium term structure. At the beginning of the financial crisis, the possibility of forced bond conversions was such that LT insured corporate bond holders realized that the existing liquidity premium did not justify their level of holdings and they migrated to short-term insured corporate bonds. Subsequently the price of insured corporate ST bonds increased and their yields fell as did the liquidity premium for holding ST bonds. Simultaneously, the departure of LT investors from the demand side meant the price of long-term insured corporate bonds fell and their rates went up as did the liquidity spread for holding LT insured corporate bonds. 7 The standardization process uses observations from all three scenarios: pre-stress, stress, and post-stress. The means for the aggregation of the intervals is clearly zero. For any one epoch, the mean is above or below zero. 25

26 Figure 6A is an empirical analog to Feldhutter s (2012) representation of the term structure of the liquidity spread under assumption of future expected selling pressure. Feldhutter s liquidity spread in such a case depicts the difference in the yields of steady state bond prices in circumstances where there is a positive probability of a financial shock, given by λλ ii, and, also, when a shock is not statistically probable. As Feldhutter changes the likelihood of the Poisson shock, he creates a family of positively sloped term structures of the liquidity premium. The representations share the same intercept but at every time to maturity greater than zero, the larger λλ ii, the greater the liquidity premium. The circumstances of stress period mimic the assumptions that Feldhutter used to create his positively sloped presentation of liquidity premium term structures. The financial crisis of 2008 occasioned a flight to safety as named by Longstaff (2004) and further documented by Beher, Brandt, and Kavajecz (2009). This movement to quality and liquidity is the market s recognition of the very real possibility of a financial shock and it produces our positively sloped liquidity term structure. Feldhutter creates a positively sloped term structure of the liquidity spread by simply making the likelihood of a shock (λλ ii )greater than zero. Clearly, our depiction of the term structure of the liquidity spread and Feldhutter s configuration are consistent with each other. As the economy moved from a period of stress to relative tranquility, not only did the magnitude of our right hand side variables reflect this migration but their impact in LT liquidity spreads retreated and, at the same time, their effect on ST spreads escalated. The combined behavior of the variates and their estimated parameters produced the negatively sloped TSLS. The dynamics that produce Figure 6B are a consequence of at least three factors of the differential financial climate. As the economy transitioned from the stress period to the relative 26

27 tranquility of the second time period, the market s perception of the likelihood of a financial shock surely fell. Early in epoch 2, LT securities become very attractive since they offered an inflated spread given the reduced likelihood of a crisis. In addition, long-term insured corporate bonds had the advantage of minimizing the frequency of incurring search costs due to their remote dates of maturity. Finally, the diminished likelihood of a forced asset conversion enabled some investors to revert to their traditional or conventional portfolio balance; that is, they likely engaged in preferred habitat (clientele) behavior. This clientele effect has been recently pointed out by Gehde-Trapp, Schuster, and Uhrig-Homburg (2016). These three factors help occasion a migration of demand to the LT segment of bond yields at the expense of demand for ST insured corporate bonds. The calculations used to construct Figure 6B detail the extent to which LT liquidity premiums fell and ST spreads increased as a function of maturity. Feldhutter (2012) also presents a negatively sloped convex term structure of the liquidity spread which he, alternatively, labels premium due to search costs and occasional selling pressure. The search premium is the average yield at which a corporate bond investor transacts in a steady state minus the steady state yield an investor, who can trade instantly, trades at. Feldhutter s configuration of the liquidity premium is falling in the time to maturity because LT bonds minimize the number of searches the investor necessarily engages in and limits the number of times transaction costs must be paid. When the threat of a financial crisis falls, these are the same considerations that drive our results and occasion Figure 6B. We now briefly discuss coefficients for explanatory variables not directly linked to hypotheses where these may be considered control variables. With regard to the maturity (TTM in days) within buckets for the stress period, there is a small statistically significant coefficient for the shorter maturity bucket which is consistent with the notion that the term structure is 27

28 positive during a stress period. The long term TTM coefficient in the stress period is negative but very small and not significant. For the non-stress period, the short bucket TTM coefficient is negative and strongly significant which is consistent with the notion of a negatively sloped term structure during a non-stress period. In contrast, the non-stress long coefficient is not significant. In summary of the above, these results support the hypothesis that the shape of the term structure changes over time dependent upon varying economic conditions where the conditions are defined as stress versus non-stress. The coefficients for Amihud market wide measures are much smaller than for the AMIHUD measure. The volatility of the Amihud measure is clearly significant in only the non-stress short maturity. We test the results of Table 2a for endogeneity difficulties in a manner similar to Dick-Nielsen, Feldhutter, and Lando (2012) in Appendix C. Issuance amount and age of issuance are used as instruments where the results are that endogeneity is not a problem. In order to further analyze the TSLS, we perform additional regressions of spreads for stress and non-stress periods and report the results in Table 2b. Here we do not use maturity buckets but combine bonds of all maturities. The same qualitative results are evident. For example, the coefficient of TTM is clearly positive in the stress period but clearly negative in the non-stress period and VIX is greatly larger in the stress period. In summary, the results given in Tables 2a and 2b and Figures 3,4,5,6A, and 6B are consistent with the Feldhutter hypothesis where expected selling pressures dominate in a stress period but search costs combined with occasional selling pressure dominate in a less stressed period. In Appendix D, we provide additional robustness tests where we regress our liquidity spreads upon the difference in liquidity measures of the insured bonds and maturity matched U.S. Treasuries. We find that similar results hold for this new specification. 28

