The financial performance of low-grade municipal bond funds.

Given the size of the U.S. tax-exempt bond market (which includes all the 50 states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands, and Guam), there is surprising little research in this area. As of 1993, the Federal Reserve estimated the overall size of the municipal bond

This study: (1) establishes the existence of the low-grade municipal bond asset class; (2) analyzes and extends the low- and high-grade corporate bond effect to municipal bonds; (3) analyzes the abnormality of the returns for low-grade municipal bonds; and (4) generally extends research on tax-exempt securities.

Over the study period, low-grade municipal bond funds return 0.63% per month with a 2.26% standard deviation, while high-grade municipal bond funds return 0.60% with a 2.40% standard deviation. Given standard quadratic utility, and assuming that risk and return are best described by historic standard deviation of returns and mean returns, low-grade municipal bond funds appear to dominate high-grade municipal bond funds. From January 1978 through September 1994, low-grade muni funds have had higher returns at a lower level of risk, than high-grade muni funds. Also, it is trivial to show that linear combinations of short-maturity and low-grade muni funds dominate intermediate and insured municipal bond funds. The apparent anomalous relation between low- and high-grade municipal bond funds is one of the issues addressed in this study. Although an equality of means t-test between the two asset-class return series shows no significant results. We ask if risk-adjusted low-grade municipal bond fund returns are greater than high-grade municipal bond fund returns.

This study examines the return experience of low- and high-grade muni funds over a long period (i.e., January 1978 through September 1994). The length of the study period allows me to compile evidence on the financial performance of low-grade munis, and to generally extend low-grade corporate bond analysis to the municipal market.

Although not statistically significant, low-grade municipal bond funds have generated a higher return at a lower standard deviation of return over the period examined. In a sense, the original Drexel hypothesis seems to hold for both municipal bond asset classes. (See Cornell and Green (1991) for a definition of the Drexel hypothesis.) In addition to low-grade municipal bonds possibly outperforming high-grade municipal bonds, there are several other seemingly anomalous low-grade corporate bond findings that I address in this study (Kihn, 1994). Specifically, they are: low-grade municipal bonds as an asset class may (1) show evidence of possessing a higher proportion of calls and/or weaker call protection than high-grade municipal bonds; and (2) demonstrate a return generation process which would suggest that changes in risk-free interest rates and/or the economy account for a significant amount of the relative return variation in the low-grade municipal market overall.

The paper is organized into five sections. Section I presents background on the data and provides summary statistics. Section II reviews the expectations/hypotheses developed from contingent claims analysis (CCA) risky-debt valuation models that are relevant to low-grade municipal bonds and their principal embedded options. Section III presents the low- and high-grade municipal bond declining-interest-rate regression results, recession regression results, and combination declining-interest-rate and recession regression results. Section IV examines how the January effect and the Tax Reform Act of 1986 may have affected low-grade municipal bond fund financial performance. Section V concludes.

I. Data and Summary Statistics

Part of the motivation behind my study is the observation by Skelton (1983) that comparably rated municipal and corporate bonds have similar risk profiles. By extension, if CCA models provide insight into corporate bond pricing they should provide comparable insight into municipal bond pricing.

This preliminary investigation of relative risk in

municipal and corporate bonds reveals that in at

least two respects they are remarkably similar. First,

the measured variances of return for portfolios of

comparably rated bonds are virtually identical.

Second, the covariances of comparably rated bond

portfolios with an index of common stock returns

are very close to one another (Skelton, 1983, p.

633).

The municipal and corporate bond data set is derived from open-end mutual funds tracked by Morningstar during the period January 1978 through September 1994. The Treasury bond data is a spliced series based on the Cornell and Green (1991) Treasury bond series (January 1978 through December 1988) and Salomon Brothers' long bond series (January 1989 through September 1994).(1) The stock series is derived from the Standard and Poor's 500 return index. Therefore, unlike the series derived from mutual fund returns, the equity and Treasury bond series are gross returns.

Like the Cornell and Green (1991) study on low-grade corporate bonds, my study uses monthly open-end mutual fund data to derive asset-class return series. Lipper definitions are used for all asset-class return series. Shares of open-end mutual funds are traded on the basis of net asset value (NAV). Monthly returns are based on the following calculation: Return, = [([NAV.sub.t] - [NAV.sub.t-1]) + [IncDist.sub.t] + [CapGainDist.sub.t]] / [NAV.sub.t-1]. As a general rule, for municipal bonds, income distributions are tax-exempt and capital gains distributions are taxable. Given that low-grade municipal bonds, like corporate bonds, have a higher incidence of capital losses (e.g., defaults), after-tax high-grade municipal bond returns could be overestimated relative to after-tax low-grade municipal bond returns. In addition, these returns take account of 12b-1 fees and management fees but not front- or back-end loads, or redemption charges.

I construct each mutual fund-based asset-class return series following the method used by Cornell and Green (1991). For each asset class, I calculate the equally weighted average of all mutual funds each month. The number of funds as of month-end September 1994 for each asset-class series derived from Morningstar data includes 101 low-grade corporate bond funds, 149 high-grade corporate bond funds, 34 low-grade municipal bond funds, and 180 high-grade municipal bond funds. Table 1 provides background on the comparable corporate and municipal bond and other asset-class return series used in this study.

It should be noted that the mutual fund return series wasn't tested for the impact of survivorship bias. (See e.g., Grinblatt and Titman, 1989; Hendricks et al., 1993; or Malkiel, 1995.) Therefore, there is a possibility that survivorship bias has an impact on the reported results. However, given that the tests focus on comparing low-grade with high-grade bond fund returns, the relevant question is whether there is reason to believe there is a bias in the difference between the two returns. Since there is no past or present evidence to suggest that one asset class is significantly more biased than another, there is no a priori reason to believe the results of this study may be biased. In addition, not all studies on survivorship bias indicate that when testing individual return series for survivorship bias, there is a significant bias. (See e.g., Grinblatt and Titman, 1989; and Elton et al., 1995.) Furthermore, those studies that do show a significant survivorship bias (e.g., Malkiel, 1995) find that only equity funds have such a significant bias -- not bond funds.(2) There is no evidence to date to suggest that bond funds have the same level of bias as equity funds.

