RadioShack held a AAA rating in 1983 and defaulted in 2015. Between those dates sat dozens of downgrades, each one repricing the bond long before any missed payment. Credit analysis models put numbers on that path.
Credit risk has two parts: how likely default is, and how much you lose when it happens. Default risk is only the first part. A collateralized loan can carry high default risk and low credit risk if the collateral covers the debt.
Three parameters drive every calculation in this reading.
- Expected exposure: the projected amount you could lose if default occurs on a given date, before any recovery.
- Recovery rate: the percentage of exposure recovered in default. The baseline working assumption is 40%. Loss severity is 1 minus the recovery rate, so 60%.
- Loss given default (LGD): exposure minus recovery. On 104 exposure at 40% recovery, LGD is 104 × 0.60 = 62.4, and the defaulted investor receives 41.6.
The third input is the probability of default (POD), the chance the issuer misses a contractual payment. Models use conditional annual PODs, called hazard rates, each assuming no prior default.
Common mistakes
- Discounting at the bond's yield. Risk-neutral valuation discounts expected cash flows at the risk-free rate. Using 3.77% instead of 3.00% double-counts credit risk.
- Using unconditional PODs. Each year's POD is the hazard rate times the prior year's survival probability. Applying 1.25% flat to all five dates overstates cumulative POD as 6.25% instead of 6.0957%.
- Adding the CVA instead of subtracting. Fair value = VND − CVA. Adding gives 89.42 rather than 83.1060 on Example 1.
Bottom line
- LGD equals expected exposure times one minus the recovery rate; expected loss equals LGD times that date's conditional POD
- CVA is the sum of PV of expected losses; fair value equals value assuming no default minus CVA
- Risk-neutral PODs exceed historical PODs; discount expected values at the risk-free rate, never at the bond's yield
- Approximate credit spread equals annual POD times one minus recovery rate (1.25% × 0.60 = 0.75%)
Exam shortcut
Build the CVA table column by column in the given order: exposure, recovery, LGD, POD, POS, expected loss, discount factor, PV. Skipping to a formula loses the conditional-POD chain, which is where the graded points sit. If the vignette gives a price and asks for POD, run the table backward and use POD ≈ spread ÷ (1 − recovery) as your first guess.
The full lesson (about 3,206 words, 21 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- credit analysis models
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