The U.S. municipal securities market is a prominent part of the fixed income landscape, with municipal bonds (e.g., debt offered by states, counties, cities) and municipal fund securities (e.g., 529 and ABLE savings programs). With municipal bonds in particular, issuers usually enjoy special taxation status and, as a result, investors seeking tax-efficient investments might generally assume they’re tax-free.
But this is not exactly true. When modeling municipal bonds, it becomes immediately clear that tax-exempt status is not absolute. The payments investors receive from the bonds are usually a mixture of tax-free interest and potentially taxable principal cash flows.
Therefore, investors may still be subject to taxation—in particular, to capital gains tax or even ordinary income tax due to the de minimis rule. This impacts investors’ after-tax cash flows, thus changing the bonds’ risk and return properties.
From an analytics perspective, it presents a problem since one cannot treat all cashflows equally and discount them with a tax-free discount curve that is normally used for the municipal market. So, what to do?
To avoid the proverbial apples and oranges conundrum, it is necessary to convert all cash flows to “after-tax” status; in other words, cash flows an investor receives after paying all taxes.
For the conversion, one can use the following expression to compute the tax due for all relevant cashflows.
One can immediately observe the de minimis rule creates a jump in taxation around the de minimis threshold. Also, if all inputs to the above formula are known, the computation is simple. In particular, if one assumes a “buy and hold” approach, it can be used in a standard valuation framework.
For example, we can compute after-tax net present value (NPV) of a bond cashflows (model price) as a function of spread. The orange line in Figure 1 presents this relation for a sample bond. We can observe discontinuity at the de minimis threshold, which is the result of the increased amount of applicable taxes when the bond is purchased below the threshold.
In reality, a jump as shown in Figure 1, never happens because there isn’t a necessary commitment from the buyer to hold to maturity. In fact, when the bond is getting close to the de minimis threshold (but still above it), a potential buyer considers the following outcome: the security price falls below de minimis in the future, and the buyer has to sell it.
Although the buyer will not pay taxes in this case (the security is bought above de minimis), the second buyer will be subject to de minimis tax, which will be reflected in the price discount. Therefore, a potential buyer is unwilling to pay the full tax-free price for that bond and applies part of that second buyer discount to the current price (See Figure 1, gray vs. blue line, OAS < 183).
Muni Bonds Priced Below De Minimis
On the other side, if a security is priced below de minimis, a potential buyer is not bound to hold it to maturity and bear the full tax burden. The investor considers a possibility of a price increase in the future and may sell the bond before maturity. In doing so, only a partial tax accreted over the holding period is due. Thus, the investor would be willing to pay a premium (gray line in Figure 1, OAS > 183) over full-tax pricing (orange line in Figure 1, OAS > 183).
Therefore, a “buy and hold” assumption is not realistic and does not provide acceptable analytics for municipal securities.
In reality, from a modeling perspective, the de minimis rule works as an embedded option. The option holder in this case is the federal government, which has the right to exercise the option (i.e., collect taxes) when the bond price falls below the de minimis threshold. It is similar to a regular imbedded option; therefore similar analytical tools could be used to price it. In particular, we use the Hull-White term structure model implemented on a trinomial tree.
Despite some similarities to regular embedded options, this one has several distinct features that make the modelling a material exercise.
Soft barrier. Tax is applied only if a security is purchased below the de minimis threshold. Thus, the threshold is similar to a knock-in barrier. However, unlike a regular knock-in barrier, it is not a sufficient condition for taxation. For de minimis tax to apply, both the security price should hit the barrier and a transaction should occur. Hence, standard ways to model knock-in barriers do not apply.
Option payoff (tax) is not fixed. It depends on several variables. One of them is purchase price, making it path dependent. Others are time of purchase and redemption, which are essentially behavioral factors. So, the usual way of option specification by setting appropriate boundary conditions is not applicable.
There is a circular dependence between the option payoff and security price. From the equation above, tax is a function of price. Since the option is embedded, price includes future taxes, thus the security price is also a function of taxes.
To handle these features within a trinomial tree framework, we are using the following approach:
Tax due is calculated for an ultimate buyer, meaning that any possible intermediate transactions are ignored.
For that ultimate buyer, we compute conditional expectations of the tax amount due at every principal cashflow point, such as maturity, call exercise, or sinking. For each point of principal cashflow, we create a two-dimensional (time and rates) conditional distribution of possible purchase points. We use this distribution to compute expected tax. Using the total expectation approach, we sum up the discounted conditional expectation to arrive at the present value of taxes.
Tax is computed recursively through multiple iterations that deal with circular price and tax dependence. At convergence, a self-consistent set of taxes and prices is achieved.
The application of this framework results in tax and option-adjusted analytics. Most notably, the tax impacts the option-adjusted spread and durations. Since taxes reduce after-tax cash flows for investors, the actual tax-adjusted spread is lower than the un-adjusted one, implying that investors earn less spread when properly accounting for taxation.
Similarly, a tax-adjusted price drops faster than a tax-free one as rates (or spreads) rise due to an increasing amount of expected tax as the price moves closer to the de minimis threshold. That implies greater sensitivity to rates and spreads and longer tax-adjusted durations.
Figure 2 shows spread sensitivity as a function of spread for a sample security. As the price drops to the de minimis threshold and below, duration is about a half-year longer compared to a tax-ignorant one.
Overall, the results show that new tax-adjusted analytics better capture risk/return properties of municipal securities. The impact depends on both market environment (high/low rates) and security properties (high/low coupon). The tax effects could be significant and should not be ignored when making investment decisions.
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