Table 1. Summary Statistics and Tests of Normality for the Returns of Low- and High-Grade Corporate Bond Funds, Low- and High-Grade Municipal Bond Funds, Treasury Bonds, and Equities

The data are monthly returns. All values are derived from Morningstar. Each return series represents the average net returns on all open-end bond funds for that asset class. Asset-class definitions are based on Lipper definitions. Low-grade corporate bond funds generally invest at least 80% of assets in corporate bond issues rated below BBB. High-grade corporate bond funds generally invest at least 80% of assets in corporate bond issues rated A or higher. Low-grade municipal bond funds invest at least 50% of assets in lower-rated municipal bond issues (issues below the top 4 credit ratings). High-grade municipal bond funds invest at least 65% of assets in municipal bond issues in the top 4 credit ratings.

                               Low-Grade   High-Grade
1978:01 to 1994:09             Corporate   Corporate

Observations = 201
Moments of the distribution:

  1st - mean                    0.8399%      0.7262%
  2nd - standard deviation      2.2726%      1.7076%
  3rd - skewness                0.3475       0.8190
  4th - kurtosis                3.1486       4.0368
Minimum                        -6.5360%     -4.1570%
Maximum                        10.9500%      9.4353%

Tests of normality#:

  T-statistic: mean = 0         5.2399       6.0297
  Prob [is greater than] T      0.0001       0.0001
  W: Normal                     0.9560       0.9589
  Prob [is less than] W         0.0001       0.0001

                                Low-Grade    High-Grade
                                Municipal    Municipal

Moments of the distribution:

  1st - mean                    0.6268%       0.5989%
  2nd - standard deviation      2.2625%       2.4037%
  3rd - skewness               -0.6664       -0.4478
  4th - kurtosis                3.6491        2.3130
Minimum                        -8.6000%      -7.9250%
Maximum                         9.1330%       8.2930%

Tests of normality#:

  T-statistic: mean = 0         3.9276        3.5325
  Prob [is greater than] T      0.0001        0.0005
  W: Normal                     0.9280        0.9502
  Prob [is less than] W         0.0001        0.0001

                                Treasury      S&P 500
                                Bonds

Moments of the distribution:

  1st - mean                    0.8042%       0.8891%
  2nd - standard deviation      3.6029%       4.4117%
  3rd - skewness                0.5662       -0.7540
  4th - kurtosis                1.5742        4.6516
Minimum                        -8.4600%      -23.9440%
Maximum                        15.2400%       13.1770%

Tests of normality#:

  T-statistic: mean = 0         3.1647         2.8572
  Prob [is greater than] T      0.0018         0.0047
  W: Normal                     0.9753         0.9694
  Prob [is less than] W         0.1033         0.0150

# The first test of normality is Student's t value for testing the null hypothesis that the population mean is 0. The second test of normality is the Shapiro-Wilk statistic for testing the null hypothesis that the values are a random sample from a normal distribution.

Over the study period (i.e., January 1978 through September 1994), low-grade corporate bonds show a higher mean and standard deviation of return than high-grade corporate bonds. The relatively recent increase in the volatility of low-grade corporate bonds relative to high-grade corporates is due to a sharp increase in low-grade corporate bond volatility from 1988 through the early 1990s. Overall, the two corporate bond asset classes display relatively similar profiles over the study period.

During the same period, low-grade munis show a higher mean and lower standard deviation of return than do high-grade munis. Unlike the two comparable corporate bond series, the two municipal bond series are slightly negatively skewed. This negative skewness is associated more with equity returns than bond returns. Also, unlike the two comparable corporate bond series, the two muni distributions show the opposite "peakedness" for their respective return distributions. That is, the low-grade corporate bond distribution of returns is less kurtotic than the high-grade distribution of returns (i.e., it has a more platykurtic distribution), while the opposite is true of the two municipal bond distribution of returns. Overall, the equity return series has the highest mean, the highest standard deviation, is the most negatively skewed, and the most platykuntic.

The test for normality suggests that at standard levels of statistical significance, only the Treasury bond return series is drawn from a random sample from a normal distribution (i.e., the Shapiro-Wilk test).(3) All five of the other asset-class return series reject the null hypothesis that the mean of each respective distribution is equal to zero (i.e., at the 5% level of significance). At normal levels of statistical significance, all the asset-class return series show means that are significantly positive. Again, five of the six return series reject the null hypothesis that the values are drawn from a random sample from a normal distribution. Table 2 provides correlation and autocorrelations for the asset-class return series used in this study.

Table 2. Tests for Autocorrelation and Correlation Coefficients for the Returns of Low- and High-Grade Corporate Bond Funds, Low-Grade and High-Grade Municipal Bond Funds, Treasury Bonds, and Equities

The data are monthly returns. All values are derived from Morningstar. Each return series represents the average net returns on all open-end bond funds for that asset class. Asset-class definitions are based on Lipper definitions. Low-grade corporate bond funds generally invest at least 80% of assets in corporate bond issues rated below BBB. High-grade corporate bond funds generally invest at least 80% of assets in corporate bond issues rated A or higher. Low-grade municipal bond funds invest at least 50% of assets in lower-rated municipal bond issues (issues below the top 4 credit ratings). High-grade municipal bond funds invest at least 65% of assets in municipal bond issues in the top 4 credit ratings.

