Default and Recovery
Connect a bond's credit spread to the chance its issuer defaults and how much investors get back: value the bond from expected losses, or work out the default probability a spread implies.
Learning focus: a credit spread pays for expected loss and then some: the rest is a premium for bearing default risk and for illiquidity.
At the BBB average default rate of 0.15% a year and 40% recovery, expected losses justify 9 bp. The rest pays investors for bearing the risk that defaults bunch up in a recession, and for a bond that is harder to sell than a Treasury. For investment-grade bonds that premium is usually most of the spread.
| Year | Exposure | Recovery | Loss given default | POD | Expected loss | DF | PV of loss |
|---|---|---|---|---|---|---|---|
| 1 | 110.9448 | 44.3779 | 66.5669 | 2.4147% | 1.6074 | 0.961538 | 1.5455 |
| 2 | 109.6626 | 43.8651 | 65.7976 | 2.3564% | 1.5504 | 0.924556 | 1.4335 |
| 3 | 108.3291 | 43.3317 | 64.9975 | 2.2995% | 1.4946 | 0.888996 | 1.3287 |
| 4 | 106.9423 | 42.7769 | 64.1654 | 2.2439% | 1.4398 | 0.854804 | 1.2308 |
| 5 | 105.5000 | 42.2000 | 63.3000 | 2.1897% | 1.3861 | 0.821927 | 1.1393 |
Per 100 face. Exposure is what bondholders would be owed if the issuer defaulted on that date: the payment due plus the default-free value of every payment after it. Their sum of PVs is the CVA.