Corporate Bond Liquidity and Its Effect on Bond Yield Spreads. April 29, 2003

Transcription

1 Corporate Bond Liquidity and Its Effect on Bond Yield Spreads Long Chen Department of Finance Michigan State University (517) David A. Lesmond A.B. Freeman School of Business Tulane University (504) Jason Wei Rotman School of Management University of Toronto (416) April 29, 2003 This paper is based on an earlier version entitled An Indirect Estimate of Transaction Costs for Corporate Bonds. We thank seminar participants at the 2001 FMA conference, 2003 AFA meetings, Louisiana State University, Michigan State University, and the University of New Orleans for their helpful comments. Sincere thanks go to Laurence Booth, Kirt Butler, John Hull, Raymond Kan, Madhu Kalimipalli, Tom McMcurdy, Chester Spatt, and Alan White for their constructive comments. We wish to thank Andre Haris, Lozan Bakayatov, and Davron Yakubov for their excellent data collection efforts. All errors remain the responsibility of the authors.

2 Corporate Bond Liquidity and Its Effect on Bond Yield Spreads

3 Abstract We provide a model to estimate liquidity costs for corporate bonds using only daily bond prices. The model yields liquidity estimates that are virtually indistinguishable from the underlying bid-ask spreads for investment grade bonds. Our mean liquidity estimate of 30 basis points for investment grade bonds is within five basis points of the underlying bid-ask spread and compares well with the trading cost estimates established by Schultz (2001) or Hong and Warga (2000). Regression tests indicate that our estimate of liquidity is associated with the bid-ask spread even after controlling for the commonly used liquidity determinants of maturity, bond age, the amount outstanding, and bond rating. Assessing the economic significance of our liquidity estimate in relation to the yield spread, we find that our estimate of liquidity is positively associated with the yield spread regardless of controlling for any of the yield spread determinants of Campbell and Taksler (2002). These results have important implications for bond investment and yield spread studies given the demonstrable influence of liquidity on bond returns and the sizeable portion of the yield spread explained by liquidity.

4 Introduction Corporate bond trading on exchange-listed and over-the-counter markets now exceeds $15 billion per day. 1 Affecting these markets is the underlying liquidity, an issue that is of increasing concern to regulators, bond traders, 2 and academicians. However, arguments concerning liquidity are often muted because of the complex problems of implementing liquidity aspects into empirical pricing analysis. Recent studies by Schultz (2001) and Hong and Warga (2000) highlight the obstacles in estimating the costs of trading corporate bonds, while Longstaff (2000) outlines the difficulties of incorporating liquidity costs into bond yield studies. 3 While a comprehensive estimate of liquidity costs for corporate bonds is crucial for studying investment strategies and understanding bond yields, such an estimate is lacking in current empirical studies. This paper attempts to fill this void by presenting an empirical model to estimate bond liquidity and by assessing the economic significance of the relationship between liquidity and bond yields. The crux of the problem in estimating liquidity and its effect on bond yields is the lack of credible information on spread prices or bond quotes (Goodhart and O Hara, 1997). 1 Thompson Financial Securities Data and the Bond Market Association (2002). 2 Arthur Levitt, as the Chairman, of the Securities and Exchange Commission, notes that The sad truth is that investors in the corporate bond market do not enjoy the same access to information as a car buyer or a home buyer or, I dare say, a fruit buyer. Improving transparency is a top priority for us (Wall Street Journal, 9/10/1998). Greg Ip of the Wall Street Journal notes that The bond market s biggest worry these days isn t default or interest rates. It s illiquidity that is crippling the very workings of the market. This concern is manifest in the spread differences between on-the-run and off-the-run treasuries that rose from 5 basis points to over 27 basis points that occurred in August of 1998 (Wall Street Journal, 10/19/1998). Reflecting bond liquidity concerns, the NASD has recently instituted TRACE (Trade Reporting and Compliance Engine) which provides real-time quote estimates for 4200 corporate bond issues (Wall Street Journal, 3/14/2003). 3 A partial listing of the studies of liquidity influences on returns and yield spreads is as follows: Garbade and Silber (1979), Amihud and Mendelson (1991), Longstaff (1992), Daves and Ehrhardt (1993), Kamara (1994), Elton and Green (1998), and Grinblatt and Longstaff (2000). 1

