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

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.