Credit · 12 lessons

Revision sheet

Every Credit lesson’s essentials, formula and takeaway on one page. Each heading opens the full lesson.

C1The credit universe and the capital structure

Credit: Lending to borrowers who might not pay you back. Bonds from the safest companies are ; riskier ones are and pay more interest for the bigger chance of default.
The capital structure: Every claim on a company, in the order it is paid in a default: first-lien loans, second-lien loans, senior bonds, subordinated bonds, preferred shares, then ordinary shares. The higher a claim, the less interest it pays.
Seniority and security: is a claim’s place in the queue; is a claim on specific assets, like a mortgage on a house. Loans are usually both, which is why they tend to recover more than bonds.
Recovery and the fulcrum: Value is paid down the stack until it runs out. A company worth £500m repays a £300m loan in full, a of 100%, and £400m of senior bonds 50%: they are the . Lower layers get nothing.
Structural subordination: Lenders to a holding company are paid only after every creditor of the operating company beneath it, because the holding company owns just its shares. Guarantees from the subsidiaries close the gap.

Recovery of one layer

Recovery = min(claim, value left) ÷ claim

claim: what the layer is owed
value left: what the company is worth after every layer above has been paid in full

Remember: Recovery = value left for the layer ÷ its claim. Value runs down the stack from the top: the layer where it runs out is the fulcrum, and everything below it gets little or nothing.

C2Ratings, default and expected loss

Credit ratings: Letter grades from agencies such as S&P, Moody’s and Fitch for how likely a borrower is to pay. From safest to riskiest: AAA, AA, A, BBB, BB, B and CCC. Default rates rise steeply down the scale.
The investment-grade line: AAA to BBB− (Baa3 at Moody’s) is ; BB+ and below is . A bond cut across the line is a , which funds limited to investment grade must sell.
PD and LGD: (PD) is the chance a borrower fails to pay within a year. (LGD) is the share lost if it does: one minus the recovery, so 60% at 40% recovery.
Expected loss: The average loss a year: PD times LGD times the amount lent. £100 lent at a 2% PD and a 60% LGD loses £1.20 a year on average; some years nothing, some years much more.
The credit triangle: A spread pays for the expected loss, so dividing it by the LGD gives the default rate it implies: 300bp at 40% recovery implies about 5% a year. Spreads also pay for uncertainty, so the implied rate usually exceeds history.

Expected loss and the credit triangle

EL = PD × (1 − R) × N; spread ≈ PD × (1 − R)

PD: probability of default in a year
R: recovery rate (40% = 0.4); 1 − R is the loss given default
N: the amount lent

Remember: PD ≈ spread ÷ (1 − recovery). A spread is the market’s price for default and loss: divide it by the loss on default to see the default rate it implies.

C3Credit spreads and quoting

Credit spread: The extra a company bond pays over a government bond of the same maturity, for the risk of not being repaid. It is quoted in : “T+150” is 150bp over the matching US Treasury.
G-spread and I-spread: The is measured over the government bond, the over the . With swaps below , the I-spread is larger: a 5.85% bond is 125bp over a 4.60% gilt and 145bp over a 4.40% swap rate.
Spread or price: Investment-grade bonds are quoted on spread, and the price follows from the benchmark. High-yield and distressed bonds are quoted on price, because the chance of default, not the government rate, drives their value.
Splitting a move: A company bond’s yield moves with its benchmark and with its spread. If government yields fall 20bp while the spread widens 10bp, the yield falls 10bp: the rates move outweighed the credit move.
What widens spreads: Recession fears, falling profits or rising debt at the company, heavy new issuance, and money leaving credit funds; the reverse tightens them. In a sell-off, flows can push spreads further than the default outlook justifies.

Spread and yield

yield = benchmark yield + spread

benchmark: the government bond of the same maturity (G-spread) or the swap rate (I-spread)
spread: the extra yield for the company’s risk, in bp (100bp = 1%)

Remember: Yield = benchmark + spread. Every company bond is a rates trade and a credit trade: split each move into the benchmark and the spread.