5 Our goal is to provide a liquidity estimate that is estimable for any bond with daily prices, supplanting the need to obtain quotes or intraday trade-specific information. We extend the model of Lesmond, Ogden, Trzcinka (1999), which is applied to liquidity estimation of common equity, to the corporate bond market. Our mean liquidity cost estimate for investment grade bonds is $0.30 per $100 value. 4 This estimate compares well with the trading cost estimates of Hong and Warga (2000), Schultz (2001), and Chakravarty and Sarkar (1999), which range from $0.13 to $0.27 per $100 par value. More importantly, our liquidity cost estimate is, on average, within four basis points of the underlying bid-ask spread, a difference that is largely insignificant. Using this liquidity cost estimate, we find that liquidity alone explains 16% of the cross-sectional variation in the yield spread regardless of investment grade or speculative grade bonds, demonstrating that liquidity is a priced component of the yield spread. At least two different approaches have been employed to estimate the transaction costs for corporate bonds. The first is to estimate the effective spread as the difference between the weighted average of the buy and sell prices during the day (Chakravarty and Sarkar, 1999 and Hong and Warga, 2000), while the second is to invoke a methodology used by Schultz (2001) that regresses the difference between the trade price and the estimated contemporaneous bid quote on a dummy variable that is assigned a zero for sells or a one 4 We use a 30 basis point liquidity estimate for a sample of bonds where Bloomberg provides bid-ask quotes. These bonds are more frequently traded by institutions such as Merrill Lynch and Lehman Brothers and these bonds more closely compares to the type of sample used in the literature. Our overall mean liquidity estimate is 43 basis points, but this sample contains bonds that lack institutional trading. Bloomberg specifically excludes bonds that have been effectively retired from the market due to their age, because few insurance firms or brokers make a market for these bonds. Because of these concerns, we use the LDV estimate matched with the bid-ask spread sample when comparing the prior literature s results. 2

6 for buys. The effective spread method has two serious limitations. To be included in the sample, selected bonds must have at least one trade at the buy price and another at the sell price within the same day. This implies that only the most liquid bonds are used and that non-traded bonds are removed, potentially causing a nonsynchronous trading bias because trades at the bid or ask do not occur at the same time within the day. These biases are reflected in the relatively low explanatory power in their regressions of the estimated spread and spread determinants (e.g., the R-square of only 2 percent in both Hong and Warga (2000) and Chakravarty and Sarkar (1999)). Schultz s (2001) method, while more comprehensive and complete, must use monthly data to infer daily quotes by assuming price changes in corporate bonds are proportional to price changes in treasury bonds. This assumption is likely to hold only for investment grade bonds. In addition, this approach requires both traded and quoted bid prices. To overcome these data limitations, this paper proposes an alternative method, termed the limited dependent variable (hereafter, LDV) model, that does not rely on the use of bid-ask quotes or spread prices. Rather, this method uses only closing daily prices to estimate liquidity costs by assuming that the trade prices reveal liquidity effects through the incidence of zero returns. Lesmond et al. (1999) and Lesmond (2002) find that this method works well for equity markets, as evidenced by an 80% correlation between the LDV liquidity estimate and the bid-ask spread plus commissions. The premise of the LDV model is that, while the true value of the bond is driven by 3

7 many stochastic factors, measured prices will reflect new information only if the information value of the informed marginal trader exceeds the total liquidity costs. This implies that a liquidity cost threshold exists for each bond, which is equivalent to the minimum information value for a trade. Within the liquidity cost threshold, the probability of observing a zero return is higher than outside the liquidity cost threshold. We use a maximum likelihood method to jointly estimate the risk factors related to market-wide information and the upper and lower liquidity thresholds that, taken as a whole, represent round-trip liquidity costs. 5 We apply the LDV model to a comprehensive sample that comprises 3829 corporate bonds including investment grade, speculative grade, and non-rated bonds. To corroborate our liquidity estimates, we also gather over 3800 annual bid-ask spread quote estimates (based on quarterly quotes). We substantiate a liquidity effect on bond returns by finding a significant association between the incidence of zero returns and the underlying bid-ask spread regardless of rated or non-rated bonds. Applying the model to investment grade bonds, we also show the LDV liquidity estimate and the underlying bid-ask spread have little systematic relation with bond rating, consistent with Shultz (2001). However, the LDV estimate and the underlying bid-ask spread are insignificantly different regardless of bond rating. Regression tests show that the LDV liquidity estimate remains significantly related to the underlying bidask spread even after controlling for the commonly used bond liquidity determinants of 5 This method is also a natural extension of Glosten and Milgrom (1985), who illustrate that trades will occur when the information value exceeds the transaction costs defined by the bid-ask spread. 4

8 maturity, age, credit rating (Chakravarty and Sarkar, 1999), and the amount outstanding (Tanner and Kochin, 1971). The results are robust to rated as well as non-rated bonds. For the whole sample of bonds using the LDV estimate as the dependent variable in the regression tests, we find that longer maturity contributes to lower liquidity. We would predict an increase of two cents in trading costs for every one-year increase in the remaining time to maturity, exactly as found by Chakravarty and Sarkar (1999). Consistent with Tanner and Kochin (1971), we find that investment grade bonds with smaller amounts outstanding are more costly to trade. However, regression tests indicate that bond age is insignificantly related to liquidity after controlling for maturity, the amount outstanding, and credit rating. Finally, credit rating for investment grade bonds is insignificantly related to bond liquidity. This counter-intuitive result is consistent with Schultz s (2001) findings for investment grade bonds. However, given a combination of investment grade with speculative bonds or non-rated bonds, we would predict that lower-rated or non-rated bonds are more costly to trade. Illiquidity and bond rating are related, but only after allowing for greater variability in the default risk. Finally, tying these liquidity estimates to the observed yield spread, regression results indicate that liquidity alone explains 13% of the cross-sectional variation in the yield spread for investment grade bonds and 20% of the cross-sectional variation in the yield spread for speculative bonds. Incremental increases in liquidity costs for investment grade bonds increases the yield spread by 37 bp, an amount that roughly equals the incremental credit rating effect on the yield spread. Incremental increases in liquidity costs for speculative 5