29 Vector Auto Regression Analysis of Spillover Effects and Impact on Term Structure of Liquidity Spreads When analyzing term structures of liquidity spreads, one should of course be aware that information, liquidity, liquidity shocks, and yield changes may be transmitted from one maturity to another. For example, Goyenko, Subrahmanyan, and Ukhov (2011) find liquidity shocks tend to be transmitted from short to long maturities. Similarly, Gehde-Trapp, Schuster, and Uhrig- Homburg (2016) find that illiquidity spills over from short-term to long-term. We note that these researchers did not divide economic conditions into stress and non-stress periods as we do below. As we noted above, Acharya, Amihud, and Bharath (2013) also divided their analysis into stress and non-stress periods. We use a vector autoregression (VAR) to analyze the potential transmission of short-term liquidity spreads, LLSS SSSS, to long-term liquidity spreads, LLSS LLLL, and vice versa. The VAR specification is KK KK LLLL SSSS tt = αα SSSS + φφ sshoooooo tt jj LLLL SSSS tt jj + φφ llllllll tt jj LLLL LLLL tt jj + uu tt jj=1 jj=1 KK LLLL LLLL tt = αα LLLL + φφ llllllll tt jj LLLL LLLL tt jj + φφ tt jj sshoooooo LLLL SSSS tt jj + vv tt jj=1 KK jj=1. The Akaike information criteria (AIC) suggests that two lags (K = 2) be used for the stress period and one lag for the non-stress period. Our VAR results further illustrate the differential behavior of spreads in stress versus non-stress periods. That is, the persistency of spreads is quite different in the stress versus the non-stress periods. 29

30 The VAR results for the stress period are given in Table 3a where both short-term and long-term spreads at time t are autoregressively dependent upon its own spread in the prior period t-1. The coefficients in the VAR also indicate that the first lag of short-term spreads is strongly significant in predicting long-term spreads where the coefficient is positive The positive coefficient means that short-term and long-term spreads tend to move in the same direction. The vector autoregression also reveals a weaker (0.163 coefficient) of long-term liquidity spreads upon short-term liquidity spreads, although only in the second lag. These results are consistent with Goyenko, Subramanian, and Uhkov (2011) who find a strong spillover impact running from short-term treasuries to long-term treasuries and a weaker impact of the reverse. As detailed previously, in a period of stress, investor flight to liquidity occasions intermarket behavior that creates the TSLS found in Figure 6A. The positively sloped TSLS is an intermarket equilibrium; consequently, a disturbance to the difference between LT and ST liquidity spreads will be promptly reverted by bond investors. In other words, in the stress period, market participants act in a fashion that preserves the existing positive difference between long-term LS and ST liquidity spreads. For instance, assume there is an exogenous shock to the short-term liquidity spread which temporarily reduces the spread in the spreads of different maturities. Consequently, the liquidity premium for holding LT corporate bonds, relative to ST corporate debt, falls. A reduced demand for LT corporate bonds decreases their price while increasing their yield and spread. The summary impact of this trading activity is reflected in Table 3a and will, in a short period of time, restore the original equilibrium spread in the spreads. That liquidity spreads flow from short to long-term is 30

31 consistent with Granger causality test in Table 3b where the evidence for the reverse is not nearly as strong. Non-stress vector autoregression results are presented in Table 4a. Again, the VAR results are that both short-term and long-term spreads in t autoregressively depend upon its own spread in the prior period t-1. However, in contrast to the stress VAR results, it is important to note that the first lagged long-term liquidity spread is positive and significant in the determination of short-term liquidity. In further contrast, short spreads do not determine long spreads in this case. That is, in periods of non-stress, corporate bond liquidity can spillover from long-term bonds to short-term bonds. In support of this relation, Granger causality tests in Table 4b indicate that short is preceded by long but not the other way around. The above is consistent with the idea that, as the economy transitioned from a period of financial stress to an epoch of lesser stress, the likelihood of forced asset conversions receded. The price of long-term bonds went up while both their yields and spreads fell relative to those of ST insured corporate bonds. These dynamics produced the negatively sloped TSLS provided in Figure 6B. The negatively sloped TSLS is an intermarket equilibrium; consequently, a disturbance to the difference between ST and LT liquidity spreads will be promptly reverted by investors. In summary of VAR for the non-stress period, market participants act in such a fashion that preserves the existing positive difference between ST liquidity spreads and LT liquidity spreads. For instance, if a market disturbance should exogenously enhance the LT spread, then the spread in the spreads for different maturities will fall. A reduced demand for ST corporate debt decreases its price while increasing ST yields and ST spreads. The summary impact of this trading will, in a short period of time, restore the original equilibrium spread in the spreads. 31

