The Credit Triangle: Spread, Hazard Rate and LGD

Three numbers describe almost every credit instrument's risk compensation: the spread investors are paid, the annual rate at which the borrower is assumed to default, and the fraction of exposure lost if a default happens. They aren't independent — under a simple, standard approximation, any one of the three is pinned down once you know the other two.

The relationship

$$s \approx h \times LGD$$

In words: the credit spread ($s$) a bond or CDS pays approximately equals the hazard rate ($h$, the annualized probability of default in any given year for a still-performing borrower) multiplied by the loss given default (the fraction of exposure not recovered if default occurs). This is an approximation — it ignores the timing of cash flows and compounding effects — but it's accurate enough to be the standard back-of-envelope tool traders use to sanity-check credit pricing.

Worked example

A 5-year CDS on a corporate name trades at a spread of 200 basis points, and the market convention assumes a standard 40% loss given default (equivalently, a 60% recovery rate).

1. Rearrange for hazard rate. $h \approx s / LGD = 2.00\% / 0.40 = 5.00\%$ per year.
2. Interpretation. The market is implicitly pricing roughly a 5% annual chance of default for this name, given the standard 40% LGD assumption.

Now suppose new information suggests this borrower's actual recovery in default would be much lower — say 20% (LGD of 80%) because its debt is unsecured and thinly covered by assets — while the spread stays at 200 basis points.

3. Recompute implied hazard rate. $h \approx 2.00\% / 0.80 = 2.50\%$ per year.

The same 200 basis point spread implies a much lower default probability once a harsher LGD assumption is used — a reminder that a spread alone never tells you default risk; it only tells you default risk multiplied by loss severity.

What this means in practice

Traders use the credit triangle constantly as a mental shortcut: given a quoted spread and a standard recovery assumption, back out an implied hazard rate to compare against a fundamental default view, or given a fundamental hazard rate estimate, check whether the market spread looks rich or cheap.