Municipal Bond Relative Value: Tax-Equivalent Spreads & Call Risk

Introduction

Municipal bond relative value is the practice of comparing tax-exempt muni yields to taxable alternatives to find mispricings and manage risk. In one sentence, this article shows you how to translate muni yields into taxable-equivalent terms, measure expected carry and roll-down, and quantify the distortions caused by embedded call options.

Why does this matter to you as an investor or trader? Because comparing a municipal bond's nominal yield to a taxable corporate or Treasury yield without adjustment gives you a misleading picture. How do you compare a tax-free muni yield to a taxable corporate yield, and how do you price the risk that the issuer will call the bond early?

You'll learn a repeatable framework: tax-equivalent yield modeling and taxable-equivalent spread calculation, curve roll-down and one-year carry scenarios, and how to incorporate option-adjusted spread (OAS) and yield-to-worst (YTW) into your relative-value decisions. There are numerical examples using $MUB and municipal callable structures so you can apply this in real trades.

Key Takeaways

• Convert muni yields to taxable-equivalent yields using your marginal tax rate and state tax treatment to make apples-to-apples comparisons.
• Tax-equivalent spread (TES) is the gap between a taxable benchmark yield and the taxable-equivalent muni yield, giving a clean relative-value signal.
• Curve roll-down and carry can add to returns even if spreads do not move, but you must model the forward curve and realistic reinvestment outcomes.
• Callable munis put a call-option premium on the issuer, creating yield compression and negative convexity when rates fall; use OAS and yield-to-worst to quantify this.
• Simple yield comparisons fail when you ignore state tax differences, AMT exposure, embedded calls, and differences in duration and liquidity.

Tax-Equivalent Yield and Tax-Equivalent Spread

Tax-equivalent yield converts a tax-exempt municipal yield into the yield a taxable investor would require to match the after-tax return. The basic formula is simple and essential.

Tax-equivalent yield formula

Tax-equivalent yield equals the muni yield divided by one minus your marginal federal tax rate, adjusted for state tax considerations. For example, a 3.00 percent muni yield with a 35 percent federal marginal rate converts as follows: taxable-equivalent yield = 3.00% / (1 - 0.35) = 4.62%.

Be careful to include state and local taxes. If the muni is issued by your state and state tax exemption applies, you do not add state taxes. If not, include state tax rate s: taxable-equivalent yield = muni yield / (1 - f - s + f*s), which approximates dividing by one minus the combined marginal rate.

Tax-equivalent spread (TES)

To compare to a benchmark, compute TES as the benchmark taxable yield minus the taxable-equivalent muni yield. If the 10-year Treasury yield is 4.00 percent and the muni taxable-equivalent yield is 4.62 percent from above, TES = 4.00% - 4.62% = -0.62 percentage points, indicating munis currently offer higher taxable-equivalent yield than the Treasury.

Use a benchmark with similar duration and credit profile. Many traders compare municipal credits to benchmark taxable municipals or to Treasuries plus spread. For retail portfolios you might use $MUB for diversification checks and then drill down to specific CUSIPs for precise TES calculations.

Sizing Carry and Curve Roll-Down

Carry and roll-down are the predictable parts of return if the yield curve and spreads remain unchanged. Roll-down is the price gain as a bond ages and moves down the yield curve toward maturity. For munis, steepness and local curves matter.

How to model roll-down

Step 1, pick a spot curve and generate forward discount factors or zero rates. Step 2, compute the price today from the cash flow discounting and derive yield to maturity. Step 3, assume the entire curve shifts unchanged, then re-price the bond one year later with one less year to maturity to estimate roll-down price change.

Example: suppose a 10-year muni coupon bond yields 4.00 percent and the 9-year point on the curve yields 3.80 percent. If yields across the curve are unchanged, the bond will likely trade closer to the 9-year yield in a year. That yield drop produces capital appreciation in addition to coupon carry. If coupon is 4.00 percent and duration is 7.5, a 20 basis point yield compression from roll-down implies an expected price gain near 1.5 percent, plus roughly 4.00 percent coupon carry over the year.

Carry vs total return

Always separate components: coupon carry, roll-down, and spread/policy movements. Roll-down is deterministic under the stationary curve assumption. But spreads may mean-revert, widen, or tighten, and taxes and reinvestment rates change realized returns. Model multiple scenarios: unchanged curve, 50 basis point compression, 50 basis point widening, and a call event.

Embedded Call Risk and Option-Adjusted Spread

Callable munis complicate relative value analysis because issuers can redeem bonds when it benefits them, usually when interest rates fall. As an investor you receive a call price, often par or a small premium, and lose future coupons. That optionality sits with the issuer and acts like a short put for the holder.

Yield-to-call, yield-to-worst, and option-adjusted spread

Yield-to-call (YTC) is the yield assuming the bond is redeemed at the first call date. Yield-to-worst (YTW) is the lowest yield across call and maturity scenarios and is conservative for return estimates. Option-adjusted spread (OAS) attempts to remove the value of embedded options by comparing a callable bond to a model of interest-rate paths, discounting expected cash flows under stochastic rates, and extracting a spread that is neutral to the option.

OAS is the number you want when comparing callable munis to taxable callable alternatives. A higher OAS implies better compensation for credit, liquidity, and option risk. When you only look at nominal yields, you miss the call option premium the issuer holds.