32 Clearly market adjustments which maintain the existing TSLS, dictate immediate changes in ST and LT spreads that are in the same direction and account for the positive coefficients found no change. 6. Conclusion Liquidity is an important dimension of the value of anything that can be traded wherein greater liquidity increases value. In fact, liquidity yield spreads for bonds have been found to sometimes be greater than default spreads. Corporate bond market liquidity has recently gained a lot of attention given the liquidity shocks of the 2008 financial crisis and, furthermore, the increased availability of data through sources such as TRACE. It is important to explain how liquidity spreads vary with maturity under differing economic conditions. However, liquidity spread modelling of corporate bonds has proven very difficult given that liquidity spreads interact with default spreads. Our research uses a special database of default free corporate bonds to model corporate bond liquidity spread term structures. We econometrically illustrate that the slope of the term structure of liquidity spreads is determined by underlying economic conditions. The slope of the term structure depends upon underlying financial and macroeconomic conditions where the slope is positive during stressed periods, but, in clear contrast, negative in non-stressed periods. The positive slope in a stress period is attributed to aggregate, market wide liquidity shocks consistent with high expected selling pressure described by Feldhutter (2012); furthermore, there is evidence that spreads in long term bonds are function of short term spreads. Non-stress periods are distinctly different. That is, in non-stress times, search costs tend to dominate which occasion a negatively sloped TSLS. Furthermore, long term spreads tend to determine short term spreads instead of the reverse. We show that the impact of VIX on liquidity 32

33 spreads is strongly dependent upon both the economic environment and the maturity of the bonds. 33

34 Appendix A: Liquidity spread under alternative epochs To alleviate concerns that our results are dependent upon the particular partitions of the data into our periods of stress and no-stress, we provide plots and regression tables using alternative methodologies for finding date intervals. That is, we now select five new epochs based on significant changes of GDP and Fed Funds futures. By identifying significant changes in the price of the Fed Funds futures (10% upwards or downwards), we believe we can identify periods of relative economic stress and also differing investor appetites for alternative segments of the maturity spectrum. We define five epochs as follows: 1) October 1, 2008 to April 1, 2009, 2) April 1, 2009 to November 30, 2009, 3) November 30, 2009 to July 4, 2010, 4) 2010 to July 1, 2011, and 5) July 1, 2011 Dec 31, Following the National Bureau of Economic Research definition of economic recession, the first two epochs coincide with stress, while the last three epochs coincide with periods of non-stress (relative calm). In Figure A1, we present the raw liquidity spreads for each of the five epochs defined above. Epochs 1 and 2, which comprise our period of stress, are clearly upward sloping, while epochs 4 and 5 are downward sloping. Period 3 may be viewed as a period of transition. These results support our prior notion that periods of stress are indicative of a positive TSLS while periods of no-stress are indicative of a negative TSLS. 34

35 Figure A1: Term structure of liquidity spread for each of five alternative epochs The below graphs are raw spreads of the insured corporate bonds (ICB) for each of the five alternative epochs. The plots are averages of all bond spreads with the same time to maturity for the epoch. These spreads are aggregated by weekly buckets to avoid noise and high dispersion in the data. 35

36 Appendix B: Regressions of liquidity spread using alternative epochs and three maturity buckets Similar to Appendix A, we split the data into five epochs in order to demonstrate robustness to alternative stress and non-stress periods. The five intervals are defined as follows: 1) October 1, 2008 to April 1, 2009, 2) April 1, 2009 to November 30, 2009, 3) November 30, 2009 to July 4, 2010, 4) July 2010 to July 1, 2011, and 5) July 1, 2011 Dec 31, Furthermore, we include a medium maturity bucket in addition to short and long maturity buckets. The three buckets are defined according to whether the time remaining to maturity is below the 25 th percentile, between the 25 th and 75 th percentile, or above the 75 th percentile of times to maturity (TTM) in that epoch. We then perform regressions where the dependent variable is the yield of the insured corporate bond minus the yield of a treasury bond, matched by maturity. As in prior results, each right hand side variable is normalized by its mean and standard deviation over the whole sample period (October 2008 to December 2012). As before, each specification regresses the spread of the insured corporate bonds upon the liquidity measure, its volatility, the VIX, time-to-maturity of the insured corporate bond, the 6-month minus the 3- month treasury slope, a measure of market-wide liquidity, and the price of the futures contracts. The regressions include firm-fixed effects, and the standard errors of the coefficients are in parenthesis. The results in general support the notion that in periods of stress, the impact of the liquidity measure is higher for long-term bonds, while in periods of non-stress, the impact is higher for short-term bonds. 36

37 Table B1: Regression for Epoch 1 (October 1, 2008 to April 1, 2009) Regression of Liquidity Spread for Epoch 1 Insured Spread minus Treasury Yield Short Medium Long (1) (2) (3) Amihud *** *** *** (0.007) (0.008) (0.010) Amihud Vola (0.008) (0.009) (0.011) TTM *** *** *** (0.008) (0.009) (0.011) VIX *** *** *** (0.007) (0.008) (0.011) TREASLP *** *** *** (0.007) (0.008) (0.011) Market Amihud (0.007) (0.007) (0.010) FFFP *** *** *** (0.007) (0.008) (0.011) Constant *** *** *** (0.161) (0.145) (0.022) Observations 1, R Adjusted R Residual Std. Error (df = 1331) (df = 900) (df = 466) F Statistic *** (df = 28; 1331) *** (df = 26; 900) *** (df = 16; 466) Note: * p<0.1; ** p<0.05; *** p<