                          Low-Grade   High-Grade  Treasury  S&P 500
1978:01 to 1994:09        Corporate   Corporate   Bonds

Autocorrelation at lag 1  0.314(***)  0.215(***)  0.081     -0.010
Test for white noise#:
  12 lags                 35.86(***)  31.62(***)  15.31     14.23

Correlation with
  High-grade corporate    0.742(***)
  Treasury bonds          0.634(***)  0.934(***)
  S&P 500                 0.524(***)  0.366(***)  0.377(***)

                          Low-Grade   High-Grade  Treasury  S&P 500
                          Municipal   Municipal   Bonds

Autocorrelation at lag 1  0.159(**)   0.116(**)     0.081     -0.010
Test for white noise#:
  12 lags                 36.00(***)  34.86(***)    15.31      14.23

Correlation with
  High-grade municipal    0.978(***)
  Treasury bonds          0.737(***)  0.772(***)
  S&P 500                 0.413(***)  0.420(***)    0.377(***)

# This is an autocorrelation check for white noise. The null hypothesis is that the autocorrelations sum to 0. The test statistic is at the 12th lag (i.e., 1 year). Therefore, the null hypothesis for the 12th lag is: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [r.sub.k[.sup.2]] is the product moment correlation between [e.sub.t] and [e.sub.t-k] (k [equivalent] 1, 2, ..., 12). If the null hypothesis is true, the statistic is distributed as a chi-square with 12 degrees of freedom. If the statistic is not significant, the null hypothesis can be accepted.

(***) Significant at the 0.01 level.

(**) Significant at the 0.05 level.

(*) Significant at the 0.10 level.

Over the study period, both the low- and high-grade corporate bond return series show evidence of autocorrelation. Other studies interpret this autocorrelation as evidence of nontrading. (See Cornell and Green, 1991.) Correlations between the taxable asset classes show that low-grade corporate bond returns are slightly less positively correlated with equity returns than are Treasury bond returns whereas high-grade corporate bond returns are significantly more positively correlated with Treasury bond returns than are equity returns. Clearly, relative to high-grade corporates, low-grade corporates are more exposed to risks associated with equities than Treasuries.

At normal levels of statistical significance, both municipal bond asset classes show evidence of autocorrelation. However, the first-order autocorrelation associated with low- and high-grade corporate bonds is significantly higher than that associated with low- and high-grade municipal bonds. If first-order autocorrelation is evidence of nontrading, the two muni asset classes show evidence of dramatically lower levels of nontrading than do their corporate bond counterparts over the same sample period. In addition, adjusting for municipal bond nontrading does not significantly decrease autocorrelation in the regressions run.(4) In examining correlations between the municipal bond asset classes and Treasury bonds and equities, the muni asset classes seem to be very similar.

I ran three additional regressions to check the robustness of the OLS results. In the regressions that follow, I make a Dimson (1979) adjustment to counteract the possible presence of nontrading. I report these results along with the standard OLS results.(5) In addition, since the Dimson adjustment does not always control for the presence of nonsynchronous trading (Fowler and Rorke, 1983) and the fact the prices for some bonds may not change that often (Lo and MacKinlay, 1990),(6) I ran Yule-Walker and maximum likelihood regressions, based on the premise that the error term is not independent across time (i.e., autoregressive errors). If autocorrelation is present, the OLS parameter estimates will not be efficient and the standard error estimates may be biased. Because the data is taken monthly, with both the Yule-Walker and maximum likelihood methods, I initially check the autoregressive process up to order 12, and set the significance level criterion at a 5% cut-off value. Since the Yule-Walker estimates are used as starting values for the maximum likelihood method, the maximum likelihood method is computationally equivalent to, or better than, the Yule-Walker method. However, there is little or no difference between the straight OLS, Yule-Walker, and maximum likelihood regression results. Therefore, I report only the OLS and Dimson results.

II. CCA, Risky Municipal Bond

Expectations, and Tests

It has been found that municipal bonds tend to be less affected by business cycles than corporate bonds. We have also carried out tests for other business cycle effects on municipal risk structure, but obtained no significant results. This should not be surprising since municipal bonds, like utility bonds already discussed, should not be appreciably affected by normal business cycle fluctuations (Jaffee, 1975, p. 318).

Contrary to their expectations, Cornell and Green (1991) find that low-grade corporate bonds become significantly more sensitive to Treasury bond market movements during recessionary periods. This section shows that this result can be expected to hold only for CCA risky-bond pricing models that do not incorporate interest-rate risk. A simplified CCA risky-bond pricing model would suggest that low-grade debt should become increasingly sensitive to equity market movements as credit quality declines during recessionary periods.

Black and Scholes (1973) suggest that their study can provide the basis for analyzing the value of other contingent claims whose values may be a nonlinear function of another asset or liability. This is the insight to which is attributed the development of the CCA-based risky-debt valuation. In particular, the Merton (1974) study on the effects of risk on the value of corporate debt laid the foundation for CCA of risky debt. Since Merton (1974), there have been several studies using CCA to value risky debt. (See, e.g., Black and Cox, 1976; Geske, 1977; Ingersoll (1977a & 1977b); and Brennan and Schwartz, 1977). All these studies assume a nonstochastic or constant risk-free interest rate.

For the purposes of this study, I focus on Merton's (1974) risky-debt model assumption, i.e., that the risk-free interest rate being nonstochastic or constant has important implications. If the risk-free interest rate cannot vary over time, then by definition it will have no impact on the valuation of a firm or on out-of-the-money interest-rate calls.(7) That is, since firm value cannot be a function of a constant risk-free interest rate, there can be no interaction between changes in the risk-free interest rate and changes in the underlying firm value (i.e., since the risk-free interest rate doesn't change). Since the risk-free interest rate is constant, out-of-the-money interest-rate call options have zero value, and in-the-money interest-rate call options have constant value. Therefore, there can be no interaction between changes in in-the-money call options and other option values (specifically, the put value). Clearly, a risky-debt model that does not incorporate a stochastic risk-free interest rate will not be affected by changes in the risk-free interest rate on either the firm value or the embedded option values that we expect to be a function of interest-rate risk (e.g., interest-rate calls).

