Debt Capital Markets puzzles, solved step by step

Puzzles: 100
Traced to a firm: 16
Topics: 13
Hard: 30

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014An issuer has a 2% chance of default in any year, independent of the past. What is the probability that it defaults at some point in the next 5 years, and why is it not 10%?Credit spreads and default probabilityCoreCredit researchRisk management
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Is the five year default probability above or below 10%?
Show the worked solution
About 9.6%. The chance of surviving one year is 98%, and surviving five independent years is 0.98 to the power 5, or 90.39%. Default at some point is everything else: 9.61%. It is below 10% because the 2% in each later year applies only to issuers still alive, a shrinking group, so simply adding the yearly rates double counts.
Why does adding 2% five times overstate it?
Think of a phone that has a 2% chance of breaking each year. A phone that broke in year 1 cannot break again in year 2. Default is a one-time event, so each year's 2% applies only to the issuers that survived until then, and that group shrinks every year. Seen from today, the chance of defaulting in year 2 is 98% times 2%, which is 1.96%; by year 5 it is 1.845%. Those five numbers sum to 9.61%, not 10%.
Seen from today, the chance of defaulting in each year falls from 2.00% to 1.84% as survivors shrink, summing to 9.61% over five years; over fifty years compounding survival gives 63.6% cumulative default while adding 2% a year would absurdly reach 100%.
What is the fastest correct route?
Go through survival. Survival over several independent years is the product of the one year survival rates, and cumulative default is one minus that product. 0.98 squared is 0.9604, times 0.98 again is 0.9412, then 0.9224, then 0.9039. Or use the shortcut that 0.98 to the fifth is about 1 minus 5 times 0.02 plus 10 times 0.0004, which is 0.904. Either way, default is about 9.6%.
The relationship
$P(\text{default by } n) = 1 - (1-p)^n = 1 - 0.98^5 \approx 1 - 0.9039 = 9.61\%$
p the default probability in any one year, 2%
n the number of years, 5
(1-p)^n the chance of surviving all n years
What it says in wordsCumulative default is one minus the chance of surviving every year.
Why does a credit desk care about a 0.4 point gap?
Over five years the gap is small, 10.0% against 9.6%. Over long horizons the difference becomes enormous: adding 2% a year says default is certain by year 50, while compounding survival says 63.6%. That matters for pricing long bonds, for reading a rating agency's cumulative default tables, and for turning a spread into an implied default rate. Say the limit too: real default rates are not independent from year to year, they cluster in recessions, so the 2% flat rate is a teaching simplification.
Where candidates lose it
Saying 10% is the whole trap, and it comes from treating the yearly probabilities as if they could stack. The interviewer is checking whether you see that default removes the issuer from later years.
The opposite slip is saying 2% because each year is independent. Independence means each year's odds are unchanged for a survivor, not that the risk over five years is the same as over one.
What the interviewer asks next
What yearly default probability gives a 20% chance of default over 10 years?
If recovery is 40%, roughly what credit spread compensates for a 2% annual default rate?
Why would a rating agency's cumulative default table not fit a constant yearly rate?
017A one-year rating transition matrix says an A-rated issuer stays A with 92% probability, moves to BBB with 7.5% and defaults with 0.5%. A BBB issuer defaults with 2% in a year. Using the same matrix each year, what is the A issuer's cumulative two-year default probability?Credit spreads and default probabilityHardRisk managementCredit research
Try it first
Before working the tree: is the two year figure above or below 1.0%, twice the one year rate?
Show the worked solution
About 1.11%. There are three ways to be in default by the end of year 2. Default in year 1: 0.5%. Stay A, then default: 92% times 0.5%, which is 0.46%. Fall to BBB, then default: 7.5% times 2%, which is 0.15%. They add to 1.11%, more than twice the one year rate, because downgrades move issuers into riskier states.
Why can you not just double 0.5%?
Think of a student who might fail an exam this year or slip into a weaker class and fail next year from there. Multi-year default risk comes from migration as well as direct default: an issuer that is downgraded in year 1 faces a higher default rate in year 2. Doubling 0.5% assumes every survivor is still A, and the independent-survival answer, 1.00%, makes the same assumption. Both miss the 7.5% who drift to BBB.
An A issuer can default in year 1 (0.5%), stay A and default in year 2 (0.46%), or fall to BBB and then default (0.15%); the three paths add to a two year default probability of 1.11%.
How do you set it up so nothing is missed?
List where the issuer can be after year 1, then ask for each state what happens in year 2. Default is an absorbing state, so a year 1 default stays counted; the other states each carry their own year 2 default rate. The A branch contributes 0.92 times 0.005 and the BBB branch 0.075 times 0.02. A small matrix multiplication does the same thing: square the one year matrix and read off the A to default cell.
The relationship
$P_2(A \to D) = p_{AD} + p_{AA}\,p_{AD} + p_{AB}\,p_{BD} = 0.5\% + 0.92 \times 0.5\% + 0.075 \times 2\% = 1.11\%$
p_AD one year default rate from A, 0.5%
p_AA chance of staying A for a year, 92%
p_AB chance of moving from A to BBB, 7.5%
p_BD one year default rate from BBB, 2%
What it says in wordsAdd every path that ends in default within two years, each path's probability being the product of its steps.