C4Spread duration, carry and breakevens

Spread duration: The percentage a bond’s price moves for a 100 change in its spread. For an ordinary fixed-coupon bond it is about the same as its duration: at 6, a 30bp widening costs about 1.8%.
CS01: The profit or loss for a 1bp move in spread: £10m of a bond with a spread duration of 6 has a CS01 of about £6,000. An owner is long credit, so 10bp of widening costs £60,000; a short position gains it.
Carry: The income from holding a bond while nothing moves. Against a government bond of the same maturity, a company bond earns roughly its spread extra: at 150bp over, about 1.5% a year more.
Breakeven widening: How far a spread can widen over a year before the price loss uses up the extra income: about the spread divided by the spread duration. A bond at 120bp with a spread duration of 6 can take about 20bp.
Three parts of a return: Carry, plus the move from government , plus the move from the spread. A bond yielding 5% with a duration of 6 returns about 4.4% in a year if government yields fall 20bp and its spread widens 30bp.

Spread P&L and the breakeven

CS01 ≈ N × Ds × 0.0001; breakeven ≈ s ÷ Ds

N: the amount of the bond you hold
Ds: spread duration
s: spread, in bp; the breakeven is in bp over a year

Remember: Breakeven ≈ spread ÷ spread duration. Spread is your income and spread duration your exposure: the ratio tells you how much bad news a bond can absorb.

C5Credit analysis for traders

EBITDA: Earnings before interest, tax, depreciation and amortisation: roughly the cash a company’s business produces in a year, and the income analysts measure its debt against.
Leverage: Debt divided by , in ‘turns’: £400m of debt on £100m of EBITDA is 4×. subtracts cash first. Strong investment-grade companies often run below about 2–3×; buyouts often start at 5× or more.
Interest cover: EBITDA divided by the year’s interest: £100m of EBITDA against £25m of interest is 4×. Companies with floating-rate debt see it fall as soon as interest rates rise.
Covenants: Promises in the debt documents. A maintenance covenant is tested every quarter, so falling earnings can breach it; an incurrence one only when the company borrows or pays out. loans have no maintenance tests.
Event risk: Company decisions that hurt lenders: a leveraged buyout, or borrowing to pay a dividend or buy back shares, adds debt and widens spreads. In a , lenders left out fall behind.

Credit ratios

net leverage = (debt − cash) ÷ EBITDA; interest cover = EBITDA ÷ interest

EBITDA: earnings before interest, tax, depreciation and amortisation, a year
interest: interest paid on the debt, a year

Remember: Net leverage = (debt − cash) ÷ EBITDA. Leverage says how much debt there is, cover says whether it can be serviced, and the documents say what lenders can do about it.

C6The primary market and bond features

Bookbuilding: How banks sell a company’s new bond: they take orders over a few hours at a starting spread and tighten it as orders build. Orders four times the deal size can bring the spread 25 in from where it started.
New-issue concession: The extra spread a new bond pays over , read off the issuer’s existing bonds, to sell quickly. With 7-year bonds at +140bp and 10-year at +155bp, an 8-year is fair at +145bp; pricing at +155bp is a 10bp concession.
Callable bonds: Bonds the company can repay early at a set price, which it does when it can borrow more cheaply, so they pay more spread. Above the call price they are quoted on : the lower of to call and to maturity.
Features and the spread: Anything that favours the company or lowers recovery adds spread, such as a call or ranking behind other bonds. Anything that protects the investor lowers it, such as a put at 100 or security over assets.
AT1: Bank bonds that never mature and are written off or turned into shares if the bank’s capital runs too low. In March 2023 FINMA ordered about CHF 16bn of Credit Suisse AT1s written off, while shareholders still received UBS shares.

New-issue concession

concession = new bond’s spread − fair spread from the existing bonds

fair spread: read off the company’s existing bonds either side of the new bond’s maturity

Remember: Concession = new spread − fair spread. New bonds pay a little over the issuer’s existing bonds to sell quickly, and every feature that favours the issuer adds to the spread.