There are now a series of CCA models that incorporate interest-rate risk into the CCA risky-debt valuation model. (See, e.g., Brennan and Schwartz, 1980; Jones et al, 1984; Ramaswamy and Sundaresan, 1988; Shimko et al., 1993; Jalilvand and Park, 1994; and Longstaff and Schwartz, 1995.) Given that firm value and interest-rate risk are explicitly incorporated into these new models, the correlation between changes in the risk-free interest rate and firm values ([Rho[.sub.r,V]]) can enter into the risky-debt valuation formula. For example, motivated by the apparent contradiction in observed corporate bond yield spreads and those estimated based on Merton's (1974) risky-debt valuation model, Kim et al. (1993) extend the model developed by Brennan and Schwartz (1980)(8) and estimate yield spreads that are consistent with observed levels. Specifically, Kim et al. find that "interactions between default risk and the call provision play an important role in determining the total spread defined in this way." In estimating realistic scenarios, most of the yield spread (callable corporates against comparable non-callable Treasuries) is determined by default risk. However, a large portion is determined by the interaction between the stochastic firm value and the stochastic risk-free interest rate. Clearly, [Rho[.sub.r,V]] can affect risky-debt valuation.

Furthermore, Longstaff and Schwartz (1995) show explicitly that as the correlation increases between changes in the value of a firm and in the level of the risk-free interest rate, credit spreads increase. By using actual corporate bond yield averages, Longstaff and Schwartz "find that credit spreads are strongly negatively related to the level of interest rates. Furthermore, changes in interest rates account for the majority of the variation in credit spreads for most bonds in the sample." Clearly, the correlation of changes in firm value with changes in the risk-free interest rate can significantly affect the valuation of risky debt.

Based on the discussion above, there can be very different expectations for the changing sensitivities of riskier debt (i.e., low-grade munis) relative to less risky debt (i.e., high-grade munis) during periods when their principal embedded options can be expected to move deeper into-the-money. For example, risky-debt valuation models that do not incorporate interest-rate risk find what seems to be anomalous behavior in low-grade corporate bond returns during recessionary periods. On the other hand, risky-debt valuation models that do incorporate interest-rate risk may be able to explain the behavior of low-grade corporate bond returns during such recessionary periods (assuming [Rho[.sub.r,V]] is significantly negative). From the CCA perspective, low-grade munis can generally be viewed as a tax-exempt version of low-grade corporate bonds, thus the empirical analysis applied to low-grade corporates can be extended to low-grade munis.

It should be noted that defaults and exchanges are events indicating that the firm's or the municipal authority's management have exercised the put option that equity holders received from bondholders when the bonds were issued. All corporate and municipal bonds are exposed to default risk, however, for municipal bonds, revenue bonds have a much higher incidence of defaults than general obligation bonds (Heide et al., 1994).(9) Therefore, it is important to note that overall, municipal bonds appear to have lower default rates than corporate bonds. Historically, revenue bond default reduces prices by more than 50% (Cirillo and Jessop, 1993), which is comparable to the figure for corporate bond default (Altman, 1992). Hence, general obligation bonds tend to be relatively insensitive to the business cycle.

Critical to this study is identifying periods when bond calls and puts can be exercised and/or the probability of exercise significantly increases relative to all other periods. For interest-rate call periods, I use periods of declining interest rates. Bonds can be called, and/or the probability of exercise increases, when interest rates decline. For put/default periods, I use periods of recession. Credit quality generally declines and defaults increase during such periods. I define a month as a period of declining interest rates if during that month, the change in yield on the 10-year constant maturity Treasury bond is less than zero. I define a recession as the period immediately following the business-cycle peak up to the month of the subsequent trough. I base the recession period definition on that of the U.S. Bureau of Economic Analysis.

Table 3 summarizes the difference in expectations for CCA "assuming no credit spread effect" and CCA "assuming a strong credit spread effect." These expectations mirror those derived for risky corporate bonds. The first set are the traditional CCA expectations that do not incorporate interest-rate risk. The second set incorporates interest-rate risk and assumes that [Rho[.sub.r,V]] is significantly negative. Of course, if [rho[.sub.r,V]] is zero or close to zero, the two should not differ substantially.

Table 3. Expectations for Periods under Study

Simple CCA Expectations

                                            Expectation
                                            for Sensitivity to
Period under Study                          Treasury Bonds

Assuming no credit spread effect:

  Interest rate call periods                   0
  Put periods                                  - or 0
  Combination periods
  (call & put periods)                         - or 0

Assuming a strong credit spread effect:

  Interest rate call periods                   0 or +
  Put periods                                  0 or +
  Combination periods
  (call & put periods)                         +

Simple CCA Expectations
                                            Expectation
                                            for Sensitivity to
                                            Stocks
Period under Study

Assuming no credit spread effect:                0

  Interest rate call periods                     +
  Put periods
  Combination periods                            +
  (call & put periods)

Assuming a strong credit spread effect:          0 or -

  Interest rate call periods                     0 or -
  Put periods
  Combination periods                            +
  (call & put periods)

The following null hypotheses are based on CCA risky-debt valuation models that do not incorporate interest-rate risk. Therefore, during interest-rate call periods we do not expect changes in the relative sensitivity of low-grade municipal bond returns to Treasury bond and equity returns. Hence, [H.sub.0]: during periods when interest rates are declining, low-grade munis should not become relatively more or less sensitive to Treasury bond and equity market movements. During put periods, the relative sensitivity of low-grade municipal bond returns to equity returns should increase. Hence, [H.sub.0]: during periods when general credit quality is declining, low-grade munis should become relatively more sensitive to equity market movements. During combination interest-rate call and put periods, the relative sensitivity of low-grade municipal bond returns to equity returns should increase. Hence, [H.sub.0]: during periods when interest rates and general credit quality are declining, low-grade municipal bonds should become relatively more sensitive to equity market movements. Essentially, put periods are the only periods that should have a significant impact on the relative sensitivities of low-grade municipal bond returns to Treasury bond and equity market returns. In addition, because puts have primary importance in the valuation of risky municipal debt, we expect that only sensitivities to the equity market may change, not the Treasury bond market.

The greatest contrast between the two sets of risky-debt valuation models occurs during combination periods. Particularly clear is the opposite expectation regarding the relative sensitivity of low-grade municipal bond returns to equity market returns. Because the signs of the two expectations are diametric opposites, this is the strongest test presented, and its results should be viewed with added interest.