38 Table B2: Regression for Epoch 2 (April 1, 2009 to November 30, 2009) Regression of Liquidity Spread for Epoch 2 Insured Spread minus Treasury Yield Short Medium Long (1) (2) (3) Amihud *** *** *** (0.003) (0.014) (0.014) Amihud Vola * (0.003) (0.016) (0.013) TTM *** (0.006) (0.017) (0.015) VIX *** ** *** (0.005) (0.020) (0.020) TREASLP *** ** (0.004) (0.018) (0.019) Market Amihud * (0.004) (0.018) (0.015) FFFP *** ** (0.005) (0.019) (0.015) Constant *** *** *** (0.012) (0.085) (0.036) Observations 1,168 2,591 1,609 R Adjusted R Residual Std. Error (df = 1150) (df = 2561) (df = 1582) F Statistic *** (df = 17; 1150) *** (df = 29; 2561) *** (df = 26; 1582) Note: * p<0.1; ** p<0.05; *** p<

39 Table B3: Regression for Epoch 3 (November 30, 2009 to July 4, 2010) Regression of Liquidity Spread for Epoch 3 Insured Spread minus Treasury Yield Short Medium Long (1) (2) (3) Amihud *** * *** (0.008) (0.023) (0.002) Amihud Vola *** (0.007) (0.027) (0.003) TTM *** *** (0.009) (0.031) (0.003) VIX *** ** *** (0.010) (0.031) (0.002) TREASLP *** (0.007) (0.023) (0.002) Market Amihud (0.009) (0.030) (0.003) FFFP *** (0.008) (0.028) (0.003) Constant *** *** (0.031) (0.221) (0.010) Observations 743 2,056 1,201 R Adjusted R Residual Std. Error F Statistic (df = 723) (df = 2026) (df = 1177) *** (df = 19; 723) *** (df = 29; 2026) *** (df = 23; 1177) Note: * p<0.1; ** p<0.05; *** p<

40 Table B4: Regression for Epoch 4 (July 4, 2010 to July 1, 2011) Regression of Liquidity Spread for Epoch 4 Insured Spread minus Treasury Yield Short Medium Long (1) (2) (3) Amihud *** *** *** (0.028) (0.004) (0.002) Amihud Vola *** (0.037) (0.005) (0.002) TTM *** *** (0.037) (0.004) (0.003) VIX *** ** (0.044) (0.005) (0.003) TREASLP *** (0.030) (0.004) (0.002) Market Amihud * (0.046) (0.005) (0.003) FFFP *** *** (0.046) (0.005) (0.003) Constant *** *** *** (0.184) (0.032) (0.007) Observations 1,146 3,529 2,069 R Adjusted R Residual Std. Error F Statistic (df = 1120) (df = 3497) (df = 2044) *** (df = 25; 1120) *** (df = 31; 3497) *** (df = 24; 2044) Note: * p<0.1; ** p<0.05; *** p<

41 Table B5: Regression for Epoch 5 (July 1, 2011 Dec 31, 2012) Regression of Liquidity Spread for Epoch 5 Insured Spread minus Treasury Yield Short Medium Long (1) (2) (3) Amihud *** *** *** (0.037) (0.008) (0.005) Amihud Vola *** *** (0.055) (0.009) (0.005) TTM *** (0.059) (0.009) (0.006) VIX ** *** (0.094) (0.015) (0.009) TREASLP * (0.057) (0.010) (0.007) Market Amihud ** (0.086) (0.014) (0.008) FFFP *** (0.085) (0.013) (0.007) Constant ** *** (0.611) (0.073) (0.018) Observations 655 2,401 1,537 R Adjusted R Residual Std. Error F Statistic (df = 625) (df = 2369) (df = 1513) *** (df = 29; 625) *** (df = 31; 2369) *** (df = 23; 1513) Note: * p<0.1; ** p<0.05; *** p<

42 Appendix C: Potential Endogeneity of the Liquidity Measures One potential shortcoming in the regressions that we present is that the liquidity measure might be correlated with the error term in the spread specification. To test for endogeneity bias, we perform a Durbin-Wu-Hausman test as specified in Greene (2003) and report it below in Tables C1 and C2. The logic of the Durbin-Wu-Hausman test is as follows: under the null hypothesis, both the OLS and the 2SLS estimators are consistent. Under the alternative hypothesis, only the 2SLS estimator is consistent. Thus, if we fail to reject the null hypothesis, we can safely conclude that the both estimators are consistent and there is no endogeneity bias in our regressions. Similar to Dick-Nielsen, Feldhutter, and Lando (2012), we use the issuance amount and age of the insured bonds as instruments for liquidity. We first present the RR 2 of the first stage regression, and we then present the Chi-square values of the Durbin-Wu-Hausman test. We perform regressions by period stress and no-stress and by maturity bucket short, medium, long. Table C1: Issuance amount as an instrument for liquidity Panel a: RR 2 of first-stage regressions R-squares of the 1 st Short Medium Long stage regression Stress Non-Stress Panel b: ΧΧ 2 values and 5% significance levels for Durbin-Wu-Hausman test Chi-square of Durbin- Wu-Hausman test Stress (33.92) Non-Stress (49.80) Short Medium Long (48.60) (50.99) (48.60) (48.60) 42

