Credit: corporate bonds, munis, ratings, spreads, default and recovery

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

Lending to someone who might not pay

Suppose two borrowers each ask you for $1,000 for five years. One is the US government. The other is a company with a decent business and a fair amount of debt. You would want more interest from the company, because there is some chance it runs into trouble and pays you back only part of what it owes, or nothing. That missed payment is a default.

When a company defaults, its bondholders rarely lose everything. A court or a negotiation usually hands them some mix of cash, new bonds or shares in the reorganised company. What they get back, as a share of what they were owed, is the recovery rate.

The spread is the price of that worry

The extra yield a bond pays over a Treasury of the same maturity is its credit spread. If a 5-year Treasury yields 4 % and a company's 5-year bond yields 5.5 %, the spread is 1.5 percentage points, or 150 basis points.

Spreads move every day. In calm years they narrow, because investors feel safe and compete to lend. In recessions they widen, sometimes very fast, because defaults rise and investors want to hold less risk. When spreads widen, the prices of existing corporate bonds fall, even if the company never misses a payment. A bond fund can lose money in a bad year from spread widening alone.

Ratings in one paragraph

Rating agencies such as S&P Global, Moody's and Fitch grade borrowers from AAA (the strongest) down to D (in default). Bonds rated BBB minus or above (Baa3 or above at Moody's) are investment grade. Everything below is high yield, also called speculative grade or, less politely, junk. Many pension funds and insurers may hold only investment-grade bonds, so the line between BBB minus and BB plus matters a great deal: a downgrade across it can force sellers into the market at once.

Munis: lending to a city

States, cities, school districts and public utilities borrow through municipal bonds. For most of them the interest is free of federal income tax, and often of state tax for residents of the issuing state. That tax break means munis yield less than taxable bonds of similar risk, and it means the right comparison depends on your tax bracket. A muni paying 3.5 % is worth 5.15 % in taxable terms to someone in the 32 % federal bracket, and much less to someone in a low bracket.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

What a spread pays for

A credit spread pays for several things at once. We can split it into parts.

Expected loss. This is the average yearly loss from defaults, after recovery. For a high-quality company it makes up a small slice of the spread.

Risk premium. Defaults cluster in recessions, when investors also lose jobs and see stocks fall. Investors want extra pay for losses that arrive at the worst time.

Liquidity. Most corporate bonds trade far less often than Treasuries. Sellers in a hurry may have to accept a lower price, and investors charge for that.

Taxes. Treasury interest is free of state income tax; corporate interest is not. That difference shows up in the spread too.

For investment-grade bonds, the expected-loss part is small and most of the spread is premium; Level 3 works an example. Researchers call the gap between spreads and expected losses the credit spread puzzle (Elton, Gruber, Agrawal and Mann, 2001).

The ratings ladder

Ratings are opinions about the chance of default over years, and they change slowly. Spreads change every minute. A bond whose spread widens far beyond its rating band is telling you that the market expects a downgrade. A bond cut from investment grade to high yield is a fallen angel; forced selling often pushes its price below what the new rating alone would justify, and patient buyers have historically been paid for taking the other side.

Default and recovery: who gets paid first

A company's creditors stand in a queue. Secured lenders, usually banks, hold a claim on specific assets and stand at the front. Senior unsecured bondholders come next, then subordinated bondholders, and shareholders come last. Standing further back means recovering less. Moody's long-run studies put average recovery on senior unsecured bonds at roughly 40 cents on the dollar, with wide swings by year and by industry (Gaps).

Each bond's indenture also carries promises, called covenants, that limit what the company may do: how much more it may borrow, whether it may pay big dividends, whether it may sell key assets. Strong covenants raise recovery; "covenant-lite" bonds and loans, common after 2010, give holders less protection.

Liquidity: the cost of selling in a hurry

A Treasury trader can sell hundreds of millions of dollars of notes in seconds at a price a fraction of a basis point from the last trade. A corporate bond may not trade at all for days. Dealers who buy it from you hold it on their books until they find a buyer, and they charge for that through the gap between the price they pay and the price they ask. In calm markets that gap is small for large investment-grade issues. In a panic it widens sharply, and the price a seller gets can fall well below what the issuer's credit alone would justify. Bond funds that promise daily redemptions while holding bonds that trade rarely carry this mismatch; March 2020 tested it.