9 grade bonds increases the yield spread by 208 bp, an amount that roughly doubles the 114 bp incremental credit rating effect on the yield spread. The liquidity estimate remains significant even after controlling for general yield spread factors of credit rating, maturity, and the amount outstanding; the tax effect determinant (Elton et al., 2001) proxied by the coupon rate (Campbell and Taksler, 2002); the option value of debt proxied by equity volatility (Merton, 1974 and Campbell and Taksler, 2002); the credit rating linked accounting variables of Campbell and Taksler (2002); and the default probability linked macro economic variables of Longstaff and Schwartz (1995), Collin-Dufresne, Goldstein, and Martin (2001), and Longstaff (2001). The results are robust to issuer fixed effects. This paper contributes to the growing debate over bond market liquidity and corporate yields. First, market liquidity is argued as a possible deterrent to arbitrage trading (Lesmond, Schill, and Zhou, 2002). Amihud and Mendelson (1991) argue that in the Treasury market, the cost of trading is increasing with longer maturity bonds, counteracting the effect of the positive relation between price differentials and maturity. Presumably with an easily estimable liquidity measure, price differential studies can be more adequately performed. Second, in the credit risk literature, it is common to assume that the yield spread, as a whole, represents default risk. Practitioners frequently draw conclusions regarding default probability from yield spreads. Our study implies that this approach is inappropriate, as the liquidity component in the yield spread is not directly related to default risk. The result also mitigates the concern that the yield spread overstates the default probability (e.g., Elton et al., 2001 and Huang and Huang, 2002). This model 6

10 thus significantly enhances our ability to more properly incorporate liquidity costs into the analysis of yield spreads (Longstaff, 2000). Finally, most asset pricing models in the corporate bond literature acknowledge the importance of liquidity, but usually abstract from this influence presumably due to difficulties in modeling liquidity effects on bond prices. Longstaff (2000) argues that the fixed-income market may be incomplete and that standard factor analysis techniques may be incapable of detecting liquidity-related variations in bond prices. Reflecting the incidence of zero returns as a pricing factor may increase our understanding of the dynamics of bond pricing. The paper is organized as follows. Section 1 outlines the theoretical underpinnings and the empirical LDV model. Section 2 presents the data and section 3 presents summary statistics and tests to validate the proposed empirical and theoretical model. Section 4 presents basic regression tests concerning the bid-ask spread. Section 5 presents multivariate tests of the proposed LDV estimator and liquidity determinants. Section 6 presents regression tests of the liquidity and yield spread. Section 7 concludes. 1. The Return Generating Model The estimation technique developed by Lesmond, Ogden, and Trzcinka (1999) forms the basis of our methodology for estimating bond liquidity. This model of informed trading utilizes only daily bond returns to endogenously estimate firm-level liquidity costs. The maintained hypothesis is that the marginal, informed investor will rationally trade only if the value of the accumulated information exceeds the transaction costs. The effect of liquidity is observable through the incidence of zero returns. If transaction costs inhibit 7

11 more informed investors from trading, then we should observe zero returns because no new information, on average, has been incorporated into the price. The higher the level of transaction costs, the more zero returns we should observe. To reflect bond pricing for both high-grade and low-grade corporate bonds, we extend the Lesmond et al. (1999) methodology to a two-factor model. 6 These factors include both interest rate and equity market effects. It is well known that bond prices are affected by interest rate changes. However, high-grade bonds are typically of longer duration than lowgrade bonds due to the credit risk of the issuing firm (Boquist, Racette, and Schlarbaum, 1975). Cornell and Green (1991) argue that low-grade bonds, because of their shorter durations, are less sensitive to changes in interest rates and more sensitive to changes in general stock prices. They model the bond return as a linear function of the movement in the S&P500 index. To reflect the uniqueness of speculative grade bonds, we include an equity market component in the objective function. As in Cornell and Green (1991), we use the daily S&P500 index return. Consistent with Jarrow (1978), we scale all risk coefficients by the daily duration. Both of these terms are representative of the specific risk factors in bond pricing. The return generating process is then given as: R j,t = β j1 Duration j,t R ft + β j2 Duration j,t S&P Index t + ɛ j,t. (1) The term Rj,t represents the unobserved true bond return for firm j and daily time period t that investors would bid given zero transaction costs. R ft is the daily change in the ten-year, risk-free interest rate. S&P Index is the daily return in the Standard & Poor s 6 Appendix A shows the theoretical basis for this approach. 8

12 500 index. We use the Macaulay duration measure measured daily. The slope coefficients then act as systematic risk parameters representing the co-variation of bond returns to both the interest rate and equity market environment conditional on the duration. Amihud and Mendelson (1986) show that actual returns require a liquidity premium over the true return. They find higher spreads for Treasury notes than for Treasury bills (by a factor of four), and that the yield to maturity for Treasury notes is higher than for Treasury bills. Therefore, the effect of liquidity costs on bond returns can be stated as: R j,t = R j,t α i,j, (2) where R j,t is the measured return, α 2,j is the effective buy side cost, and α 1,j is the effective sell side cost for firm j. Thus, the desired return and the measured return are related, but only after taking transaction costs into account. The general methodology for limited dependent variable models is detailed in Maddala (1983). The effect of liquidity on bond prices is then modeled by combining the objective function with the liquidity constraint and is given as: R j,t = β j1 Duration j,t R ft + β j2 Duration j,t S&P Index t + ɛ j,t. (3) Where: R j,t = R j,t α 1,j if R j,t <α 1,j and α 1,j < 0 R j,t =0 if α 1,j R j,t α 2,j R j,t = R j,t α 2j if R j,t >α 2,j and α 2,j > 0 9