43 In panel a, we present the RR 2 of the first-stage regressions liquidity measure on issuance amount and other explanatory variables. The values for the coefficient of determination are high and we conclude that the issuance amount is a strong instrument for the liquidity measures. In panel b we present the Chi-square values for the Durbin-Wu-Hausman tests along with the 5% significance level. We can see that in all the epochs and maturity buckets, the test fails to reject consistency of both estimators. The results for using only two maturity buckets are very similar. Table C2 repeats the analysis but uses age as the instrument. Similar results hold. Thus, we can conclude that endogeneity is not a concern in our models. Again, the results for using only two maturity buckets are very similar. Table C2: Using age of the bond as an instrument for liquidity Panel a: RR 2 of first-stage regressions R-squares of the 1 st Short Medium Long stage regression Stress Non-Stress Panel b: ΧΧ 2 values and 5% significance levels for Durbin-Wu-Hausman test Chi-square of Durbin- Wu-Hausman test Short Medium Long Stress (32.67) Non-Stress (48.60) (47.40) (49.80) (48.60) (47.40) 43

44 Appendix D: Regressions with difference in liquidity measure We perform similar regressions as in Table 2, but, in contrast, use the difference in the liquidity measure of the corporate bonds and the U.S. Treasuries as our measure of liquidity. The regressions are for the periods of stress October 2008 and November 2009 and non-stress December 2009 to December We further classify the daily bond transactions into shortterm and long-term depending on whether the time to maturity is above or below the median in that epoch. The dependent variable is the yield of the insured bond minus the yield of a treasury bond, matched by maturity. Each right hand side variable is normalized by its mean and standard deviation over the respective epoch, stress or non-stress. BIDASK- BIDASKMKT is our liquidity measure, FFFP is the price of the price of the Fed funds 30-day futures, TREASLP is the slope of the 6-months Treasury bonds relative to the 3-months, TTM is the time-to-maturity of the insured bond, BIDASKMKT is the aggregate bid-ask measure for all outstanding corporate bonds, and BIDASKVOL is the volatility of the Bid-Ask liquidity measure for the insured bonds. The regressions include firm-fixed effects, and the standard errors of the coefficients are in parenthesis. The results in general support the notion that in periods of stress, the impact of the liquidity measure is higher for long-term bonds, while in periods of non-stress, the impact is higher for short-term bonds. 44

45 Regression Analysis of the Liquidity Spread (LS) BIDASK BIDASK_TREA Stress Short (1) Stress Long (2) Non-Stress Short (3) Non-Stress Long (4) *** *** *** (0.003) (0.006) (0.013) (0.007) VIX *** *** * *** (0.007) (0.017) (0.029) (0.011) FFFP *** (0.005) (0.011) (0.026) (0.009) TREASLP *** ** *** (0.006) (0.013) (0.021) (0.011) Control Variables TTM *** *** (0.004) (0.010) (0.021) (0.011) BIDASKMKT *** *** (0.006) (0.012) (0.028) (0.013) BIDASKVOL *** *** *** (0.004) (0.009) (0.017) (0.009) 45

46 Constant *** *** (0.030) (0.289) (0.260) (0.184) Observations 1,880 2,514 2,793 5,122 R Adjusted R Residual Std. Error (df = 1854) (df = 2481) (df = 2760) (df = 5090) F Statistic *** (df = 25; 1854) *** (df = 32; 2481) *** (df = 32; 2760) *** (df = 31; 5090) *p<0.1 ; **p<0.05; ***p<

47 Acknowledgments: We are grateful for very valuable comments from Richard Herron (discussant), and seminar participants at the 2017 Financial Management Association Annual Meeting in Boston, MA, and the 7th Financial Engineering and Banking Society (FEBS) International Meeting at the University of Strathclyde. We appreciate the comments of Etienne Borocco (University of Paris, Dauphine). 47