III. Regressions that Test the Impact of

Call and Put Periods

I hypothesize that periods in which the volatility and sensitivity (i.e., to the Treasury bond and equity markets) of low-grade munis relative to high-grade munis is due in part to the fact that the low-grade bonds are hybrid securities. It is a central argument of this study that one of the possible causes of the seemingly abnormal behavior of low-grade municipal bonds relative to high-grade municipal bonds is that relatively less creditworthy bonds are significantly more affected by the correlation between changes in the risk-free rate of interest and changes in firm value (i.e., [[rho].sub.r,V] is significantly negative) than are more creditworthy bonds.

As with corporate bonds, the critical method for examining the return behavior of high- and low-grade munis is to isolate periods when calls and puts will likely be exercised, and/or the probability of exercise significantly increases. I assume that for embedded put options (i.e., defaults and outright bankruptcies), the appropriate periods to examine are recessions, while for calls the appropriate periods are those of declining interest rates. By examining low- and high-grade municipal bond returns during these periods, I can examine the impact that puts and calls have on the relative returns of the two municipal bond asset classes.

As a baseline to the regression analysis that follows, I run the regression models shown below to evaluate the sensitivity of low- and high-grade munis to Treasury bond and equity market movements:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

LGR = low-grade municipal bond return HGR = high-grade municipal bond return TBR = Treasury bond return SMR = stock market return (i.e., the return of the S & P 500 index) e is the error term.

This equation was designed to control for Treasury bond and equity market risk via TBR and SMR.

The return spread results are critically important. At a general level, there is something surprising, namely, the estimated intercept for the return spread regressions is significantly positive (i.e., at the 5% level for all but the Dimson regression). This suggests that after controlling for Treasury bond and equity market risk, low-grade municipal bonds outperform high-grade munis over the study period. Second, low-grade munis are not significantly more equity-like than high-grade munis. Since municipal bonds are not in general as equity-like as corporate bonds, this is a surprising, but not a completely unexpected result. Clearly, low-grade munis can be exposed to additional risk(s) that go beyond corporate equity risk. However, since municipalities do not issue equity, it is empirically difficult to control for municipal equity risk. Finally, high-grade munis are more risk-free bond-like (i.e., Treasury bond-like) than low-grade municipal bonds.

A. Call Periods

If low-grade munis have significantly less interest-rate call protection and/or a higher call rate than high-grade municipal bonds, there should be a significant decline in the sensitivity of their returns to risk-free bond returns during periods when the interest-rate call option should be exercised. This assertion can be tested by examining the behavior of low- relative to high-grade municipal bond returns during periods of declining interest rates. If there is a significant difference, the sensitivity of low-grade municipal bond returns to Treasury bond market movements should significantly decrease during periods of declining interest rates.

Although low-grade munis are less volatile than their high-grade counterparts during periods of declining interest rates, low-grade munis are not significantly less volatile. For months in which interest rates decline, the ratio of low- to high-grade municipal bond standard deviation is approximately 0.94 versus 0.94 for all months.(10) It appears to be incorrect to state that the greater relative number of calls and/or weaker call protection afforded low-grade munis is the cause of their lower volatility. Over the study period, low-grade munis are not more or less sensitive to declining interest rates than high-grade munis.

In order to further test this contention, I run the following regression models to test for the significance of call periods on the returns of low- and high-grade municipal bonds.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where DIR = a dummy variable equal to one if interest rates decline, and zero otherwise. The call dummy variable is intended to isolate the effect of periods when calls are more frequent and/or more probable.

The results indicate that after controlling for periods of declining interest rates, there is a significant difference in the return performance of the two asset classes. Therefore, after controlling for Treasury bond and equity market risk, low-grade munis outperform high-grade munis during periods when interest rates are stable or increasing.

Based on the estimated coefficient for the sensitivity of the spread between low- and high-grade municipal bond returns to Treasury bond returns during call periods, there is reason to reject the hypothesis that low-grade munis have significantly weaker and/or less interest-rate call protection than do high-grade munis. If, due to greater call protection, high-grade municipal bonds were significantly more sensitive to interest-rate movements relative to low-grade munis, then the estimated coefficient [[beta].sub.3] should be significantly greater than the same coefficient for the low-grade muni regression. The fact that the reverse is true casts doubt on the notion of a significant difference between the number of calls and/or the call protection associated with the respective asset classes. If there is a difference in asset-class interest-rate call protection, it is against high-grade municipal bonds, not low-grades. The regressions show that high-grade munis become significantly less government bond-like, while low-grade municipal bonds become significantly less equity-like during interest-rate call periods.

Regarding the risky-debt model(s) that explains interest rate call period behavior more accurately, the overall results of my regressions tend to support the strong credit-spread effect risky-debt models over more traditional risky-debt models. In all the return-spread regressions, the estimated coefficient [[beta].sub.4] is negative and significant at the 1% level. In addition, in all the return-spread regressions, the estimated coefficient [[beta].sub.3] is positive and significant at the 5% level. Clearly, these are not the results we would expect under risky-debt valuation models that do not incorporate interest rate risk.

B. Put Periods

With low-grade municipal bond puts or defaults, if there is a significant effect of the exercise and/or increase in the probability of exercise of low-grade muni puts relative to high-grade muni puts, it will show up during periods when the economy is performing poorly. If low-grade municipal bonds are significantly more exposed to business-cycle risk during recessions, their returns should be more sensitive to equity market movements during periods when more defaults could occur. Therefore, traditional risky-debt valuation models hypothesize that during recessionary periods, low-grade municipal bond returns are significantly more affected by movements in the equity market than at other times. However, risky-debt valuation models that incorporate interest-rate risk may not agree with that hypothesis, especially if interest rates tend to decline during recessions and [[rho].sub.r,V] is assumed significantly negative.

Although low-grade munis are less volatile than high-grade munis during recessionary periods, they are not significantly less so. For recession months, the ratio of low- to high-grade municipal bond standard deviation is approximately 0.98 versus 0.94 for all months. Like interest-rate calls, defaults alone cannot explain the volatility differential between high- and low-grade munis. Over the period analyzed, low-grade munis are only slightly less sensitive to recessionary periods than high-grade corporates.

