An Empirical Measurement of Default Premium on Municipal Bonds and the Miller Hypothesis

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An Empirical Measurement of Default Premium on Municipal Bonds and The Miller Hypothesis

According to Miller[8], under the assumption of complete capital market and escapable taxes on equity, the personal tax rate of the marginal bond holder is equal to the corporate tax rate. Thus, the ratio of the return on tax-exempt bonds to the return on taxable bonds should be equal to one minus the corporate tax rate.

Figure 1 plots the ratio of return on newly-issued prime-grade municipal (tax-exempt) bonds to the return on the U.S. Treasury (taxable) bonds with five and ten years to maturity for the period January 1980 to December 1985. Since the maximum corporate tax rate has remained at 46 percent for the period, the Miller Hypothesis predicts that the ratios should be equal to 54 percent. However, for almost all months, the ratios are higher than 0.54 (54 percent). According to Table 1, the average ratio is 62.5 percent for bonds with a maturity of five years, and the average ratio is 70 percent for bonds with a maturity of ten years, which are both substantially higher than 54 percent.

Following the argument similar to the one put forward by Trzcinka[9], such behavior of the ratio can be explained by the existence of default premium in municipal yields and the fact that the default premium changes over time. In order to estimate what he calls the "differential risk premium," Trzcinka assumes that the premium follows a random walk process over time. In this paper, an alternative way of estimating the default premium is provided. Furthermore, the Miller Hypothesis has also been tested using empirical data.

The Miller Hypothesis has an important empirical implication. If the taxes are not assumed to be zero, then the equilibrium relationships between various returns are expressed in after tax returns. Thus, for the empirical test of the equilibrium relationship, one has to obtain the after tax returns. The measurement of the after tax returns is possible if the marginal tax rate of the marginal investor is observable. But the marginal tax rate is not observable. However, if the Miller Hypothesis holds, then the marginal tax rate is equal to the corporate tax rate, which is observable. This makes the marginal tax rate observable provided the Miller Hypothesis is valid.

In recent years a considerable amount of research has been directed to the study of behavior of "differential risk premium" and the pricing of municipal bonds. Interested readers are referred to the papers by Benson and Rogowski[1], Jaffee[4], Kidwell and Koch[7], Kidwell and Trzcinka[5, 6] and Sorensen[10].


Equilibrium Relationship between Taxable and Tax-exempt Yields on bonds

Let us consider two bonds that are both default free, but the return on one is taxable and the return on the other is tax-exempt. Then, in equilibrium, the relationship between the return on taxable bond (R) and the return on tax-exempt bond ([R.sub.0]) must satisfy (1) [R.sub.0] = (1 - [Tau])R,

where [Tau] denotes the marginal tax rate on the interest income of the marginal investor. Any investor who is in the tax brackets higher than [Tau] will hold the tax-exempt bond, and the investor who is in the tax brackets lower than [Tau] will hold the taxable bond.

To see if the above given relationship holds in the observed bond market, we need to observe the marginal tax rate of the marginal investor. However, it is difficult to observe this marginal tax rate. Thus we need some theory to link this marginal tax rate with some observable tax rates or some other economic variables.

Miller[8], in his analysis of bond market equilibrium, has provided us with the required theory. He has shown that, if the tax on income from equity escapes personal taxation, the marginal rate of personal income tax of the marginal investor ([Tau]) is equal to the cororate tax rate ([Tau.sub.c]). According to Miller, there exists a trade-off between the advantage of tax deductibility of interest payments on the part of the corporation and the disadvantage of tax paid by the recipient of the interest payment. …


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