Loans, private credit and who else lends

Bonds are one way companies borrow. Banks lend directly, and leveraged loans to lower-rated companies are pooled and sold to investors, many of them through collateralised loan obligations. Since the 2010s a large private credit market has grown, in which funds lend directly to mid-sized companies and hold the loans to maturity. These loans usually pay floating rates, so they carry little duration, and they sit higher in the creditor queue than unsecured bonds. They trade rarely, if at all, and their reported values move slowly, which can make them look calmer than the credit risk they hold.

High yield and the business cycle

High-yield spreads track the economy. In good years the spread on a broad high-yield index might sit around 300 to 400 basis points. In recessions it has more than doubled. The ICE BofA US High Yield index's option-adjusted spread reached about 2,000 bp in December 2008 and about 1,100 bp in March 2020 (ICE data, as published on FRED before FRED shortened the series' history).

A wide spread reflects two things together: more defaults ahead, and investors demanding more pay for bearing them. That second part explains why spreads overshoot, and Level 4 shows how far. For a bond fund holder the practical point is simpler: a high-yield fund can post a deep loss in a recession year with few defaults among its own holdings, because the whole market reprices risk at once.

Municipal bonds: general obligation and revenue

Two kinds of munis dominate. A general obligation bond carries the issuer's pledge of its taxing power: a city pledges its full faith and credit to repay. A revenue bond relies only on the income from one project, such as a toll road, a water system or a hospital. Revenue bonds pay more because a single project can fail while the city as a whole does fine.

Muni defaults have been far rarer than corporate defaults of the same rating, according to Moody's municipal default studies, yet they cluster in a few sectors (hospitals, housing projects, project finance) and a few troubled places. Detroit and Puerto Rico, in Level 4, show what happens when a general obligation pledge meets a government that cannot pay everyone.

The tax lens decides who should hold munis. The table shows the taxable-equivalent value of a 3.5 % tax-free yield at several federal brackets.

For an investor in the 12 % bracket, a taxable bond yielding 4.5 % beats the muni; for one in the 37 % bracket, the muni wins against anything that pays less than 5.56 % before tax. Munis held inside an IRA waste the tax break entirely (Chapter 22 covers where to hold what).

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

Expected loss

Three inputs set the average credit loss on a loan or bond: the chance of default over a year, the share lost if it happens, and the amount at stake.

In words, expected loss equals the probability of default times the loss given default times the exposure at default.

Spread as expected loss plus premium

A simple model of a spread $s$ adds the expected loss rate to a premium $\phi$ for risk and liquidity.

In words, a credit spread is roughly the yearly expected loss rate plus a premium for bearing default risk and illiquidity.

The breakeven default rate

Flip the question. Given a spread, how many defaults would it take to leave the holder no better off than in Treasuries?

In words, the breakeven default rate is the spread divided by one minus the recovery rate.

Cumulative default and survival

Yearly default rates compound over a bond's life. With a constant yearly default probability $p$, the chance of surviving $n$ years and the cumulative default rate follow.

In words, the chance of no default for n years is one minus the yearly rate, multiplied by itself n times, and the cumulative default rate is one minus that.

A 2 % yearly rate gives a five-year survival of 90.4 % and a cumulative default rate of 9.6 %. Agencies publish cumulative default tables by rating and horizon; the yearly rates rise steeply as ratings fall, and for the lowest grades they rise with time, because survivors of a bad start often stay weak. Chapter 17 turns this into the hazard rate behind credit default swaps.

Recovery and the creditor queue

Under the absolute priority rule, each class of creditor is paid in full before the next class gets anything. Take a company that owes $300 million to secured lenders, $400 million to senior unsecured bondholders and $200 million to subordinated bondholders, and suppose the business is worth $600 million in bankruptcy.

A fall of a third in the firm's value cuts the senior class's recovery from 75 % to 25 % and leaves the subordinated class with nothing in both cases. So LGD is far from a constant: it depends on what the business is worth when it fails, and businesses tend to fail in recessions, when values are low. This link between default rates and recovery rates, both worsening together, is one reason the risk premium in spreads exists. In practice courts often depart from strict priority, and junior classes sometimes receive a little to win their votes for a plan.

