CFA Program Level I

Credit risk, expected loss and credit spreads: CFA Level I

Expected credit loss is probability of default x exposure at default x loss given default, where loss given default is 1 minus the recovery rate. The credit spread is a corporate bond's yield minus a government bond yield of similar maturity. It covers more than expected default loss: liquidity, tax and risk premiums are part of it too.

The three inputs to expected loss

Probability of default (PD): the chance the borrower defaults within the period, usually one year.

Exposure at default (EAD): the amount outstanding if default happens.

Loss given default (LGD): the percentage of the exposure lost after recoveries from collateral and work-out. LGD = 1 - recovery rate.

Expected loss = PD x EAD x LGD. As a percentage of the exposure, it is PD x LGD. The Basel Committee notes that banks treat expected loss as a cost of doing business and cover it through pricing and provisions; capital is held for losses above it.

Worked example

A EUR10,000,000 loan has a one-year PD of 1.2%. The lender expects to recover 35% if the borrower defaults, so LGD = 65%.

Expected loss = 0.012 x 10,000,000 x 0.65 = EUR78,000, or 0.78% of the exposure.

A common mistake is to multiply by the recovery rate: 0.012 x 10,000,000 x 0.35 = EUR42,000, which is the expected recovery on default, not the expected loss.

What a credit spread pays for

The San Francisco Fed measures the credit spread as the yield on a corporate bond minus the yield on a government bond of comparable maturity. Spreads widen in recessions and narrow in expansions.

Default risk is only part of the spread. One estimate cited there puts expected default losses at under 20% of the spread. Other parts are state taxes on corporate interest and compensation for the bond market's illiquidity.

Measured default probabilities vary less over the cycle than spreads do. In bad times, investors demand more compensation for risk than fundamentals explain, so spreads widen more than default risk alone would imply.

Seniority, collateral and recovery

A secured bond is backed by specific pledged assets. On default, its holders have a legal right to foreclose on that collateral.

Unsecured bonds, or debentures, have a general claim on the issuer's assets and cash flows. Senior debentures rank ahead of junior (subordinated) debentures.

The Basel note says LGD depends, among other things, on the type and amount of collateral. A credit rating estimates relative default risk; it does not measure liquidity risk or say whether a price is good value.

Where the exam catches people

Believing LGD is the recovery rate: LGD is 1 minus the recovery rate.
Believing the whole credit spread is compensation for expected default losses: liquidity, tax and risk premiums make up much of it.
Believing spreads widen in recessions only because default risk differences between rating classes grow: research finds default probabilities vary less than spreads do.
Believing a senior unsecured debenture ranks ahead of a secured bond on the pledged collateral: the secured holders have the claim on that asset.
Believing two bonds with the same rating have the same liquidity or value: a rating addresses default risk only.

Written from CFA Institute's documentation

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

A bank has a loan exposure of EUR8,000,000 to a borrower whose one-year probability of default is 2.5 percent. If the borrower defaults, the bank expects to recover 40 percent of the exposure by selling collateral. The bank's one-year expected loss on this exposure is closest to:
Right. In the game that’s Renown for your Fixed Income building.
Not that one: B is right. In the game your Fixed Income building would lose a little Renown, and this question would come back later.
Your answerA.EUR80,000This multiplies by the recovery rate instead of the loss rate: 0.025 x 8,000,000 x 0.40 = EUR80,000. Loss given default is the part not recovered, 60 percent.The answerB.EUR120,000Expected loss = probability of default x exposure at default x loss given default. Loss given default is the share of the exposure that is not recovered: 1 - 0.40 = 60%. EL = 0.025 x 8,000,000 x 0.60 = EUR120,000.Your answerC.EUR200,000This stops at 0.025 x 8,000,000 = EUR200,000, as if nothing were recovered. The 40 percent recovery means only 60 percent of the exposure is lost on default.
Written from www.bis.org/publications/explanatory-note-basel-ii-irb-risk-weight-functions.pdf
Over a business cycle, the gap between yields on speculative-grade and investment-grade corporate bonds swings by several percentage points, widening in recessions and narrowing in expansions. Which explanation is most consistent with research on what determines corporate credit spreads?
Right. In the game that’s Renown for your Fixed Income building.
Not that one: B is right. In the game your Fixed Income building would lose a little Renown, and this question would come back later.
Your answerA.Government bond yields climb in recessions as investors sell safe assetsIn a weakening economy investors move toward safe-haven investments rather than selling them, and corporate spreads widen because high-yield bonds lose demand, not because government yields rise.The answerB.A non-default component, such as illiquidity compensation, rises in bad timesExpected default losses explain only part of a corporate credit spread; one estimate puts them at under 20 percent of it. The rest includes a premium for the bond market's illiquidity and for risk, and in bad economic times investors demand more of that compensation than fundamentals explain, so spreads widen by more than default risk alone would imply.Your answerC.Default risk differences between rating classes grow sharply in recessionsIf the swing came from growing default risk differences between rating classes, default probability measures would move as much as spreads. Research finds they are much less variable than spreads, so default risk alone cannot explain the swing.
Show the full explanation and doc quotes
Measures of firms' default probabilities do not vary over the cycle as much as the spread does.
Written from www.frbsf.org/research-and-insights/publications/economic-letter/2004/12/what-determines-the-credit-spread/
Halvern Foundry has defaulted and entered bankruptcy. Its debt includes Series K bonds, for which it pledged its main factory as collateral, and Series M senior debentures, which have no collateral pledged to them. With respect to the factory, whose claim most likely takes priority?
Right. In the game that’s Renown for your Fixed Income building.
Not that one: B is right. In the game your Fixed Income building would lose a little Renown, and this question would come back later.
Your answerA.Series K and M holders equallyBondholders do not all share equally. The bond's terms set its place in line, and a secured bond gives its holders a legal right to foreclose on the pledged collateral that unsecured debenture holders lack.The answerB.Series K holdersThe Series K bonds are secured: the company pledged the factory as security for them, so on default their holders have a legal right to foreclose on that collateral to satisfy their claims.Your answerC.Series M holdersSenior debentures are still unsecured. Their seniority gives them a higher-priority claim than junior (subordinated) debentures, but only a general claim; the holders who were pledged the factory have the right to foreclose on it.
Show the full explanation and doc quotes
The Series M debentures have no collateral and only a general claim on the company's assets and cash flows; being senior ranks them ahead of junior debentures, not ahead of secured holders on the pledged asset.
Written from www.sec.gov/files/ib_corporatebonds.pdf