48 References Acharya, V.V., Pedersen, L. H., Asset pricing with liquidity risk. Journal of Financial Economics 77, Acharya, V. V., Amihud, Y., and Bharat, S.T., Liquidity risk of corporate bond returns: a conditional approach. Journal of Financial Economics, 110, Amihud, Y., Illiquidity and Stock Returns: Cross-section and Time-series Effects. Journal of Financial Markets. 5, Amihud, Y., Mendelson, H., Liquidity, Maturity, and the Yields on U.S. Treasury Securities. The Journal of Finance 46(4), Bansal, N., Connolly, R., Stivers, C., The Stock-Bond Return Relation, the Term Structure s Slope, and Asset-Class Risk Dynamics. Journal of Financial and Quantitative Analysis.49 (3), Bao, J., Pan, J., Wang, J., The Illiquidity of Corporate Bonds. Journal of Finance. 66, Bao, J., and J. Pan Bond illiquidity and excess volatility. Review of Financial Studies. 26, Bauer, M., Rudebusch, G., The Signaling Channel for Federal Reserve Bond Purchases. International Journal of Central Banking 10 (3), Beber, A., Brandt, M., Kavajecz, K., Flight-to-Quality or Flight-to-Liquidity? Evidence from the Euro-Area Bond Market. Review of Financial Studies, 22, Black, J., Stock, D., Yadav, P., The pricing of different dimensions of liquidity: Evidence from government guaranteed bonds. Journal of Banking and Finance. 71, Bongaerts, D., de Jong, F., and Driessen, J., An Asset Pricing Approach to Liquidity Effects in Corporate Bond Markets. Review of Financial Studies, 30(4), Christensen, J., Gillan, J., Does Quantitative Easing Affect Market Liquidity? Working Paper. Christensen, J., Krogstrup, S., Transmission of Quantitative Easing: The Role of Central Bank Reserves. Working Paper. Dick-Nielsen, J., Liquidity Biases in TRACE. Journal of Fixed Income, 19, (2), Dick-Nielsen, J., Feldhütter, P., Lando, D., Corporate Bond Liquidity Before and After the Onset of the Subprime Crisis. Journal of Financial Economics 103, Driessen, J., Nijman, T.E., Simon, Z. (2017) Much ado about nothing: A study of differential pricing and liquidity of short and long term bonds, Financial Management Association meetings. 48

49 Edwards, A., Harris, L., and Piwowar, M. (2007). Corporate Bond Market Transactions Costs and Transparency. Journal of Finance. 62 (3), Ericcson, J., Renault, O., Liquidity and Credit Risk. Journal of Finance. 61, Estrella, A., Hardouvelis, G., The Term Structure as a Predictor of Real Economic Activity. Journal of Finance. 46 (2), Feldhütter, P., The same bond at different prices: identifying search frictions and selling pressures. Review of Financial Studies. 25 (4), Fontaine, J., and R. Garcia Bond Liquidity Premia. Review of Financial Studies. 25, Gagnon, J., Raskin, M., Remache, J., Sack, B., Large-Scale Asset Purchases by the Federal Reserve: Did They Work? International Journal of Central Banking, 7 (1), Gehde-Trapp, M., Schuster, P., Uhrig-Homburg, M A Heterogeneous Agents Equilibrium Model for the Term Structure of Bond Market Liquidity, working paper. Goyenko, R., Subrahmanyan, A., Ukhov, A., 2011, Journal of Financial and Quantitative Analysis. 46 (1), Greene, W., Econometric Analysis. Pearson Education, New York. He, Milbradt, Endogenous liquidity and defaultable bonds. Econometrica. 82, He, Z., Xiong, W., Rollover Risk and Credit Risk. Journal of Finance. 67, Helwege, J., Turner, C., The Slope of the Credit Yield Curve for Speculative-Grade Issuers. Journal of Finance. 54 (5), Hong, G., Warga, A., An Empirical Study of Bond Market Transactions. Financial Analysts Journal. 56, Krishnamurthy, A., Vissing-Jorgensen, A., The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy. Brookings Papers on Economic Activity, Kyle, A, Continuous Auctions and Insider Trading. Econometrica. 6, Lin, H., Wang, J., Wu, C., Liquidity risk and expected corporate bond returns. Journal of Financial Economics. 99(3), Longstaff, F., Schwartz, E., A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance. 50 (3), Longstaff, F., The Flight to Liquidity Premium in U.S. Treasury Bond Prices. The Journal of Business 77(3), Longstaff, F., Mithal, S., Neis, E., Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market. The Journal of Finance, 60(5),

50 Merton, R On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance Musto, D., Nini, G., and K. Schwarz Notes on Bonds: Illiquidity Feedback During the Financial Crisis. Working paper at Wharton School, University of Pennsylvania. Roll, R., A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market. Journal of Finance. 4, Schestag, R., Schuster, P., Uhrig-Homburg, M., Measuring Liquidity in Bond Markets. Review of Financial Studies. 29 (5),

51 Table 1: Liquidity Measure Statistics Panel A reports summary statistics for the four daily liquidity measures of all corporate bonds in the period from 2008 to The bid-ask spread, Amihud measure and interquartile range are calculated from the fixed-income transaction data available in TRACE. Details about the procedure to calculate these measures are provided in the methodology section. The bid-ask spread is the weighted average difference between sells and buys, the Amihud measure is the change in price by transaction volume, the interquartile range is the 75th percentile minus the 25th percentile divided by the median, and the roundtrip measure is the difference between the maximum and the minimum price for transactions that occur at the same time and have the same volume. Panel B reports summary statistics for the sub-sample of insured corporate bonds. The same liquidity measures are shown as in panel A, and the calculation procedure is equivalent. Panel A: All corporate bonds in TRACE Statistic N Mean St. Dev. Min Pctl(25) Median Pctl(75) Max Bid-Ask 5,163, Amihud 5,460, IQR 6,591, Roundtrip 4,045, Panel B: Insured corporate bonds Statistic N Mean St. Dev. Min Pctl(25) Median Pctl(75) Max Bid-Ask 31, Amihud 34, IQR 39, Roundtrip 24,