What does the migration path tell a credit investor?
The downgrade path is only 7.5% likely but supplies 14% of the two year default risk. For a high rated issuer, most of the medium-term risk is the chance of becoming a weaker credit, which is why investors watch outlooks and migration as closely as default rates. Downgrades also cost money before any default, through wider spreads. Say the limits: real matrices are estimated from history, the same matrix is unlikely to hold every year, and defaults cluster in downturns, so treat this as the arithmetic, not a forecast.
Where candidates lose it
The fast wrong answer is 1.0%, doubling the one year rate, or 0.9975%, compounding it as if the issuer could only ever be A. Both are the same error: ignoring that the issuer's rating can change before it defaults.
The second loss is forgetting the year 1 default path, adding only the two year 2 paths to get 0.61%. Default is absorbing: once in, the issuer stays counted.
What the interviewer asks next
BBB issuers can also fall to BB, which defaults at 8% a year. What else would you need to add a third year?
How would you compute the same answer with a matrix multiplication?
Why might a transition matrix estimated from a calm decade understate this risk?
038Loan A is Rs 50 crore to a borrower with a 1% default probability, secured so that loss given default is 20%. Loan B is Rs 20 crore unsecured, with a 3% default probability and 75% loss given default. Which has the larger expected loss?Credit spreads and default probabilityCoreCorporate bankingCredit research
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Which loan loses more on average each year?
Show the worked solution
Loan B, with an expected loss of Rs 0.45 crore against Rs 0.10 crore for Loan A. Expected loss is exposure times default probability times loss given default. Loan A: 50 x 1% x 20% is Rs 10 lakh. Loan B: 20 x 3% x 75% is Rs 45 lakh, 4.5 times as much on a loan less than half the size. Security and borrower quality matter more than the headline amount.
What goes into expected loss?
Imagine lending your bicycle to two friends. One borrows the expensive one but always returns things and leaves his phone as a deposit; the other borrows a cheap one, loses things often, and leaves nothing. What you expect to lose depends on how much you lend, how likely it is to go wrong, and how much you get back if it does, multiplied together. Lenders write those three as EAD, PD and LGD.
The relationship
$EL = EAD \times PD \times LGD \qquad A: 50 \times 0.01 \times 0.20 = 0.10 \qquad B: 20 \times 0.03 \times 0.75 = 0.45$
EAD exposure at default, the amount owed if the borrower defaults, Rs crore
PD probability of default over the year
LGD loss given default, the share of the exposure lost after recoveries
What it says in wordsExpected loss is how much is at risk, times how likely a default is, times how much of it would be lost.
Loan A's large Rs 50 crore exposure is offset by a 1% default probability and a 20% loss given default, for an expected loss of Rs 0.10 crore, while Loan B's Rs 20 crore at 3% and 75% gives Rs 0.45 crore, 4.5 times as much.
What does the answer mean for pricing?
Express each loss as a rate on the loan. Loan A costs 0.2% a year in expected losses; Loan B costs 2.25%, so B needs roughly two points more of spread just to break even on credit losses. Two factors did that. The default probability tripled, and the lack of security nearly quadrupled the loss when things go wrong. Security is why a secured loan to a weaker borrower can be safer than an unsecured loan to a stronger one.
Say the limit. Expected loss is an average; it covers the cost of doing business, not the bad year. A credit portfolioA book of many loans, where losses depend on how many default together, not only on each loan alone. with a few large loans can lose far more than its expected loss when one of them fails. Loan A's Rs 10 lakh expected loss hides a Rs 10 crore hit if it defaults, which is why lenders hold capital for unexpected loss as well.
Where candidates lose it
The instinctive answer is Loan A because it is bigger. The interviewer chose a large, safe, secured loan against a small, risky, unsecured one precisely to see whether you multiply all three factors or anchor on size.
The second loss is multiplying by the recovery rate instead of the loss rate: 80% for A and 25% for B. Say LGD is the share lost, not the share recovered, before you multiply.
What the interviewer asks next
What spread over funding cost would Loan B need to cover expected loss and still earn 1% a year?
Loan A's collateral value halves. What happens to its LGD and expected loss?
Why is expected loss not enough to set how much capital a bank holds?
054A 3-year floating rate note pays the benchmark plus 100 basis points, resetting quarterly. The issuer's market spread widens to 150 basis points. Roughly what price does the note fall to, and why does a floater still lose money?Credit spreads and default probabilityHardSyndicate desksFixed income asset management
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Before any maths: what happens to the note's price?
Show the worked solution
The note falls to about 98.7. The benchmark part of the coupon resets every quarter, so benchmark moves barely touch the price. The 100 basis point margin is fixed, and the market now wants 150. That 50 basis point shortfall runs for 12 quarters; discounted, it is worth about 1.32 per Rs 100, so the price is roughly 100 minus 0.50 x 2.64, about 98.7.
Which part of a floater's coupon resets, and which does not?