Quantifying call-option traps with an example

Consider a 15-year callable muni with 10 years to first call, priced to yield 4.50 percent nominal, and a noncallable comparable 10-year muni yielding 4.00 percent. At first glance the callable seems to offer a 50 basis point pick-up. But simulate interest-rate paths or compute OAS: if the option value is worth 30 basis points (the issuer's right to call reduces holder yield), the OAS-adjusted pick-up is only 20 basis points. If rates fall, the callable will likely be redeemed, capping capital gains. If rates rise, you keep the higher yield but you already suffered price losses. Callable bonds often show higher yield but lower convexity than noncallables.

Also track negative convexity: when rates drop, price appreciation is limited because of call probability. That makes callable munis more vulnerable in volatility-driven markets where rates fall then rise again.

Putting It Together: A Relative-Value Framework

Combine tax-equivalent conversion, duration matching, roll-down modeling, and OAS adjustments into a disciplined process for muni relative-value decisions. Here is a step-by-step checklist you can apply to a candidate trade.

1. Identify the investment objective and tax status. Specify federal and state marginal tax rates and AMT exposure, if relevant.
2. Select comparable benchmarks with similar duration, liquidity, and credit type. For short municipals you might use short Treasuries; for long credits use municipals of similar structure or a broad ETF like $MUB for context.
3. Compute taxable-equivalent yield and TES to screen candidates. Convert all muni yields into the same taxable-equivalent basis.
4. Match duration and calculate expected roll-down under an unchanged-curve scenario. Quantify carry, expected price change, and total return for one-year and full-hold horizons.
5. For callable issues, compute YTC, YTW, and estimate OAS using a short-rate model or vendor OAS. Deduct the option value from the headline spread to see real compensation.
6. Stress-test: run scenarios for rates up 50 bps, down 50 bps, and a call event. Evaluate realized total returns and worst-case outcomes.
7. Adjust allocation for liquidity, issuer concentration, and tax diversification. Decide position sizing based on expected return and downside risk.

Real-world example, simplified: you find a 10-year taxable corporate at 5.00 percent and a 10-year triple-A muni yielding 3.10 percent. If your federal tax rate is 37 percent, taxable-equivalent yield = 3.10% / (1 - 0.37) = 4.92 percent. TES = 5.00% - 4.92% = 0.08 percent, a small pick-up for the taxable corporate. If the muni is callable with an estimated option cost of 25 basis points, the net pick-up flips to favor the corporate once option risk is considered.

Common Mistakes to Avoid

• Comparing nominal muni yield to taxable yields without converting to taxable-equivalent yields. How to avoid: always convert using your marginal tax rate and state treatment before comparing.
• Ignoring state and local tax differences and AMT exposure. How to avoid: model both federal and relevant state taxes, and note whether a bond is AMT subject.
• Using yield-to-maturity for callable bonds as the primary metric. How to avoid: calculate yield-to-call, yield-to-worst, and OAS to capture embedded option cost.
• Neglecting curve roll-down and duration mismatches. How to avoid: model one-year roll-down and match duration to your benchmark or hedge.
• Overlooking liquidity and transaction costs, especially in lower-tier municipal credits. How to avoid: include bid-offer, dealer inventory, and execution slippage in return assumptions.

FAQ

Q: How do I pick the right tax rate for taxable-equivalent yield?

A: Use your marginal federal tax rate because that determines the tax on incremental income. Then include state and local marginal rates if the muni is not exempt for your residency. If AMT applies, compute both standard and AMT-adjusted taxable-equivalent yields and compare.

Q: When should I prefer OAS over yield-to-worst?

A: Use OAS when comparing callable securities across markets or prepayment regimes because OAS attempts to strip out option value under stochastic interest-rate assumptions. YTW is a conservative single-path metric and useful for worst-case yield, but it does not price option value consistently across securities.

Q: Can I use an ETF like $MUB as a benchmark for muni relative value?

A: Yes for broad market context, liquidity, and quick exposure checks. But ETF yields and durations are averages. For precise relative-value trades you need to analyze specific CUSIPs for maturity, call structure, credit, and tax treatment.

Q: How large is the call-option premium typically for munis?

A: It varies with maturity, coupon, volatility, and economic conditions. In normal markets option value on long-dated callable munis can range from a few basis points to 50+ bps. Use vendor OAS, model-based valuation, or bootstrapped historical analysis to estimate it for a given issue.

Bottom Line

At the end of the day, municipal relative value is about converting yields into comparable terms, isolating predictable carry and roll-down, and quantifying embedded option risk so you do not get surprised. Tax-equivalent yield and TES give you the apples-to-apples screen. Roll-down and carry modeling estimate the deterministic component of return, and OAS and YTW guard you against call-option traps.

Next steps you can take today: determine your marginal federal and state tax rates, run taxable-equivalent conversions on muni candidates, and build simple one-year roll-down scenarios for your target duration. If you trade callable munis, get OAS figures from a pricing vendor or incorporate a short-rate model to estimate option value before you size positions.

Keep learning by backtesting your framework across different market regimes and issuing states. That will help you see when TES and OAS signals historically produced repeatable excess returns and when liquidity or credit events dominated outcomes.