52 Table 2a: Regression Analysis of the Liquidity Spread This table reports regressions of insured corporate bond liquidity spreads dependent upon our hypothesized determinants. The regressions are for the periods of stress October 2008 to November 2009 and non-stress December 2009 to December We further classify the daily bond transactions into short-term and long-term depending on whether the time to maturity is above or below the median in that epoch. The dependent variable is the yield of the insured bond minus the yield of a treasury bond, matched by maturity. Each right hand side variable is normalized by its mean and standard deviation over the respective epoch, stress or non-stress. AMIHUD is our liquidity measure, FFFP is the price of the price of the Fed funds 30-day futures, TREASLP is the 6-month Treasury yield relative to the 3-month yield, TTM is the time-to-maturity of the insured corporate bond, AMIHUDMKT is the aggregate Amihud measure for all outstanding corporate bonds, and AMIHUDVOL is the volatility of the Amihud liquidity measure for the insured bonds. The regressions include firm-fixed effects, and the standard errors of the coefficients are in parenthesis. Regression Analysis of the Liquidity Spread (LS) Stress Short (1) Stress Long (2) Non-Stress Short (3) Non-Stress Long (4) AMIHUD 0.044*** (0.004) 0.156*** (0.009) 0.286*** (0.011) 0.048*** (0.007) VIX 0.129*** (0.006) 0.223*** 0.015) 0.045*** (0.017) 0.034*** (0.008) FFFP (0.005) *** (0.010) (0.017) 0.013* (0.008) TREASLP 0.027*** (0.005) 0.039*** (0.012) (0.014) 0.027*** (0.009) Control Variables TTM 0.048*** (0.004) (0.009) *** (0.014) (0.009) AMIHUDMKT (0.006) * (0.013) 0.035** (0.017) (0.010) AMIHUDVOL (0.004) (0.009) 0.069*** (0.014) (0.008) Constant 0.240*** (0.021) 1.012*** (0.273) 0.356*** (0.100) (0.120) Observations 2,285 2,850 4,126 6,376 52

53 R Adjusted R Residual Std. Error F Statistic (df=2259) (df=2816) (df=4092) (df=6344) *** (df=25;2259) *** (df=33; 2816) *** (df=33;4092) 8.896*** (df=31;6344) *p<0.1 ; **p<0.05; ***p<

54 Table 2b: Differential Impact of Time to Maturity in Stress and Non-Stress Periods In an effort to further analyze the contrasting shapes of the term structures of liquidity premia spreads during stress and non- stress periods, we perform a pooled regression of the liquidity spreads on all the covariates for each period. The main coefficient of interest is time to maturity, TTM where TTM is drawn from the total sample and not within a bucket. The table below shows that the signs of TTM are positive for the stress period and, in distinct contrast, negative for the non- stress period. Both coefficients are significant at the 1% level. Liquidity Spread Stress Non-Stress (1) (2) Amihud *** *** (0.005) (0.007) Amihud Vola *** (0.005) (0.008) TTM *** *** (0.006) (0.012) VIX *** *** (0.013) (0.009) TREASLP *** *** (0.008) (0.009) Market Amihud *** *** (0.009) (0.012) FFFP *** (0.008) (0.008) Constant *** * (0.041) (0.075) Observations 5,135 10,502 R Adjusted R Residual Std. Error (df = 5097) (df = 10467) F Statistic *** (df = 37; 5097) *** (df = 34; 10467) Note: * p<0.1; ** p<0.05; *** p<

55 Table 3a: Spillover Analysis of Daily Liquidity Premiums for Period of Stress This table presents a vector autoregression (VAR) of aggregated monthly liquidity premiums on lagged liquidity premiums for the period of stress. Panel A analyzes short-term spreads and Panel B analyzes long-term spreads. The optimal number of monthly lags (2) was chosen based on the Bayesian Information Criterion. The liquidity premiums are calculated as the actual yield on the insured corporate bonds (ICBs) minus the yield of maturity matched U.S. Treasuries. The breakpoints between short and long-term bonds is the 50 th percentile of time-to-maturity in the period of non-stress. The sample period is from October 2008 to November Spillover analysis: daily liquidity premiums Panel A: Short-term bonds sshoooooo φφ tt *** (10.72) sshoooooo φφ tt (-0.27) llllllll φφ tt (0.02) llllllll φφ tt *** (3.44) Intercept *** Panel B: Long-term bonds (3.57) sshoooooo φφ tt *** (6.08) sshoooooo φφ tt (-0.93) llllllll φφ tt *** (4.91) llllllll φφ tt *** (5.01) Intercept *** (3.70) N 140 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p <

56 Table 3b: Granger Causality Tests for Spillover Effects in Liquidity Premiums for Period of Stress This table presents χχ 2 statistics as well as the p-values (in parentheses) of pairwise Granger causality tests between the endogenous variables in the VAR for the spillover effect in liquidity premiums during the period of stress. The null hypothesis is that the row variable does not Granger-cause the column variable. The liquidity premiums are the liquidity yield of the insured corporate bonds minus the yield of maturity matched U.S. Treasuries for the stress period. Short-term bonds Long-term bonds Short-term bonds (0.001) Long-term bonds (0.00) - 56