Picture a shop lease with rent set at inflation plus a fixed Rs 5,000. When inflation rises, the rent rises with it, so the landlord is protected. If rents on the street jump to Rs 8,000 over inflation, the landlord is still stuck at Rs 5,000 until the lease ends. A floating rate note resets its benchmark every quarter, but its credit margin is fixed at issue for the life of the note. Interest rate risk is almost gone; credit spread risk is not.
The benchmark part of the coupon resets, but the fixed 100 basis point margin now falls 50 basis points short of what the market wants; twelve quarterly shortfalls of 0.125, discounted, are worth 1.32 per Rs 100, so the note trades near 98.68.
How much is a 50 basis point shortfall worth today?
The note pays benchmark plus 1.00%; a new note from the same issuer would pay benchmark plus 1.50%. The holder is short 0.50% a year, 0.125 per Rs 100 each quarter, for 12 quarters, and the price falls by today's value of that stream. Assume the benchmark sits flat at 6.50%, so the discount rate is 8.00% a year, 2% a quarter. Twelve payments of 0.125 at 2% a quarter are worth 1.32, so the note trades near 98.68.
The relationship
$P \approx 100 - \Delta s \times D_s = 100 - 0.50 \times 2.64 \approx 98.68$
Delta s the widening in the issuer's spread, 0.50 percentage points
D_s spread duration, the price change per point of spread, about 2.64 years here
100 the price at a reset when the margin is fair
What it says in wordsA floater loses the spread change times its spread duration, and a floater's spread duration is close to its remaining life.
Say the shortcut first, then the refinement. A floater's spread duration is a little under its remaining life, so a 50 basis point widening on a 3-year note costs about 1.3 to 1.5 points. Using 3 years gives 98.5; discounting each shortfall gives 98.7, because the later shortfalls are worth less today. Either is a good answer if you say which one you did. The limit: this assumes a flat 6.50% benchmark, and a different curve moves the second decimal, not the story.
Where candidates lose it
The trap is saying a floater always trades near par because it resets. That is true for rate moves and false for credit moves: the margin is locked at issue, so a wider market spread leaves the note underpaying every quarter until maturity.
The second loss is using the maturity for both risks. Rate duration runs only to the next reset, about 0.25 years; spread duration runs to maturity, about 2.6 years here. Keep the two apart out loud.
What the interviewer asks next
The same 150 basis point widening hits a 7-year floater from the same issuer. Roughly how far does it fall?
What is this note's interest rate duration, and why is it so much smaller than its spread duration?
If the issuer's spread tightens back to 100 basis points after a year, where does the note trade?
068Two loans each have a 10% chance of default. What is the probability that at least one defaults if the defaults are independent, and if they are perfectly correlated? Why does a portfolio lender care?Credit spreads and default probabilityCoreRisk managementCredit research
Try it first
If the defaults are independent, what is the chance that at least one loan defaults?
Show the worked solution
Independent: 19% that at least one defaults and 1% that both do. Perfectly correlated: 10% for at least one and 10% for both. Independent loans survive together 0.9 x 0.9 = 81% of the time, so one or more defaults 19% of the time. Perfectly correlated loans default together or not at all. The expected number of defaults is 0.2 in both cases; what changes is how defaults bunch, and the chance of losing both loans is ten times higher.
Why is the answer not simply 10% plus 10%?
A 10% chance of rain on Saturday and 10% on Sunday is not a 20% chance of a wet weekend: some outcomes rain on both days and would be counted twice. The chance that at least one of two events happens is the sum of their chances minus the chance that both happen. For independent loans both default 0.1 x 0.1 = 1% of the time, so at least one defaults 10% + 10% - 1% = 19%. The quicker route is through survival: 1 minus 0.9 squared.
With independent loans the two 10% default regions overlap in only 1% of outcomes, so at least one loan defaults 19% of the time; with perfect correlation the regions sit on top of each other, so at least one defaults only 10% of the time but both default in all of those 10%.
The relationship
$P(\text{at least one}) = 1 - (1 - 0.1)^2 = 19\% \qquad P(\text{both}) = 0.1^2 = 1\%$
0.1 each loan's chance of default
(1 - 0.1)^2 the chance both repay, if the defaults are independent
What it says in wordsAt least one default is everything except the case where both loans repay.
What does perfect correlation change?
With perfect correlation the two loans default in exactly the same states of the world, so at least one defaults 10% of the time, and whenever one does, both do. The average is unchanged: 0.2 loans default on average in both worlds. But the independent pair loses both loans only 1% of the time, while the correlated pair loses both 10% of the time, ten times as often.
Outcome Independent Perfectly correlated
Neither defaults 81% 90%
Exactly one defaults 18% 0%
Both default 1% 10%
Expected defaults 0.2 0.2
The expected number of defaults is 0.2 loans in both cases, but the chance of losing both loans rises from 1% to 10% when the defaults are perfectly correlated.
Why does a portfolio lender care?
A lender holds capital against bad years, not average years, and correlation decides how bad the bad years are. Loans to one sector, one city or one promoter group tend to default together, which is why banks cap their exposure by sector and by group. Diversification works only when defaults are not strongly linked: ten independent loans with a 10% default chance all repay 35% of the time, but ten loans to one industry can behave like one big loan. The limit: real correlations sit between zero and one and rise in downturns, exactly when they hurt most, so the two cases here are the bounds, not the answer.
