Credit risk and CDS intro

~8 min read

Interview occasional

Why it matters

Credit is the risk that a promised cash flow is not paid in full. A credit default swap (CDS) is insurance on that event: the protection buyer pays a spread, the protection seller covers the loss given default. You will not be asked to build a full hazard-rate engine in most generalist FE interviews, but you will be expected to explain a CDS, read a par spread, and connect spread \(\approx\) hazard \(\times\) LGD.

Core concepts

Two numbers: probability of default (PD) and loss given default (LGD). Expected loss on a loan \(\approx PD \times LGD \times EAD\). Recovery \(R = 1 - LGD\) is often assumed 40% for senior unsecured in a pinch; it is not a law.
Credit spread is compensation for expected loss plus risk premium plus funding/liquidity. A corporate yield minus the matched Treasury/swap rate is not pure expected loss. Risk-neutral (CDS-implied) PDs are usually higher than real-world (rating) PDs — same pattern as equity risk premium.
A CDS, mechanically. Protection buyer pays a running spread \(s\) (quarterly, on notional) until default or maturity, plus maybe an upfront. On a credit event, seller pays \(N \times (1-R)\) (cash auction) or takes delivery of a defaulted bond vs. par. Standard SNAC/ISDA docs define events: bankruptcy, failure to pay, (sometimes) restructuring.
Par spread. The \(s\) that makes the CDS worth zero at inception (upfront \(\approx 0\) on old running-spread conventions; today many names trade with a standardized coupon + upfront). Rough no-arbitrage: PV(spread leg) = PV(protection leg).
The interview approximation: \(s \approx \lambda_{\text{hazard}} \times LGD\) for a flat hazard rate \(\lambda\) and continuous payment, when \(\lambda T\) is not huge. So a 100bp par spread at 40% recovery \(\Rightarrow \lambda \approx 100\text{bp}/0.6 \approx 167\)bp hazard per year. This is the credit analogue of “carry ≈ spread.”
Survival probability. With constant hazard, \(P(\tau > t) = e^{-\lambda t}\). Risky cash-flow PV \(\approx \sum CF_i\, DF(t_i)\, e^{-\lambda t_i}\) plus recovery on default (simplified). This is how a risky bond is a defaultable version of TVM.
CDS vs. cash bond (basis). Buying a bond and buying protection is roughly a synthetic risk-free (plus funding). CDS–bond basis = CDS spread − bond’s Z-spread (signs vary by shop). Can be nonzero because of funding, cheapest-to-deliver, counterparty risk, and technicals.
Counterparty risk on the CDS itself. Bilateral OTC; now a lot of index CDS is cleared. CVA is the topic behind “what if the protection seller defaults when you need them” — know the word; don’t overclaim a full CVA engine unless the seat is XVA.

Mental model

  Protection buyer                     Protection seller
  (long protection,                    (short protection,
   short credit)                        long credit)
         |                                    |
         |  pay spread s until default/T      |
         | ---------------------------------> |
         |                                    |
         |  if default: receive N(1-R)        |
         | <--------------------------------- |

  Rough:  s ≈ λ × LGD
  Bond yield ≈ risk-free + s  (plus premia / basis)

Think of the spread as the carry you collect (or pay) for being short (or long) default risk, with a jump-to-LGD on the event.

Interview questions

A 5y CDS par spread is 120bp, assumed recovery 40%. Rough hazard rate? Rough 5y risk-neutral PD? Answer: \(\lambda \approx 0.012 / 0.60 = 2\%\) per year. Survival \(\approx e^{-0.02\times 5} \approx 90.5\%\), so PD \(\approx 9.5\%\). (Continuous, flat-hazard approximation; good enough for a screen.)
You buy a corporate bond and buy CDS protection on the same name/maturity. What risk did you (approximately) kill, and what remains? Answer: You killed jump-to-default / credit-spread risk of that issuer (to first order). Remaining: funding of the bond, CDS–bond basis, cheapest-to-deliver option in the CDS, counterparty/CVA, interest-rate duration if not hedged, and recovery vs. assumed recovery.
Why are CDS-implied default probabilities typically higher than historical default rates for the same rating? Answer: CDS prices under a risk-neutral measure: they include a credit risk premium, liquidity, and dealer balance-sheet costs. Historical PDs are real-world frequencies. Same wedge as equity implied vs. realized vol, or as \(Q\) vs. \(P\) in Black–Scholes.
What is a credit event, and why does ‘restructuring’ matter? Answer: Typically bankruptcy and failure to pay; restructuring (modified-mod-R, etc.) may or may not be included depending on the contract (North America SNAC often omits it). It matters because it changes when protection pays and which deliverable obligations qualify.
A trader says the name ‘widened 20bp.’ Who won if they sold protection? Answer: Seller of protection is short protection / long credit: they collect spread but lose when spreads widen (mark-to-market) or when default hits. Widening 20bp hurts the protection seller, helps the buyer.

Watch

Credit default swaps — Khan Academy. Why someone would buy protection in order to lend, and the running premium in basis points.
Credit default swaps (CDS) intro — Khan Academy. Short, mechanical intro to the contract.