57 Table 4a: Spillover Analysis of Daily Liquidity Premiums for Period of Non-stress This table presents a vector autoregression (VAR) of aggregated monthly liquidity premiums on lagged liquidity premiums for the period of non-stress. Panel A analyzes short-term spreads and Panel B analyzes long-term spreads. The optimal number of monthly lags (1) was chosen based on the Bayesian Information Criterion. The liquidity premiums are calculated as the actual yield on the insured corporate bonds minus the yield of maturity matched U.S. Treasuries. The breakpoints between short and long-term bonds is the 50 th percentile of time-to-maturity in the period of non-stress. Spillover analysis: daily liquidity premiums Panel A: Short-term bonds sshoooooo φφ tt *** (6.08) llllllll φφ ** tt 1 (2.70) Intercept *** (6.09) Panel B: Long-term bonds sshoooooo φφ tt (-0.28) llllllll φφ *** tt 1 (12.67) Intercept *** (6.92) N 378 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p <

58 Table 4b: Granger Causality Tests for Spillover Effects in Liquidity Premiums for Period of Non-stress This table presents χχ 2 statistics as well as the p-values (in parentheses) of pairwise Granger causality tests between the endogenous variables in the VAR for the spillover effect in liquidity premiums during the period of non-stress. The null hypothesis is that the row variable does not Granger-cause the column variable. The liquidity premiums are the liquidity yield of the bank insured bonds minus the yield of maturity matched U.S. Treasuries for the non-stress period. Short-term bonds Long-term bonds Short-term bonds (0.001) Long-term bonds (0.362) - 58

59 Figure 1: Time series of Liquidity Measures for All Corporate Bonds The figure below shows the time series plot from 2008 to 2012 of four liquidity measures for all corporate bonds in TRACE: The bid-ask, Amihud, Roundtrip, and interquartile range. To remove errors, cancellations, corrections, and reversals in the TRACE data, we filter the intraday transaction data according to the procedure described in Dick-Nielsen (2009). The formulas for the computation of these measures as well as the description of the data are presented in the methodology section. The liquidity measures are standardized by subtracting the mean and dividing by the standard deviation of the full window which shows that all measures behave similarly. 59

60 Figure 2: VIX and Fed Fund Futures Prices This figure plots the VIX (blue circle, axis on the left) and the price of the Fed Fund Futures (red triangle, axis on the right) for our period of interest, October 2008 to December We define the epochs that we use in this study according to significant changes in the VIX and the Fed funds futures price. Epochs 1 and 2 below are considered periods of stress, while Epochs 3, 4, 5, are considered periods of non-stress. The vertical lines divide the sample into the periods 1) October 1, 2008 to April 1, 2009, 2) April 1, 2009 to November 30, 2009, 3) November 30, 2009 to July 4, 2010, 4) July to July 1, 2011, and 5) July 1, 2011 Dec 31,

61 Figure 3: Term Structure of Raw Spreads for Insured Corporate Bond Spreads This figure depicts the raw spreads of the insured corporate bonds over equal maturity Treasury bonds for the two periods: stress and non-stress. The vertical axis is raw spread in basis points and the horizontal time to maturity. The period of stress is from October 1, 2008 to November 30, 2009, while the period of non-stress goes from November 30, 2009 to Dec 31, Bond yields are obtained from TRACE and cleaned according to the Dick-Nielsen (2009) filter. Treasury yields are obtained from the H-15 website for a set of fixed maturities. The Treasury yields are interpolated to exactly match the maturity of the bonds for any given day. The plots are averages of all bond spreads with the same time to maturity. These spreads are further aggregated by weekly buckets to avoid noise and high dispersion in the data. 61

62 Figure 4: Term Structure of Fitted Liquidity Spreads for Insured Corporate Bonds for Period of Stress This figure depicts the term structure of fitted spreads of the insured corporate bonds over equal maturity Treasury bonds for the period of stress from October 1, 2008 to November 30, The fitted spread is the predicted value of the liquidity spread (LS) from the regression of spread on the liquidity measure, the VIX, the Fed Fund futures, and other explanatory variables. Insured corporate bond yields are obtained from TRACE and cleaned according to the Dick-Nielsen (2009) filter. Treasury yields are obtained from the H-15 website. The plots are averages of all insured corporate bond spreads with the same time to maturity. These spreads are aggregated by weekly buckets because of noise and high dispersion in the data. 62

63 Figure 5: Term Structure of Fitted Liquidity Spreads for Insured Corporate Bonds for Period of Non-Stress This figure depicts the term structure of fitted spreads of the insured corporate bonds over equal maturity Treasury bonds for the period of non-stress from November 30, 2009 to Dec 31, The fitted spread is the predicted value of the liquidity spread (LS) from the regression of spread on the liquidity measure, the VIX, the Fed Fund futures and other explanatory variables. Bond yields are obtained from TRACE and cleaned according to the Dick-Nielsen (2009) filter. Treasury yields are obtained from the H-15 website. The plots are averages of all bond spreads with the same time to maturity. These spreads are aggregated by weekly buckets because of noise and high dispersion in the data. 63