Module 30 · Computing credit risk
Municipal bond credit risk
Here's the muni puzzle: a 10-year muni yields lessthan a 10-year Treasury, even though a city can default and the US Treasury (practically) can't. Read that yield naively and the market is telling you munis are safer than risk-free — which is nonsense. The resolution is tax: muni coupons are exempt from federal (and often state) income tax, so the quoted yield is an after-tax number. Before you can say anything about muni credit risk, you have to undo the tax effect.
That's the first computation: the taxable-equivalent yield (TEY) — muni yield ÷ (1 − marginal tax rate). A 3.2% muni is a 5.4% taxable bond to someone in a 40.8% bracket. Now compare against Treasuries: the gap is the gross spread, and it splits into a liquidity premium (most muni CUSIPs trade a handful of times a year) and, only after that, a genuine credit spread — usually the smallest of the three components. From there the machinery is the standard credit triangle from Module 23: hazard rate, cumulative default probability, expected loss.
The second half of muni credit is what secures the bond, because it drives both default probability and recovery:
- GO (general obligation) — backed by the issuer's taxing power. Credit analysis looks at the tax base, pension and OPEB burden, reserve fund balance, and — crucially — whether the state even permits a Chapter 9 bankruptcy filing.
- Revenue bonds — backed by a specific stream: water bills, tolls, airport fees. Here the analysis is closer to corporate credit: DSCR (pledged revenue over debt service), the rate covenant (a promise to set rates high enough), and the additional bonds test that caps how much new debt can dilute your coverage.
Defaults are rare, but when they happen recovery is slow and widely dispersed — Detroit, Jefferson County and Puerto Rico produced very different outcomes for holders of different liens of the same issuer. Legal structure (statutory liens, special revenue status) drives recovery more than financial ratios do, which is why the lab lets you set recovery directly and see how much the implied default probability moves.
🎛 Muni credit lab
Taxable-equivalent yield decomposition (5.41% = 541bp)
Taxable-equiv. yield
5.41%
muni ÷ (1 − tax)
Muni / Treasury ratio
76%
the market's shorthand
Implied credit spread
61bp
TEY − Tsy − liquidity
Hazard rate λ
1.73%
spread ÷ (1 − R)
Cum. PD 10y
15.88%
1 − e^(−λt)
Expected loss 10y
5.56%
cum PD × LGD
Revenue-bond coverage check
For a revenue bond, credit lives in the pledged revenue stream, not a tax base.
DSCR
1.50x
revenue ÷ debt service
Additional bonds test (1.25x)
+$20M
debt-service headroom for new debt
The observed muni yield is converted to a taxable-equivalent yieldfor this buyer's marginal rate, then decomposed against the Treasury curve: what's left after the liquidity premium is the credit spread, and the credit triangle turns it into a hazard rate, cumulative default probability and expected loss. Educational tool — not investment advice.
How the lab computes it
TEY = muni yield / (1 − tax rate) gross spread = TEY − Treasury yield credit spread = gross spread − liquidity premium λ (hazard) = credit spread / (1 − recovery) cum PD(T) = 1 − e^(−λT) expected loss = cum PD × (1 − recovery)
The revenue-bond panel is the coverage side: DSCR = pledged revenue ÷ debt service, and the additional bonds test asks how much more debt service the issuer could layer on before coverage drops to the covenant floor (1.25x here). That headroom is your dilution risk.
Three muni-specific traps
- Insured bonds are dual-obligor. A monoline-wrapped muni has two credits: the underlying issuer and the insurer. Carry both ratings, and count the exposure against the insurer for concentration — every wrapped bond in the book fails together if the monoline does. That correlation was the 2008 failure mode.
- Ratings aren't comparable to corporates. Muni scales were historically tougher (Moody's recalibrated in 2010), so a corporate-calibrated migration matrix applied to munis gives the wrong transition risk. Use muni-calibrated default studies.
- Part of the “spread” is a pricing artifact. Most CUSIPs are matrix-priced from sparse trades. Some of what looks like spread volatility is the pricing model, not the market — which is why marking quality matters as much as the model.
And one systematic risk with no CUSIP attached: tax policy. Cut the top marginal rate and every muni cheapens at once, with zero change in anyone's credit. For a muni book, that scenario belongs next to the default scenarios.
Things to try
- • Drop the tax rate from 40.8% to 25% — the TEY falls, the implied credit spread collapses and can go negative: the same bond is rich to one buyer and cheap to another. That's why the marginal muni buyer's bracket sets the price.
- • Set recovery to 80% (statutory-lien GO) vs 30% (subordinate revenue pledge) — the same spread implies a very different default probability, because λ = spread ÷ (1 − R).
- • Raise the liquidity premium and watch the credit spread shrink to nothing — for high-grade munis, most of the spread was never credit at all.
- • In the coverage panel, push debt service up until DSCR hits 1.25x — the additional-bonds headroom hits zero exactly there: the covenant is doing its job.