Where candidates lose it
The quick wrong answer is 20%, adding the probabilities and double counting the 1% of outcomes where both loans default. Work from the chance that both repay and the error cannot happen.
The second loss is saying correlation does not matter because the expected loss is the same. The average is identical; the chance of losing both loans goes from 1% to 10%, and that tail is what a lender's capital is for.
What the interviewer asks next
With a correlation between the two extremes, is the chance of at least one default above or below 19%?
You hold 10 independent loans, each with a 10% default chance. What is the chance that none defaults?
Why do default correlations tend to rise in a recession?
072A bond trades 300 basis points over the risk-free curve, and investors expect 40% recovery if it defaults. Using the credit triangle, what annual default probability is the market implying?Credit spreads and default probabilityCoreCredit researchFixed income asset management
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What annual default probability does the spread imply?
Show the worked solution
About 5% a year. The credit triangle says the spread pays for expected loss: spread = probability of default x loss given default. With 40% recovery the loss given default is 60%, so 3.0% = PD x 60% and PD = 5.0%. Treat it as an upper-bound reading, because real spreads also pay for liquidity and for bearing risk, so the default rate the market truly expects is usually lower.
Why does a spread imply a default probability at all?
An insurer charging Rs 3,000 a year to cover a Rs 1 lakh motorbike, where a stolen bike is usually recovered at 40% of its value, is pricing in some chance of theft; work backwards and you can read that chance off the premium. A credit spread is the premium a lender demands for expected loss: roughly, the chance of default each year times the share of the money lost when it happens. Everything else equal, a lender earning 300 basis points over the risk-free curve is being paid to lose about 3% a year on average.
The 300 basis point spread equals the default probability times a 60% loss given default, which implies 5.0% a year; the same spread implies 3.0% if nothing is recovered and 10.0% if 70% is recovered.
The relationship
$s \approx PD \times (1 - R) \;\Rightarrow\; PD = \frac{3.0\%}{1 - 0.40} = 5.0\%$
s the credit spread, 3.0% a year
PD the annual probability of default
R the expected recovery rate, 40%
1 - R loss given default, 60%
What it says in wordsThe spread roughly equals the yearly chance of default times the share lost when it happens.
How does the recovery assumption change the answer?
The higher the recovery, the higher the default probability a given spread implies, because each default costs the lender less. At 40% recovery, 300 basis points implies 5%; at 0% recovery it implies only 3%; at 70% recovery it implies 10%. So the recovery assumption is not a detail. Two analysts reading the same spread with different recovery views can disagree by a factor of two on how risky the credit is.
Expected recovery Loss given default Implied annual PD
0% 100% 3.0%
40% 60% 5.0%
70% 30% 10.0%
The same 300 basis point spread implies a 3.0%, 5.0% or 10.0% annual default probability depending on whether investors expect to recover nothing, 40% or 70% in default.
What does the credit triangle leave out?
The triangle treats the whole spread as payment for expected loss, but part of any spread pays for liquidity and for the discomfort of carrying credit risk. Default probabilities read off spreads therefore tend to sit above the default rates actually seen for similar credits. Use the triangle to compare credits and to sanity-check a spread, and say out loud that it gives an upper bound, not a forecast. Held for five years, 5% a year compounds to about 23% cumulative. The limit: it is a one-period shortcut that ignores when in the year default happens.
Where candidates lose it
The quick wrong answer is 3%, reading the spread as the default probability. That assumes lenders lose everything in default; with 40% recovery they lose 60%, so the same spread implies more defaults, not fewer.
The second slip is dividing by the recovery rate instead of the loss rate and getting 7.5%. Say loss given default out loud, 1 minus recovery, before you divide.
What the interviewer asks next
A secured bond from the same issuer has expected recovery of 70%. Roughly what spread should it trade at?
Why do default probabilities implied by spreads usually sit above historical default rates?
At 5% a year, what is the cumulative chance of default over five years?
084A 5-year credit default swap trades with a standard running coupon of 100 basis points, but the market spread for the name is 400 basis points and the risky duration is 4.0. What upfront payment changes hands, and who pays it?Credit spreads and default probabilityHardSyndicate desksCredit research
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Who pays the upfront amount, and roughly how much?
Show the worked solution
The protection buyer pays about 12% of notional upfront. The contract's running coupon is 100 basis points but fair protection costs 400, so the buyer underpays by 300 basis points a year. Multiply by the risky duration of 4.0, the present value of one basis point a year until default or maturity, and the shortfall is 1,200 basis points, or 12 points: Rs 12 crore on Rs 100 crore of protection.
Why does a standard coupon create an upfront payment?