C7Credit default swaps

Credit default swap: A contract that insures against a company defaulting. The protection buyer pays a yearly fee and is short credit, gaining as the company weakens; the seller covers the loss in a default and is long credit, like owning the bond.
Credit events and the auction: A payout needs a : usually bankruptcy or a missed payment, in some contracts a forced restructuring. An then sets one recovery price: at 35, sellers pay 65% of the amount covered.
Standard fee and upfront: Standard contracts pay a fixed yearly fee, usually 100 or 500bp, and settle the gap to the market spread at the start. With a of 4.4, 180bp against a 100bp fee costs the buyer about 3.5% upfront.
Marking to market: An existing contract’s value changes by about the change in spread times risky duration times the amount covered. €10m bought at 180bp is up about €308,000 if the spread reaches 250bp; the seller is down the same.
The CDS–bond basis: The gap between a company’s CDS spread and its bond spread, which should be close because both pay for the same default risk. When the bond pays more, buying it and buying protection earns the gap with default covered.

CDS upfront

Upfront ≈ (spread − fee) × RD × amount covered

spread: what the market says protection is worth, a year
fee: the contract’s standard yearly fee: 100bp or 500bp
RD: risky duration: about 4 for a 5-year contract

Remember: Upfront ≈ (spread − fee) × risky duration. Buying protection is short credit: you pay the fee, settle the difference upfront, and gain as the spread widens.

C8Indices and macro credit

CDS index: Protection on a basket of companies in one trade, each an equal share. The main ones are IG (125 names) and CDX HY (100) in North America, and Europe (125) and the Crossover (75, high yield) in Europe.
When a name defaults: Only its slice pays out, and the contract carries on for the rest at a smaller size. $50m of CDX HY has $500,000 on each name: a default at 30% recovery costs a seller $350,000 and leaves $49.5m.
Fees and quoting: Indices pay a fixed yearly fee: 100 for CDX IG and 500bp for the high-yield indices. CDX HY is quoted as a price, 100 minus the upfront, so a 350bp spread with a of 4 shows as 106.
Rolls and on-the-run: Every March and September a new series starts, maturing six months after the last, with its companies re-picked for rating and liquidity. The newest series is and gets most of the trading.
Hedging with an index: The quickest hedge for a bond portfolio: buy index protection with the same . If the bonds lose $45,000 per bp and $1m of CDX IG moves $450, buy about $100m. Names outside the index leave gaps.

One default in an index

Payout = N ÷ n × (1 − R); amount left = N × (n − 1) ÷ n

N: the amount of index protection
n: the number of companies in the index
R: recovery on the defaulted company

Remember: Payout per default = notional ÷ names × (1 − R). An index spreads one default across all its names, which makes it the fast way to hedge or trade a whole credit market.

C9Leveraged loans and private credit

Leveraged loans: Loans to riskier companies, often ones owned by private-equity firms. They are usually secured and first in line in a default, and many are bought by , funds that buy loans in bulk.
Base rate plus margin: Loan rates float: a fixed margin over a base rate, which is for dollars, for sterling and EURIBOR for euros. A sets a minimum base: SOFR + 3.5% with a 0.5% floor pays at least 4%.
Discount margin: Loans often trade below 100, and buyers spread the discount over an assumed life, often three years. At 98.5 with a 350 margin, that adds 1.5 ÷ 3 = 0.5% a year: a of about 400bp.
Repricing: Loans can be repaid at 100 almost any time, so when one trades above 100 the borrower asks lenders to accept a lower margin. Most agree rather than be repaid, which is why loan prices rarely climb far above 100.
Private credit: Funds and insurers lending directly to companies and holding the loans. Lenders get a higher margin and tighter terms for having no market to sell into; with no market price, losses can show up slowly.

Loan rate and discount margin

rate = max(base, floor) + margin; DM ≈ margin + (100 − price) ÷ life

base: the base rate: term SOFR, SONIA or EURIBOR
floor: the lowest base rate the loan will use
margin: the fixed extra rate over the base
life: the assumed life in years, often 3
DM: discount margin

Remember: DM ≈ margin + (100 − price) ÷ expected life. Loans float, sit first in line and can be repaid at 100, so lenders earn the margin but rarely see price gains.