13 The resulting log-likelihood function 7 is stated as: LnL = 1 Ln (2πσ 1 j 2 )1/ Ln (2πσ 2 j 2 )1/ σ 2 j 1 2σ 2 j (R j + α 1,j β j1 Duration j,t R ft β j2 Duration j,t S&P Index t ) 2 (R j +α 2,j β j1 Duration j,t R ft β j2 Duration j,t S&P Index t ) Ln(Φ 2,j Φ 1,j ), (4) For purposes of liquidity estimation, we focus only on the α 2,j and α 1,j estimates. Taken in difference form, α 2,j α 1,j, represents the liquidity effects on bond returns related to round-trip transaction costs. 8 Φ i,j represents the cumulative distribution function for each bond-year evaluated at (α i,j β j1 Duration j,t R ft β j2 Duration j,t S&P Index t )/σ j. 1 (region 1) represents the negative non zero measured returns, 2 (region 2) represents the positive non zero measured returns, and 0 (region 0) represents the zero measured returns. Maddala (1983) and Lesmond et al. (1999) outline the estimation procedure. 9 7 Daily bond returns may depart from normality, but the likelihood function of the limited dependent variable model (LDV) is based on the underlying distribution of true returns, not measured returns. The LDV model assumes that true returns are normally distributed. Additionally, White (1982) argues that even when the true distribution is not normal, maximum likelihood carried out under the assumption of normality yields consistent estimates of the mean and variance of distributions for which these quantities are finite. 8 Note that this liquidity estimate is most representative of the spread normalized by price, not par value. Given that we are including zero coupon debt, whose price is distant from a $100 par value, this definition is necessary. 9 We find that for those bonds where the number of zero returns is less than 5% of the trading pattern, sign differences of the buy side costs, α 2, and sell side costs, α 1, can occur. We adopt the following rule for assigning the costs. If both intercept terms are negative, we sum the two intercept terms and take the absolute value. If both intercept terms are positive we sum the two intercept terms. If the sign on α 2 is negative and the sign on α 1 is positive we take as the estimate of liquidity costs the difference of α 1 α 2. 10

14 2. Data The data cover 3829 corporate bonds that are traded on the U.S. market. Datastream is used to provide prices, bond characteristics, and yield spreads 10. Datastream uses Merrill Lynch as a data source for bond prices. We choose the start date of 1995 since daily prices are more regularly available through Datastream only after We record the clean, non-matrix price of each bond on a daily basis. Matrix prices are calculated prices, rather than actual trade prices. We separate the data into bond-years from January to December; that is, using daily data for each bond within each year, we jointly estimate the return generating function and liquidity costs applicable to that bond, for that year. 11 This allows time-series variations in the bond liquidity estimates to be adequately represented. 12 We begin with 6231 bond-year observations. The daily bond prices are scanned for data errors and omissions. A data error filter eliminates daily prices that are ±50% of the prior day s price; in this case, that day s price as well as the prior day s price are deleted. The remaining price data are used to calculate daily returns. The LDV model requires a sufficient number of non-zero returns to properly estimate the liquidity cost parameters. If the number of missing daily data returns and zero returns exceeds 80% (or 210 missing 10 Datastream calculates the yield spread as the difference between the corporate bond yield and the yield of a comparable Treasury bond using linear interpolation for a constant maturity yield published by the Financial Times. 11 It should be noted that our sample is largely restricted to 2001 and We have approximately 130 bonds in each year from 1995 to 1999, 175 bonds in 2000, 2299 bonds in 2001, and 2996 bonds in In addition, as bonds age, they are increasingly likely to be held to maturity and effectively retired from the market. Bond liquidity is unlikely to stay constant over a protracted period of time. Using bond years separately can, at least in part, control for the aging effects. 11

15 prices out of 262 possible daily returns) of the annual trading pattern, that bond-year is dropped from the estimation. This requirement reduced the sample to 6120 bond-year observations for use in the LDV model. Data on the quarterly bid-ask quotes are hand-collected from Bloomberg. Usingthe bond Cusip number, we match the bonds to those on Bloomberg andthenrecordthe quarterly bid and ask quotes. Most quotes are available from the years 2000 to If quarterly bid prices exceed ask prices or either ask-bid quotes are missing, that quarter s proportional spread is deleted from the average bid-ask spread calculation. The bondyear s proportional bid-ask spread is calculated as the ask minus the bid divided by the average bid and ask prices using, at a minimum, a single quarter s quote for that year. A single quarter minimum is established to include as many bond observations as possible. We obtain 2783 bond-year proportional bid-ask observations across the corporate bonds with associated bond ratings, and an additional 1043 bond-year observations without assigned bond ratings. Unlike the price data, these quotes are matrix price quotes; that is, they are a constructed quote, not an actual quote. This use of matrix quotes for the bid and ask price will likely introduce noise into our measure of immediacy costs due to the combination of various price quotes. However, noise will not bias our results; instead noise will reduce the efficiency of our estimates. This will bias against our liquidity hypothesis when we use the bid-ask spread as the dependent variable in regression tests. Finally, we use the Compustat Annual Industrial database and collect all firm-level data for both active and inactive firms to minimize any survivorship bias in the liquidity 12