Think of a gym that charges every member the same Rs 1,000 a month but costs Rs 4,000 a month to run for some members. It can only take them if they pay the Rs 3,000 a month difference as a lump sum on joining. Standardised credit default swaps work that way. The running coupon is fixed by the contract rather than set to the market, so the gap between the market spread and the coupon, for every year the protection is expected to run, is settled as one payment on the first day.
Paying a running coupon of 100 basis points for protection the market prices at 400 leaves 300 basis points a year missing, and 300 times a risky duration of 4.0 is 12 points, which the protection buyer pays upfront.
The relationship
$\text{Upfront} \approx (S - C) \times RD = (400 - 100)\text{ bp} \times 4.0 = 1{,}200\text{ bp} = 12\%$
S the market spread, 400 bp a year
C the contract's fixed running coupon, 100 bp a year
RD risky duration: the present value of 1 bp a year, paid until default or maturity
What it says in wordsThe upfront payment is the yearly shortfall in the coupon multiplied by how many risky years it is paid for.
Why is the risky duration less than five?
Premiums on a credit default swap stop the moment the name defaults, so the expected number of payments is lower than five, and each one is discounted. A risky duration of 4.0 sits below the 4.33 of a plain five-year annuity at 5% because some of those payments will never be made. The riskier the name, the lower the risky duration, which is why a desk re-computes it rather than assuming it stays fixed as the spread moves. The formula above is the market's first approximation; the full calculation also nets accrued premium and uses a model of default timing.
What happens when the spread is below the coupon?
The sign flips. If the market spread were 50 basis points against a 100 coupon, the buyer would overpay by 50 a year and the seller would pay the buyer about 2 points upfront. Whoever is getting the better running deal pays the difference on day one.
Where candidates lose it
The common mistake is the sign. Candidates say the seller pays because the seller is taking the risk, but the seller is being underpaid at 100 basis points, so it is the buyer who owes the difference.
The second is forgetting the multiplication: 300 basis points is a yearly shortfall, and it has to be turned into a present value with the risky duration before it is a payment.
What the interviewer asks next
The spread widens to 500 the next day. Roughly what is the buyer's gain on Rs 100 crore?
Why would a market move to fixed coupons with upfront payments instead of quoting a running spread?
What default probability does a 400 basis point spread imply if you expect 40% recovery?
092A high yield bond portfolio earns a spread of 450 basis points and an investment grade portfolio earns 120. Recovery on high yield defaults is 30%, and investment grade defaults are negligible. What annual default rate can the high yield portfolio absorb before it earns less than investment grade?Credit spreads and default probabilityCoreCredit researchFixed income asset management
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Roughly what default rate wipes out the extra spread?
Show the worked solution
About 4.71% of the portfolio defaulting each year. High yield earns 330 basis points more than investment grade. Each default costs 70% of face, since 30% is recovered, so each 1% of defaults costs 70 basis points. 330 divided by 70 is 4.71%. Below that default rate high yield still earns more; above it, less.
Why divide by the loss, not the default rate?
A shop that sells on credit loses less than the full bill when a customer fails to pay, if it can take back some of the goods. Bonds work the same way. The annual cost of defaults is the default rate times the loss given defaultThe share of face value lost when a borrower defaults, which is one minus the recovery rate., so the extra spread covers defaults up to the extra spread divided by the loss given default. With 30% recovered, each default loses 70%, and 330 basis points of extra spread covers 4.71% a year.
Annual credit loss rises by 70 basis points for each 1% of defaults and crosses the 330 basis points of extra spread at 4.71%, so high yield earns more than investment grade only while defaults stay below that rate.
The relationship
$d^{*} = \frac{s_{HY} - s_{IG}}{1 - R} = \frac{450 - 120}{0.70} = 471\text{ bp} = 4.71\%$
s_HY, s_IG the two portfolios' spreads, in basis points a year
R recovery on high yield defaults, 30%
d* the break-even annual default rate
What it says in wordsThe default rate that exactly uses up the extra spread is that spread divided by the loss on each default.
What does the number leave out?
A break-even default rate is a cushion, not a forecast: whether 4.7% is comfortable depends on how often default rates have run above it and for how long. It also assumes investment grade loses nothing; if investment grade lost 10 basis points a year, the break-even would rise to 4.86%. Recovery is the soft number: it tends to fall in exactly the years defaults rise, so a 30% assumption can flatter the cushion. And the calculation ignores price volatility, which matters to anyone who must mark the portfolio before the bonds mature.
Where candidates lose it
The frequent slip is saying 3.3%, treating every default as a total loss. With 30% recovery, each default costs 70%, and dividing by 0.7 is the whole point of the puzzle.
The second is using the full 450 basis points rather than the 330 excess over investment grade. The question compares two portfolios, so only the difference in spread buys the cushion.
What the interviewer asks next
If recovery falls to 20% in a downturn, what is the new break-even default rate?
What default rate does the full 450 basis point spread cover if investors demanded no extra return for risk?
Why do recoveries tend to fall when default rates rise?