Expected return on a risky bond

A bond's yield is a promise. Its expected return held to maturity is lower by the expected loss.

In words, the expected return on a bond held to maturity is about its yield less the expected yearly loss from defaults.

A high-yield bond at 8 % with a 4 % yearly default probability and 60 % loss given default has an expected return of about 5.6 %. Compared with a 4 % Treasury, the holder still expects to come out ahead, and the variance of that outcome is much higher.

Spread duration and the cost of a downgrade

The duration tools of Chapter 8 apply to spreads. A bond's spread duration tells how far its price moves when its spread moves, with Treasury yields held still. A BBB bond with a spread duration of 6 whose spread widens from 150 bp to 300 bp after a downgrade to BB loses about −9.0 % of its price. That loss comes on top of any move in Treasury yields, and in a recession the two can partly offset, because Treasury yields often fall while spreads widen.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

2008: spreads priced a depression

Run that spread through the breakeven formula with 40 % recovery and it implies a yearly default rate of 33.3 %: one high-yield issuer in three defaulting every year. Moody's speculative-grade default rate did rise sharply, peaking in the low teens in late 2009 (Gaps), yet that was far below a third. The rest of the spread was premium: investors who could hold risk were scarce, and those who could demanded a very high price for it.

What did that mean for a buyer? Suppose an investor bought the index at 2,000 bp, and over the next year the spread halved to 1,000 bp, one issuer in ten defaulted, and the index's spread duration was about 4. The carry adds 20 %, the narrowing spread adds about 40 %, and defaults subtract 6 %, for an excess return over Treasuries of about +54 %. Those inputs are illustrative, yet the reported return of the high-yield index in 2009 was of that order (Gaps). Spread levels at the depths of a panic have paid the people able to buy them.

March 2020: the spike and the backstop

At 1,100 bp and 40 % recovery, the breakeven default rate was 18.3 % a year. Defaults did rise in 2020, concentrated in energy and retail, yet nowhere near that rate. The Fed's promise to buy shrank spreads within weeks, before it had bought much. The lesson for credit investors is uncomfortable: in a systemic panic the path of spreads can depend on a policy decision, and nobody can model that decision with PD and LGD.

The fallen angels of 2020 show the forced-selling effect. Companies such as Ford lost their investment-grade ratings that spring (Gaps), and funds restricted to investment grade had to sell. Buyers who could hold high yield picked up the bonds at prices that assumed worse than the downgrade meant.

Detroit, 2013: a general obligation meets a bankruptcy court

Detroit's case tested an idea many muni investors had treated as settled: that a general obligation bond backed by the full faith and credit of a city comes before almost everything else. In the bankruptcy, bondholders shared losses with pension funds and retirees, and different classes of general obligation bonds received different recoveries (Gaps). Where a bond insurer had guaranteed a bond, the insurer paid holders in full and took the loss itself.

For the maths, the lesson sits in the LGD term. Investors had priced Detroit's bonds as if recovery on a city's pledge would be close to full. Once the court made pension claims rank alongside bonds, expected recovery fell, LGD rose, and the expected-loss formula gave a larger number at the same default probability.

Puerto Rico, 2016: the tax lens as a trap

Puerto Rico's bonds were free of federal, state and local tax for holders anywhere in the US, a feature that made them popular with muni funds hunting for yield. Here the taxable-equivalent formula can mislead. A tax-free yield of 8 % looks like 11.76 % to a holder in the 32 % bracket. That figure compares the bond with a taxable bond of the same risk; it says nothing about the risk itself. Investors who reached for the tax-adjusted yield took on credit risk that no tax saving covered.

What the four cases share

In every case the spread or yield told investors that something was wrong well before the default or the bottom. The breakeven default rate gives a quick reading of how much bad news a price already holds: in 2008 and 2020 the spreads assumed far worse than happened, and buyers were paid; in Detroit and Puerto Rico the yields looked high, and recoveries turned out lower than buyers assumed. The difference lay mainly in LGD. Corporate bankruptcy law sets a clear queue for creditors; municipal and territorial debt sits under special rules, where politics can reorder who gets paid.