16 determinant and yield spread regressions. 13 Each variable is collected in the year prior to the yield spread measurement. We have 1615 bond-years with available accounting information and market capitalization information. The volatility estimate is gathered from the daily CRSP file using 252 daily returns for the year prior to the bond liquidity estimate. 3. Preliminary Findings 3.1 Summary statistics Table 1 contains the summary statistics. Several observations are apparent. First, investment grade bonds are traded more often than speculative grade bonds. There are 7.85% zero returns for investment grade bonds compared to 30.20% zero returns for speculative grade bonds. Second, non-rated bonds experience substantially better liquidity costs than speculative grade bonds. There may be many reasons for this observation. Firms may seek not to have their issues rated out of fear of being rated speculative grade rather than investment grade, and yet the issue may attract sufficient trading interest. Also, issue size may be important for credit ratings as non-rated issues are also shown to be smaller than investment grade issues (Barclay and Smith, 1995). The relation between the various classes of bonds using the bid-ask spread sample shows that investment grade and non-rated bonds trade with relatively the same cost, both of which are less costly 13 We collect the operating income after depreciation (item 178) and the interest expense (item 15) to determine the pre-tax interest coverage. For the operating income to sales we collect the firm s operating income before depreciation (item 13) divided by the net sales (item 12). We use two definitions for debt: total long term debt (item 9) divided by total assets (item 6), and total long term debt plus debt in current liabilities (item 34) plus short-term borrowings (item 104) divided by total liabilities (item 181) plus market capitalization. 13

17 to trade than speculative grade bonds. 14 Third, speculative grade bonds have slightly shorter maturities, are relatively younger, and have a somewhat shorter duration than do investment grade bonds or non-rated bonds. Finally, relating yield spreads to liquidity, we can see that lower liquidity (i.e., higher transaction costs) is associated with a higher yield spread. For instance, investment grade bonds experience a 43 basis point LDV liquidity cost matched to a 193 basis point yield spread, while speculative grade bonds experience a 294 basis point LDV liquidity cost matched to a 899 basis point yield spread. 3.2 Model Validation As a model specification check, we examine how well the market risk factors i.e., interest rate changes and equity returns are predictive of bond returns using the proposed LDV model and a naive ordinary least squares (hereafter, OLS) model. The OLS model specifically neglects the influence of the zero returns. For each bond-year, both the LDV and the OLS model are used to estimate the risk-factor coefficients. The comparison of estimated coefficients can shed light on whether zero returns influence the estimated return generating process. If the model is correctly specified, we would expect several patterns to appear. First, the interest rate coefficient should be negative, because an increase in interest rates will cause a negative bond return. However, moving from high to low-grade bonds, this rela- 14 The large difference in the LDV estimate and bid-ask spread is due to the bid-ask spread sample that focuses on more actively traded bonds while the whole sample of investment grade bonds includes many inactively traded bonds that have substantial liquidity costs. Bloomberg specifically excludes bonds that have been effectively retired from the market due to their age because few insurance firms or brokers make a market for these bonds. We use the LDV estimate matched with the bid-ask spread sample when comparing the prior literature s results due to these concerns. 14

18 tionship is expected to become weaker (Schultz 2001). Second, the equity return coefficient should be positive for low-grade bonds (Cornell and Green, 1991). Intuitively, a positive equity return, signaling an improvement in the firm s business operation, will have a positive effect on the bond return. However, the effect of the equity return on high-grade bonds is not clear. On the one hand, a positive equity return might increase bond price, as in the low-grade bond case. On the other hand, the positive equity return might be caused by capital flows from the corporate bond market into the equity market, in which case a negative return on corporate bonds is expected. 15 The estimation results are summarized in Panel A of Table 2. Panel A breaks down the risk coefficient estimates by rating. The first three columns present the rating, sample size, and the percentage of zero returns, respectively. Columns four through six provide the LDV estimates of liquidity, interest rate coefficient, and equity return coefficient, respectively. Columns seven and eight show the naive model estimates for interest rate and equity market coefficients, respectively. A comparison of the LDV results with those of the naive OLS model provides a clear indication of the influence that zero returns have on the estimation results. The LDV model s interest rate estimates are mostly negative and significant, as expected, while the interest rate influence is decreasing with decreasing bond ratings. The latter result is consistent with Schultz (2001), who finds that the average percentage change in the 15 Kwan (1996) finds a positive equity return coefficient for investment grade bonds. Cornell and Green (1991) find that, when both the interest rate and the S&P500 equity return are considered, the sign of equity return coefficient changes from positive to negative for the period 1977 to