To test the recession put hypothesis, I run the following regression models to test for the impact of put periods on the returns of low- and high-grade municipal bonds.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where Rec = a dummy variable equal to one if the economy is in a recession, and zero otherwise. The put dummy variable is intended to isolate the effect of recessionary periods when puts are more frequent and/or more probable for low-grade municipal bonds.

Except for the Dimson regression, the estimated intercept for the return spread regressions suggests that after adjusting for the various movements of the independent variables, low-grade munis return significantly more than high-grades. In this case, the results indicate that after controlling for recessionary periods, there is a significant difference in the return performance of the two asset classes. Also, note that all the regressions generally assign the same sign and level of significance to each comparable estimated coefficient.

Based on the estimated coefficient for the sensitivity of the spread between low- and high-grade municipal bond returns to Treasury bond market returns during put periods, there is no strong reason to reject risky-debt valuation models that do not allow for a credit-spread effect. That is, risky-debt valuation models that do not incorporate interest-rate risk cannot explain why riskier debt becomes more sensitive to interest-rate movements during recessions. My regressions do not provide strong evidence of this. In this case, the estimated coefficient [[beta].sub.6] is approximately zero. Actually, both asset classes become significantly more government-bond-like, but this effect is approximately the same for each asset class.

Based on the estimated coefficient for the sensitivity of the spread between low- and high-grade municipal bond returns to equity market returns during put periods, there is a weak reason to reject risky-debt valuation models that do not allow for a credit-spread effect. Risky-debt valuation models that do not incorporate interest-rate risk project that low-grade bonds will become more sensitive to equity market movements during recessions. If low-grade municipal bonds are significantly more sensitive to equity market movements during recessions, due to their puts moving deeper into-the-money relative to high-grade munis, then the estimated coefficient P. should be significantly greater than the same coefficient for the high-grade municipal bond regression. Although not significantly different, the fact that this is not the case casts doubt on the usefulness of risky-debt valuation models that cannot explain this result.

These results are different from the results for low-and high-grade corporate bonds, where high-grade corporates behave more like equities during business-cycle contractions than during expansions. Besides being exposed to different kinds of equity risk, another possible explanation for the lack of a recession effect on low- and high-grade munis may be that unlike corporate bonds, there is no large increase in perceived credit risk during recessionary periods. As some low-grade municipal bonds default, thus removing them from and lowering the duration of the asset class, a relatively equal amount of high-grade munis are downgraded. During economic booms, high-grade munis can be upgraded, but the upgrades may be a direct function of the length and magnitude of the expansion. Downgrades are a direct function of the length and magnitude of the contraction. Either way, the results suggest that defaults do not significantly affect the two return series under study.

In the issue of the risky-debt model, which explains put-period behavior more accurately, the overall results of my regressions weakly support those models with a credit-spread effect. Overall, the results suggest that during periods when low-grade munis, relative to high-grade municipal bonds, should show a great deal more sensitivity to equity market movements, they do not. However, high-grade munis do not behave significantly more like equities during business-cycle contractions than expansions. In addition, both low-and high-grade munis act significantly more like government bonds during recessions. During recessions, both asset classes seem to maintain their relative Treasury bond and equity market sensitivities.

C. Combination Call and Put Periods

With the increased probability of low-grade municipal bond puts and low- and high-grade municipal bond interest rate calls, if there is a significant effect of the exercise, and/or increase in the probability of exercise, of the options of low-grade municipal bonds relative to high-grade municipal bonds, it should show up during periods when the economy is performing poorly and interest rates are declining. Therefore, at least relative to high-grade municipal bonds, I hypothesize that during recessionary periods, low-grade municipal bond returns will be significantly more affected by interest-rate movements and less affected by movements in the equity market than at other times. Essentially, this is the strongest test for evaluating the appropriateness of risky-debt valuation models that incorporate interest-rate risk relative to the models that do not.

Low-grade municipal bonds are slightly less volatile than high-grade munis during recessions, but not significantly so. During recession and declining-interest-rate months, the ratio of low- to high-grade municipal bond standard deviation is approximately 0.96 versus 0.94 for all months. During months when we can expect puts and interest-rate calls on low-grade munis to be exercised more frequently than those for high-grade munis, there is some increase in volatility for low-grade returns versus that of high-grade munis, but that difference is not significant.

In order to test the recession put and declining-interest-rate call hypothesis, I run the following regression models to test or the significance of combination put and interest rate call periods on the returns of low- and high-grade municipal bonds:

These regressions capture the effect of the combination of puts and interest-rate calls for low-and high-grade municipal bonds. The coefficient [[beta].sub.9] isolates the effect of changes in government bond prices on changes in low- and high-grade muni prices during recessionary and declining interest rate months. The coefficient [[beta].sub.10] isolates the effect of changes in equity prices on changes in low- and high-grade municipal bond prices during recessionary and declining interest rate months.

The declining-interest-rate effect is accentuated during periods of recession. That is, during combination business-cycle contraction and declining-interest-rate periods, low-grade munis act even less like equities than during business-cycle contraction periods alone (compare the model 9 and 12 results for the estimated coefficients [[beta].sub.7] and [[beta].sub.10], respectively). The sign and significance of the estimated coefficients [[beta].sub.9] and [[beta].sub.10] for the model 12 regressions suggest that periods of declining interest rates combined with recession significantly affect the return relationship between low- and high-grade munis.

Based on the estimated coefficient for the sensitivity of the spread between low- and high-grade municipal bond returns to Treasury bond returns during combination interest-rate call and put periods, there is reason to reject risky-debt valuation models that do not allow for a credit-spread effect. That is, risky-debt valuation models that do not incorporate interest-rate risk cannot explain why more riskier debt is more sensitive to interest-rate movements during combination declining-interest-rate and recession periods. In this case, the estimated coefficient [[beta].sub.9] is positive and significant at the 5% level in all regressions.

