Credit Spreads & Default Risk

Until now every cash flow was a certainty — a government that prints its own currency essentially always pays. But a corporation, a city, or a shaky sovereign might not. The moment default is possible, the bond must offer extra yield to compensate, and that extra is the credit spread: the gap between a risky bond’s yield and the matching risk-free yield. This lesson cracks that spread open. Part of it is cold arithmetic — fair compensation for the average loss you’ll suffer. The rest is a risk premium — payment for bearing the uncertainty. Knowing which is which is the difference between a credit investor who gets paid for risk and one who’s just gambling.

The credit spread: extra yield for the risk of not being paid

Analogy. Lending to the government is like lending to a vault — it’ll pay you back. Lending to a company is like lending to a friend starting a restaurant: probably fine, but there’s a real chance the place folds and you get cents on the dollar. You’d demand a higher interest rate to take that bet — and the credit spread is exactly that demanded extra.

The definition. The yield on a risky bond decomposes as

where the spread $s$ is the additional yield over the matched-maturity risk-free benchmark. A wider spread means the market judges the issuer riskier. Spreads move with the issuer’s health and with the market’s overall appetite for risk — they blow out in crises (everyone flees to safety) and tighten in calm.

Decomposing the spread: expected loss + risk premium

The two pieces. Crack the spread open and it splits in two:

where:

• PD = probability of default (per year) — the odds the issuer fails to pay.
• LGD = loss given default — the fraction of your money you lose if it defaults, equal to $1 - \text{recovery rate}$. If you recover 40 cents on the dollar, LGD = 60%.
• Expected loss = $PD \times LGD$ — the average annual loss from default. This part of the spread merely makes you whole on average; it’s not profit, it’s the actuarially fair price of the risk.
• Risk premium — the extra yield beyond expected loss that pays you for bearing the uncertainty (defaults cluster in bad times, exactly when you can least afford them). This is the part that, in expectation, actually compensates you for the risk.

Worked example. A corporate bond has a 2% annual default probability and a 60% loss given default (40% recovery). The risk-free yield is 4%, and investors demand a 0.8% risk premium.

• Expected loss $= PD \times LGD = 0.02 \times 0.60 = 0.012 = 1.2\%$.
• Credit spread $= \text{expected loss} + \text{risk premium} = 1.2\% + 0.8\% = 2.0\%$.
• Risky yield $= y_{\text{risk-free}} + s = 4\% + 2.0\% = 6.0\%$.

So you earn 6%, but only 0.8% of that spread is genuine compensation for risk — the other 1.2% just offsets the average loss you’ll actually suffer. A naïve investor sees “2% extra yield!” and feels rich; a credit analyst sees that most of it is a rebate for losses to come.

Recovery, seniority, and LGD

Analogy. When a company collapses, its assets are a carcass picked over in a strict pecking order. Senior secured lenders eat first (they hold collateral); senior unsecured bondholders next; subordinated bondholders scrape what’s left; equity holders usually get nothing. Where you sit in that queue is your recovery rate — and therefore your LGD.

The mechanics. Two bonds from the same issuer with the same PD can have very different spreads if they sit at different seniority levels, because their LGDs differ:

• Senior secured: high recovery (say 70%), so LGD = 30% — low expected loss, tight spread.
• Subordinated: low recovery (say 20%), so LGD = 80% — high expected loss, wide spread.

This is why “the issuer’s credit risk” isn’t one number — it’s a layered cake, and your slice depends on your seniority. The same default event hits a sub bondholder far harder than a senior secured one.

Hazard rates and the term structure of default

Analogy. Default isn’t a one-shot coin flip — it’s a hazard that lurks over the bond’s whole life, like the per-mile risk of a flat tyre on a long drive. The hazard rate (or default intensity) $\lambda$ is the instantaneous, conditional probability of defaulting in the next instant given survival so far. From it, the probability of surviving to time $t$ is

the same exponential-decay law as radioactive half-life. A constant hazard rate $\lambda$ produces a clean approximation that risk desks love:

the spread is (roughly) the hazard rate times the loss severity. This is the reduced-form view of credit: don’t model why the firm defaults, just model the intensity with which it does, and back it out of market spreads.

The credit curve. Just like interest rates, default risk has a term structure. A healthy firm has an upward-sloping credit curve (more time = more chance something goes wrong). A distressed firm often has an inverted credit curve: if it survives the next year it’s probably fine, so near-term spreads are huge and longer-term ones lower. Reading the shape tells you whether the market fears imminent or eventual trouble.

Ratings, defaults, and the limits of the model

Ratings as a shorthand. Agencies (Moody’s, S&P, Fitch) compress credit risk into letters: investment grade (AAA down to BBB−) versus high yield / junk (BB+ and below). Historically, default rates climb steeply as you descend: AAA issuers almost never default in a year; CCC issuers default at double-digit annual rates. Ratings are a useful map — but a lagging one.

When to use it

Use the spread decomposition to judge whether a bond pays you enough for its risk: estimate PD and LGD, compute the expected loss, and see how much risk premium is left over — that surplus is your real compensation. Use hazard rates when pricing credit derivatives (CDS) or building a credit curve from market spreads. Use ratings as a quick screen and for regulatory buckets, but never as your only input — they lag, and the market’s spread usually knows first. Above all, remember the model is a clean lens on a messy, correlated, fear-driven reality.

Putting it together

A risky bond yields the risk-free rate plus a credit spread, and that spread decomposes into the expected loss ($PD \times LGD$) — fair compensation for average losses — and a risk premium for bearing the uncertainty. LGD is $1 - \text{recovery}$, so your seniority in the capital structure sets your loss severity even at fixed PD. Hazard rates give the instantaneous default intensity ($s \approx \lambda \times LGD$) and a credit term structure that can invert for distressed names. Ratings are a lagging shorthand, and the whole tidy decomposition cracks in crises when PD, LGD and correlation all surge together. Know which slice of your spread is a rebate and which is real pay, and you’re a credit investor instead of a gambler.

Next — immunization and hedging — we put the whole toolkit to work: match duration (and convexity) to a liability so a rate move barely scratches your surplus, and compute the DV01 hedge ratio that neutralizes an entire rate book.