19 bond s price explained by changes in the Treasury bond falls from 63.26% to only 17.40% when moving from investment grade to speculative grade bonds. In sharp contrast, the naive OLS model produces interest rate estimates that are largely insignificant from zero. In addition, the interest rate effect has little apparent trend with bond rating, a result contrary to commonly held assumptions concerning the interest rate-price effect. The falloff in interest rate influence for the LDV model is offset by a concomitant increase in the S&P500 equity return influence, especially for speculative grade bonds. Also evident is the switch in sign for the S&P500 coefficient from investment grade to speculative grade bonds. This would indicate that signaling effects prevail in the case of speculative grade bonds while substitution effects prevail for investment grade bonds. Similar, but more muted patterns are apparent for the naive OLS model s estimates. Turning to Panel B of Table 2, we now compare the LDV liquidity estimates with the bid-ask spread classified by bond ratings. Notwithstanding the smaller sample size for some rating categories, our LDV liquidity estimates are clearly correlated with the bid-ask spreads. All the correlations are positive and significant, ranging from a low of 12.4% to a high of 35.6%. For investment grade bonds, AAA rated bonds paradoxically experience the largest percentage of zero returns. AAA bonds also experience the highest liquidity costs, using either the LDV liquidity cost estimate or the bid-ask spread. However, liquidity costs do not appear to vary systematically with investment grade bond rating. The lack of systematic covariation between trading costs with bond rating is consistent with the findings of Schultz 16

20 (2001), as is the feature that AAA bonds experience the highest level of trading costs. Finally, the relation between the bid-ask spread and the LDV liquidity cost estimate for investment grade bonds is striking. For all investment grade bond rating categories, the difference between the spread estimated cost and the LDV liquidity cost is insignificant. The t-test results in the last column of Panel B of Table 2 confirm this finding. However, the liquidity costs increase dramatically as we move from investment grade to speculative grade bonds. For speculative grade bonds, the LDV estimates are substantially higher than the bid-ask spreads. Although there is a corresponding increase in the bid-ask spreads, the difference between the LDV liquidity estimates and the bid-ask spreads widens. The LDV estimates are based on the informed traders reservation price, which incorporates all relevant costs such as commission costs, credit spread costs, and search costs, in addition to the bid-ask spread. Garbade and Silber (1976) contend that expected cost of liquidity services in a competitive dealer is the spread between the expected transactions price plus the search costs. Both of these elements depend upon the reservation bid and ask prices of the investor, which in turn depend upon the size of the contemplated transaction, the cost of contacting a dealer, and the pattern of price dispersion. Our results would indicate that search costs and the increasing default risk effects on liquidity inflate the LDV liquidity estimates relative to the bid-ask quotes, and those additional costs are more pronounced for speculative grade bonds. Finally, in Panel C of Table 2 we regress the percentage of zero returns on the bid-ask 17

21 spread. The maintained hypothesis is that the informed trader will rationally trade only if the value of information exceeds the liquidity costs, and therefore the liquidity influence is evidenced by zero returns. The sign for the bid-ask spread is expected to be positive, indicating that increased spread costs should be associated with increased numbers of zero returns. The regression results confirm the association for both rated and non-rated bonds. 4. Bid-Ask Spread Regression Tests To further quantify the association between the LDV model s liquidity estimate and the most demonstrable estimate of immediacy costs, the bid-ask spread, we perform the following regression test using the bid-ask spread as the dependent variable and the liquidity determinants as the independent variables: Bid-Ask it = η 0 + η 1 (α 2 α 1 ) it + η 2 Maturity it + η 3 Age it + η 4 Amount Outstanding it + η 5 Bond Rating i + η 6 Bond Rating Dummy + ɛ t The subscript it refers to firm i and time period t. Bond maturity is a commonly used proxy for return volatility (Chakravarty and Sarkar, 1999). Sarig and Warga (1989) also note that illiquid bonds are more prevalent among longer maturity bonds. The amount outstanding is shown by Fisher (1959) and Garbade and Silber (1976) to be positively related to the volume of trade. The volume of trade has been shown by Stoll (2000) to be inversely related to the bid/ask spread. Schultz (2001) also utilizes the amount of bond outstanding as a liquidity characteristic. We include bond age (or the years subsequent to issuance) as an independent variable 16 to be consistent with the previous literature 16 Amihud and Mendelson (1991) show that on-the-run Treasury bills are traded more frequently than 18

22 (e.g., Chakravarty and Sarkar 1999 or Sarig and Warga 1989). Bond rating proxies for default risk. For the overall regressions, bond ratings are assigned a cardinal scale ranging from one for AAA rated bonds to seven for CCC to D rated bonds. For speculative grade bonds, these are renumbered from one to three for BB rated bonds and CCC to D rated bonds, respectively. In the overall regressions, the dummy bond ratings are assigned zero for investment grade bonds, one for non-rated bonds, and two for speculative grade bonds. For the separate bond classes, we assign the non-rated bonds a one or a zero for investment grade and speculative grade bonds, respectively. Finally, we include the LDV estimator (α 2 α 1 ) as the liquidity cost measure to test whether our estimator has additional explanatory power over the other liquidity determinants. Table 3 presents the results. We run successive regression tests on each of the variables, beginning with the combined investment grade and speculative grade categories. The LDV estimator alone explains 6.85% of the cross-sectional variation in the bid-ask spread across both investment grade and speculative grade bonds. In contrast, Schultz (2001) reports an R 2 of only 3.43% in regressions on all microstructure trading cost determinants using only investment grade bonds. The relatively small LDV coefficient, , indicates that the LDV liquidity estimator is substantially larger than the underlying proportional spread, especially for speculative grade bonds as illustrated in Table 1. As noted previously, this is due to our off-the-run Treasury notes. Accordingly, Treasury notes have bid/ask spreads four times that of Treasury bills. In addition, Treasury bills have lower yields than do Treasury notes. Krishnamurthy (2002) shows that once newer Treasury bonds are issued, the yield spread between the original on-the-run and off-the-run Treasury bonds becomes minimal. This implies that, cross-sectionally, the age effect on bond liquidity is more prominent for newly issued securities. 19