Based on the estimated coefficient for the sensitivity of the spread between low- and high-grade municipal bond returns to equity market returns during combination interest-rate call and put periods, there is additional reason to reject risky-debt valuation models that do not allow for a credit-spread effect. If low-grade munis are significantly more sensitive to equity market movements during recessions, because their puts move deeper into-the-money relative to high-grade municipal bonds, then we can expect the estimated coefficient [[beta].sub.10] to be significantly greater than the same coefficient for the high-grade municipal bond regression. In all the regressions, the estimated coefficient [[beta].sub.10] for the model 12 regression is negative and significant at the 1% level. Thus, in risky-debt models that do not incorporate interest-rate risk into their valuation model we can expect that the estimated [[beta].sub.10] coefficients for the model 12 regressions will have a positive sign. Therefore, the fact that the sign is strongly negative casts doubt on risky-debt valuation models that cannot explain this result.

On the issue of the risky-debt model that explains combination interest-rate call and put-period behavior more accurately, the overall results of the above regressions strongly support those models with a strong credit-spread effect. Overall, the results suggest that during periods when we can expect low-grade municipal bonds to show a great deal more sensitivity to equity market movements relative to high-grade munis, and little or no change in sensitivity to government bond market movements, they do not. During combination declining-interest-rate and recession periods, the two asset classes seem to partially reverse their roles. Low-grade municipal bonds become less equity-like and significantly more Treasury-bond-like, while high-grade municipal bonds become significantly more equity-like and less Treasury-bond-like.

Finally, I run the following regressions to test the extent to which effect dominates (i.e., interest-rate call, put, or combination interest-rate call and put):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Risky-debt valuation models that include interest-rate risk and assume a significantly negative [[rho].sub.r,V] imply that [[beta].sub.9] and [[beta].sub.10], rather than [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] should pick up most of any significant changes in the sensitivities of the risky municipal debt return spread.

Except for the Dimson regression, the return spread regression results support the hypothesis that it is the combination of interest-rate call and put periods that principally cause riskier municipal bonds to become significantly less sensitive to equity market movements than more creditworthy municipal bonds (i.e., estimated coefficient [[beta].sub.10] in the return spread regression). Therefore, these final regressions strongly favor risky debt valuation models that incorporate both interest-rate risk and a significantly negative [[rho].sub.r,V].

IV. Municipal Bonds, the January Effect,

and the Tax Reform Act of 1986

Part of my motivation for examining low- and high-grade municipal bond returns is the controversy surrounding the comparison of low- and high-grade corporate bond returns. Some studies support the proposition that over long periods of time, low-grade corporates have returned more than high-grade corporates. (e.g., Hickman, 1958; and Fitzpatrick and Severiens, 1978.) Other studies suggest that there is no significant difference between the two corporate bond asset classes. (e.g., Fraine and Mills, 1961; Blume and Keim, 1987; Weinstein, 1987; Cornell and Green, 1991; and Blume et al., 1991.) Since this study finds that low-grade municipal bond funds outperform their high-grade counterparts, some further analysis is in order. Specifically, I evaluate the January effect and the Tax Reform Act of 1986 as possible sources of this seeming anomaly.

For the sake of clarity in the analysis that follows, all regression results reported in this section are simple OLS. Table 9 provides a comparison of the two sets of risky-bond asset classes.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

Over the sample period and after controlling for government bond and equity market movements, we see that low-grade corporate bond funds return slightly more than high-grade corporate bond funds, but not significantly more. On the other hand low-grade municipal bond funds return significantly more than high-grade municipal bond funds. As other studies (e.g., Cornell and Green, 1991) show, low-grade corporates are significantly less sensitive to government bond market movements than are high-grade corporates, but significantly more sensitive to equity market movements than are high-grade corporates. As noted previously, the same cannot be said of low- and high-grade municipal bonds. Although low-grade munis are significantly less sensitive to government bond market movements than are high-grades, they are approximately as sensitive to equity market movements as high-grade municipal bonds. Again, the whole issue of seemingly positive abnormal returns accruing to low-grade municipal bondholders over the study period may be the result of the inability to appropriately specify municipality equity risk. Other explanations may involve the nature of the municipal market itself.

In addition to the significant difference in the sensitivity of low- and high-grade corporate bonds to Treasury bond and equity market risk, other studies (see, e.g., Blume et al., 1991, and Cooper and Shulman, 1994.) find that low-grade corporate bonds have a significant January effect that high-grade corporates do not have. Does this result extend to municipal bonds- Specifically, after controlling for Treasury bond and equity market movements, do any of the municipal bond asset classes show a January effect?

I run the following regression model for both corporate bond asset classes and the two municipal bond asset classes.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where AC1sR w asset class return, and JanDV = a dummy variable equal to one if the month is January, and zero otherwise.

As noted by Blume et al. (1991), low-grade corporate bonds have a January effect, but high-grade corporates do not. The results for municipal bonds are striking. There is a strong January effect for both municipal bond asset classes. Also, the estimated intercept for the low-grade municipal bond regression is no longer significant when I introduce the January dummy. This suggests that the positive abnormal returns associated with low-grade munis are principally determined during the month of January. A more detailed analysis of municipal bonds and the January effect would be worthwhile.

In addition to a municipal bond January effect, are there any other effects that might have a significant influence on muni returns- Much of the more recent municipal bond literature discusses the Tax Reform Act of 1986.(11) (See Poterba, 1989; Fortune, 1991; and Lovely and Wasylenko, 1992.(12)) The Tax Reform Act of 1986 decreased the demand for municipal bonds by dramatically reducing bank demand, and decreased supply by dramatically reducing the ability of issuing authorities to earn arbitrage profits on their borrowings. Did the Tax Reform Act of 1986 significantly influence the returns of low- and high-grade munis? Table 11 provides regression results that examine low- and high-grade municipal bond returns before and after 1986.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

There is clearly a significant difference between the results before 1986 and after 1985. Before 1986, there is no significant estimated intercept term for any of the three regressions, after 1985 all three regressions have significant estimated intercept terms. This suggests that after controlling for Treasury bond and equity market risk, positive abnormal returns accrued to both asset classes, and more so to low-grade than high-grade munis (i.e., post 1985). In addition, after 1985, both asset classes became less sensitive to Treasury bond market movements, but low-grade munis became even less sensitive than did high-grade munis. In short, after 1985, municipal bonds in general acted less like Treasury bonds. Do the abnormal returns still hold after 1985 if 1 control for the January effect? Table 12 provides regression results with the January dummy variable included.