C10CLOs: collateralised loan obligations

Collateralised loan obligation (CLO): A vehicle that buys a pool of a couple of hundred and pays for them by selling notes. A manager picks and trades the loans; a trustee collects their cash and pays the notes in order.
Tranches and subordination: The notes are slices paid in order: AAA, AA, A, BBB, BB, then equity. Cash flows from the top and losses from the bottom, so the slices beneath are a cushion: in an illustrative $500m CLO, 38% must be lost before $310m of AAA is hit.
OC and IC tests: Quarterly checks that must stay above set triggers. The divides the loans’ face value by the notes from AAA down to a slice: $500m against $425m is 117.6%. The does the same for interest.
When a test fails: Cash meant for the lower slices and the equity repays AAA notes instead, until the ratio is restored. Defaults lower the ratios, and so do downgrades: CCC loans above a set limit count at market value, not face value.
The reinvestment period: A CLO is assembled in a warehouse, then for its first few years the manager uses money from repaid loans to buy new ones. After that, repayments pay off the AAA notes first and the deal shrinks.

The OC test

OC = loans’ face value ÷ notes from AAA down to the slice

OC: overcollateralisation ratio: it must stay above the slice’s trigger
notes: the face value of the slice and every slice above it

Remember: OC = loans’ face value ÷ notes down to the slice. A CLO pays its notes from the top and takes losses from the bottom; when a test fails, cash is redirected to protect the AAA.

C11Mortgage-backed securities I: prepayment

Pass-through MBS: A bond that passes a pool of home loans’ monthly interest and principal to investors, less fees: 6.85% mortgages might pay 6.0%. In the US most are guaranteed by Fannie Mae, Freddie Mac or Ginnie Mae, so default losses are slight.
Prepayment and extension risk: US homeowners can repay a fixed-rate mortgage early without a penalty. When rates fall they refinance and money comes back early, to be reinvested lower; when rates rise repayments slow and the bond lasts longer as its value falls.
Negative convexity: An shortens when fall, capping its gains, and lengthens when they rise, deepening its losses, because its holder is short the homeowners’ option to repay. MBS pay extra yield to make up for it.
CPR and SMM: is the share of remaining loans repaid early in a year; SMM is the monthly rate, so 6% CPR is about 0.514%. Faster speeds shorten the : about 9 years at 8% CPR, under 3 at 30%, for one pool.
What sets the speed: Speeds rise when mortgage rates sit well below the loans’ rate and when more people move house; they are slower for new loans and for pools already through a refinancing wave. 100% ramps CPR to 6% by month 30.
UK mortgages: Most UK mortgages fix their rate for two or five years, with a fee for repaying early during the fix. So borrowers refinance when the fix ends, not whenever rates fall, and UK mortgage bonds carry far less prepayment risk.

Monthly prepayment speed

SMM = 1 − (1 − CPR)^(1/12)

CPR: share of the remaining balance repaid early over a year
SMM: the same speed per month (single monthly mortality)

Remember: SMM = 1 − (1 − CPR)^(1/12). MBS holders are short the homeowner’s option: the bond shortens when rates fall and lengthens when they rise.

C12Mortgage-backed securities II: market structure

TBA trade: How most US trade: the coupon, maturity, price and settlement month are agreed, and the seller names the pools two days before settlement. It delivers the that qualify, so TBA prices reflect them.
Specified pools and pay-ups: Pools whose borrowers repay slowly, such as small loans, are worth more than the TBA and trade at a pay-up, quoted in 32nds like Treasuries: 102-00 against 101-08 is 24/32, or 0.75 points.
CMOs: A splits a pool’s payments into classes. In a sequential CMO, class A takes all principal until it is repaid, then class B. A PAC keeps a set schedule within a band of speeds; a support class absorbs the rest.
IO and PO: of a pool’s interest (IO) and principal (PO). Falling rates speed up repayment, so the PO, bought below 100, gains. The IO loses then, as interest stops on each loan repaid, so it gains when rates rise.
Convexity hedging: When rise, lengthen, so holders who keep their fixed sell Treasuries or pay fixed in swaps, pushing yields higher still; when yields fall they buy. Their hedging adds to rate moves.

Specified-pool pay-up

pay-up = specified-pool price − TBA price

pay-up: the premium for a pool that repays slowly, usually quoted in 32nds

Remember: Pay-up = specified pool − TBA price. The TBA prices the worst pools; anything that slows repayment earns a pay-up, and hedging MBS adds to rate moves.