23 liquidity measure including other related costs such as commission costs, price impact costs, and opportunity costs (Lesmond, Schill, and Zhou, 2002). Also, Schultz (2001) notes that bid-ask spread quotes are indicative and not firm, so effective trading costs may deviate substantially from the quote. Additionally, Garbade and Silber (1976) find that the cost of liquidity services in the Treasury markets is determined by price dispersion as well as search costs, and is not equal to the bid-ask spread. Adding maturity, age, and the amount outstanding shows the LDV estimate to remain positively and significantly related to the bid-ask spread. Including bond rating increases the fit of the regression to 22.46%, a substantial improvement over using only the LDV estimate, but does not remove the LDV estimate from significance. Including non-rated bonds shows the LDV estimate to remain positively and significantly associated with the bid-ask spread. More importantly, the LDV coefficient remains relatively the same regardless of the included liquidity determinants indicating, that the LDV estimate has sufficient power to explain the bid-ask spread. When restricting the sample to only investment grade bonds, the LDV estimator remains positive and significant regardless of whether the full menu of liquidity determinants is included. Including non-rated bonds while increasing the sample size does not affect the significance or sign of the LDV coefficient. The sign for the amount outstanding differs from that found by Turner and Kochin (1971) and Crabbe and Turner (1995). Turner and Kochin find a negative relation between issue size and liquidity, while Crabbe and Turner find no relation. Sample differences or a greater dispersion of issue sizes may contribute 20

24 to these results. The negative sign for the bond age is contrary to Sarig and Warga (1989) and Elton and Green (1998), after controlling for the amount outstanding, maturity, and bond rating. Finally, focusing only on speculative grade bonds, we find the LDV estimator to remain positively and significantly related to the bid-ask spread. Given the large differences between the LDV estimate and the bid-ask spread, the reduced significance levels for the LDV coefficient are not surprising. Nor are the reduced levels of the goodness of fit compared to the overall and the investment grade bond only regressions. Including non-rated bonds in a dummy regression context does not alter these results. 5. The LDV Liquidity Estimate and Related Proxies 5.1 LDV liquidity estimate by credit risk and maturity In this subsection, we analyze LDV liquidity rankings sorted by maturity (a proxy for return volatility) and rating (a proxy for default risk). Chakravarty and Sarkar (1999) find that maturity and credit rating are the dominant factors explaining spread costs. Maturity will also proxy for search costs because most trades in investment grade bonds occur soon after issuance and, once acquired, these bonds are often held to maturity. Thus, the ranking by credit rating controls for default risk, while the ranking by maturity controls for return volatility and search costs. Following Duffee (1998), we group the bonds by maturity, classifying them as shortterm (zero to seven years to maturity), medium-term (seven to 15 years to maturity), and 21

25 long-term (15 to 40 years remaining to maturity). We report the results separately for investment and speculative grade bonds. The significance of the trend in liquidity costs across the separate bond rating and maturity groupings is examined using a bootstrap statistic. We use a bootstrap P-value in place of a t-test (or χ 2 test) because of the perceived non-normality of the liquidity estimates across each maturity class and bond rating cell. 17 To evaluate statistical significance, we create bootstrap sample sizes from 15 to 700, depending on the number of observations within each cell, by randomly drawing with replacement from the liquidity estimates. We then calculate the mean liquidity cost for each of the samples. Finally, these mean estimates are used to determine the bootstrap standard deviations and confidence intervals. We assess trends in the liquidity estimates across either maturity or bond rating classes by assigning a numerical value of one to four for investment grade categories, or one to three for speculative grade categories. We cull rating classes CCC to D to obtain a sufficient number of observations. Our bootstrap P-value then assesses not only the significance of the overall liquidity difference across each cell, but whether the trend is monotone. Table 4 contains the results. Generally, the results indicate a significant trend in liquidity across maturity structure for investment grade bonds and a significant trend in liquidity costs across debt rating for speculative grade bonds. For instance, for AAA investment grade bonds, liquidity costs rise from 9 bp to 147 bp from short-term to long-term bonds. Similar trends are 17 These concerns notwithstanding, virtually the same results are obtained using the χ 2 statistic to test for overall differences across the cells. 22