After 1985, the positive abnormal returns persist after controlling for the January effect. In addition, the January effect seems to persist over the full study period. Clearly, there seems to be some structural shift that takes place in the markets for low- and high-grade munis at or around 1986. It is possible that prior to the effect of the Tax Reform Act of 1986 there were fewer structural differences between the corporate and municipal bond markets. For example, especially with respect to Treasury bond market movements, low-grade municipal bonds became significantly less sensitive to those movements after 1985. After 1985, their sensitivity to those movements was almost halved (i.e., estimated coefficient [[beta].sub.1]. It is possible that municipal bonds have become more a market of their own as supply has been constrained and effective tax rates have increased for particular institutional buyers. Especially for institutional investors, as effective tax rates increase, taxable bonds become more imperfect substitutes for tax-exempt bonds.

Overall, much of the low-grade municipal bond positive abnormal returns can be explained by the January effect and/or the effect of the Tax Reform Act of 1986. Further refinement and analysis of these issues represents possible future research in the area.

V. Summary and Conclusions

In the overall performance of low-grade municipal bonds, the results presented here suggest there is a significant difference in the financial performance of low-grade municipal bond funds relative to high-grade municipal bond funds. After controlling for government bond and equity market movements, low-grade municipal bond funds outperform their high-grade counterparts. The tests performed in this study do not support the hypothesis that low-grade municipal bonds have significantly weaker interest-rate call protection or relatively more interest rate calls.

Both municipal bond asset classes show a significant January effect. Furthermore, the abnormal returns associated with low-grade municipal bonds seem to be largely due to the January effect. However, the apparent outperformance of low-grade munis relative to high-grade munis is more likely the result of the Tax Reform Act of 1986. Sorting the effect of these two influences on low-grade municipal bond financial performance is a possible subject for future research.

During periods of declining interest rates, recession, or a combination of declining interest rates and recession, low-grade municipal bond funds do not demonstrate significantly different volatility compared to high-grade municipal bond funds. Nevertheless, periods of declining interest rates significantly affect the relative sensitivity of low- and high-grade munis to movements in the government bond and equity markets. Also, periods of recession do not significantly affect the relative sensitivity of low- and high-grade municipal bonds to movements in the government bond and equity markets.

Finally, periods of declining interest rates combined with recession significantly affect the relative sensitivity of low- and high-grade municipal bonds to movements in both the government bond and equity markets. Table 13 provides a summary of the tests conducted.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

During periods of declining interest rates, low-grade munis become more government-bond-like and less equity-like compared to high-grade municipal bonds. During business-cycle contractions, low-grade munis are less government-bond- or equity-like compared to high-grade municipal bonds. During combination periods, low-grade munis become more government-bond-like and less equity-like compared to high-grade municipal bonds. These results support risky-debt valuation models that incorporate interest-rate risk and a significantly negative correlation between changes in interest rates and changes in the value of the firm. If interest-rate risk and a significantly negative value for [[rho].sub.r,V] were not important in valuing risky municipal bonds, the overall results would be about the opposite of those found. Clearly, low-grade municipal bonds are complex securities. A relatively accurate valuation model must take account of this fact. n

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[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

(1) There was overlap between these two series over the period 4/84 through 12/88. Over that period, the correlation between the two series is approximately 0.969.

(2) Regarding equity indices survivorship bias, what may seem like a significant positive bias (Garcia and Gould, 1993) could turn out to be a significant negative bias (Blitzer, 1995 and Garcia et al., 1995). Therefore, even the direction of a survivorship bias can be a topic of debate.

(3) Equities might have rejected the normal distribution null hypothesis due to their general run-up during most of the 1980s and early 1990s.

(4) Results not reported.

(5) In fact, Bartholdy and Riding (1994) find that neither the Dimson (1979), Scholes and Williams (1977), or Fowler et al. (1980) methods reduce the potential bias more than simple OLS. In addition, many studies that analyze nonsynchronous trading tend to suggest that monthly data does not possess nearly the same magnitude of the problem as weekly and especially daily data. (See Perry, 1985, Shaken, 1987, and Lo and MacKinlay, 1990.) In addition, portfolio betas tend to be "extremely stable" relative to individual betas (Dimson and Marsh, 1983). Therefore, regardless of the correction for suspected nontrading, monthly portfolio data can be viewed as a significantly more reliable source of estimating beats that individual daily data.

(6) That is, it could be that nonsynchronicity is the result of economic forces. Thus, the serial dependence in bond returns might be the result of economic source, not mismeasurement. Therefore. what is assumed to be evidence of nontrading might not be nontrading at all. However, with asset prices, it is usually assumed that serial dependence is the result of institutional features.

(7) Although in-the-money interest rates calls are, for the puposes of this study, assumed to follow conventional valuation processes, it should be noted that it could be rational for callable bond prices to exceed their call prices. (See, e.g., Longstaff and Tuckman, 1994.)

(8) Their model was also based in part on the Black and Cox (1976) model, and their study was at least in part motivated by the Jones et al. (1984) study.

(9) Historically, revenue bonds have been at least ten times more likely to default than general obligation blinds. (See Cirillo and Jessop, 1993.) (10) It should be noted that due to the tax treatment of discount municipal bonds, there is increased volatility associated with discount municipal bonds. (See, e.g., Mailman, 1981; Leibowitz, 1981; and Arak and Silver, 1989.) This should have little or no impact on the results over the full period, but may produce extra volatility during periods following a general decline in municipal bond market values.

(11) It became effective October 22, 1986.

(12) In addition, Robin (1991) found that ex-dividend day abnormal returns declined significantly in both the NYSE and ASE after the Tax Reform Act of 1986.