26 evident in each of the remaining investment grade bond rating categories. Across bond ratings, liquidity costs are monotone increasing for short-term bonds, but liquidity costs are monotone decreasing for long-term bonds. The declining trend in liquidity costs for long-term bonds may indicate more liquidity trading for lower-rated bonds because of their increased availability. AAA bonds are frequently held to maturity and, in essence, leave the market. Liquidity costs would rise for these bonds due to increased search costs. The lack of a consistent trend in the LDV estimates across the credit rating for investment grade bonds is consistent with Schultz s (2001) results, which show little association between the S&P bond rating and liquidity costs. These results indicate that return volatility and search costs dominate default risk in assessing liquidity costs for investment grade bonds. Speculative grade bonds, on the other hand, show liquidity costs varying significantly with default risk rather than with return volatility. For instance, within the short-term bonds, the LDV liquidity costs are shown to increase from 1.76% for bonds rated BB to 5.92% for bonds rated CCC to D. For long-term bonds, the LDV liquidity costs are shown to increase from 1.70% for bonds rated BB to 4.58% for bonds rated CCC to D. Little trend in liquidity costs is apparent across the maturity structure for any bond rating. 23

27 5.2 Multivariate regression tests of the LDV liquidity hypothesis In this subsection, we regress the LDV liquidity estimates on a menu of liquidity determinants in order to further validate the LDV liquidity cost estimate. The regression is stated as: (α 2 α 1 ) it = η 0 + η 1 Maturity it + η 2 Age it + η 3 Amount Outstanding it + η 4 Bond Rating i + η 5 Bond Rating Dummy it + ɛ t The subscript it refers to firm i and time period t. To reflect the differences in liquidity trends with respect to maturity and bond rating presented previously, we split the regression tests into investment grade and speculative grade bond categories. The liquidity determinants are maturity, age, the amount outstanding, bond rating, and a bond rating dummy. We assign dummy ratings given the results of Table 1, where nonrated bonds experience LDV-based liquidity costs in between those of investment grade and speculative grade bonds. In the overall regressions, the bond rating dummy is assigned a zero for investment grade bonds, one for non-rated bonds, and two for speculative grade bonds. The investment grade regressions assign a bond rating dummy of zero for rated bonds and one for non-rated bonds, while the speculative grade regressions assign a bond rating of zero for non-rated bonds and one for rated bonds. Table 5 presents the results. For the investment grade regressions, maturity and the amount outstanding are shown to dominate the liquidity costs. The positive coefficient for maturity indicates that longer maturity, as a proxy for volatility and search costs, may cause lower trading frequency and thus lower liquidity. This is consistent with an investment horizon argument offered by 24

28 Amihud and Mendelson (1991). Also of note is the magnitude of the maturity estimate, which indicates an incremental increase of two cents (per $100 par) for every added year in the maturity structure, consistent with Chakravarty and Sarkar (1999). These results hold regardless of whether any of the other liquidity determinants are included. The negative sign for the amount outstanding in the bond rating regression is consistent with Tanner and Kochin (1971) and Schultz (2001). Bond age is insignificantly related to bond liquidity. Chakravarty and Sarkar (1999) find that bond age and liquidity costs are related, but their results are weak for this one variable. The bond rating coefficients are insignificant for investment grade bonds, implying little relation between bond rating and liquidity costs. This is consistent with Schultz (2001), who finds that AAA rated bonds tend to be less liquid than A rated bonds. However, including non-rated bonds restores the positive and significant relation between ratings and liquidity. Including non-rated bonds increases the liquidity costs in accordance to the underlying rating structure. Speculative grade bonds, on the other hand, show few significant liquidity determinants except for bond rating. These results are not surprising because speculative grade bonds may not survive to maturity reducing the impact of return volatility on bond liquidity. The same arguments extend to bond age. Finally, we run a full regression by combining the investment grade and speculative grade bonds to induce greater variability in the independent variables. Maturity, age, and bond ratings are significant. The maturity results are virtually identical to those of the investment grade regressions, indicating the strength of the maturity results. The amount 25

29 outstanding is again negative for the bonds rated by S&P, but not for the bonds that forgo a bond rating. This indicates that larger bond sizes for rated firms yield smaller liquidity costs, while firms that forgo a bond rating have smaller issue bond sizes (as shown in Table 1) and demonstrate much less variability across the issuers. Bond age is significantly and negatively related to liquidity costs for rated bonds, indicating that older bonds are more expensive to trade. Including both investment grade and speculative grade bonds restore the significance of the bond age because of the increased variability in the bond age liquidity costs. 6. Liquidity Effects on the Yield Spread 6.1 Yield spreads by LDV liquidity estimate and bond rating It is well known that the yield spread cannot be explained by default risk alone. Elton et al. (2001) show that there is a large, unexplained component of the yield spread after adjusting for the fair compensation for default risk and tax effects. Collin-Dufresne, Goldstein, and Martin (2001) find that yield spread changes cannot be fully explained by commonly used yield spread determinants. Delianedis and Geske (2001) and Huang and Huang (2002) also reach a similar conclusion. Longstaff (2000) argues that the fixed income markets are incomplete due to security-specific features such as liquidity. Amihud and Mendelson (1986) develop a model where investors require an illiquidity premium in the expected return. Amihud and Mendelson (1991), by studying short-term Treasury notes and bills with the same maturity, find that Treasury notes have bid-ask 26