p	the default probability in any one year, 2%
n	the number of years, 5
(1-p)^n	the chance of surviving all n years

p_AD	one year default rate from A, 0.5%
p_AA	chance of staying A for a year, 92%
p_AB	chance of moving from A to BBB, 7.5%
p_BD	one year default rate from BBB, 2%

EAD	exposure at default, the amount owed if the borrower defaults, Rs crore
PD	probability of default over the year
LGD	loss given default, the share of the exposure lost after recoveries

Delta s	the widening in the issuer's spread, 0.50 percentage points
D_s	spread duration, the price change per point of spread, about 2.64 years here
100	the price at a reset when the margin is fair

Try it first

Why does adding 2% five times overstate it?

What is the fastest correct route?

Why does a credit desk care about a 0.4 point gap?

Where candidates lose it

What the interviewer asks next

Try it first

Why can you not just double 0.5%?

How do you set it up so nothing is missed?

What does the migration path tell a credit investor?

Where candidates lose it

What the interviewer asks next

Try it first

What goes into expected loss?

What does the answer mean for pricing?

Where candidates lose it

What the interviewer asks next

Try it first

Which part of a floater's coupon resets, and which does not?

How much is a 50 basis point shortfall worth today?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the answer not simply 10% plus 10%?

What does perfect correlation change?

Why does a portfolio lender care?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a spread imply a default probability at all?

How does the recovery assumption change the answer?

What does the credit triangle leave out?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a standard coupon create an upfront payment?

Why is the risky duration less than five?

What happens when the spread is below the coupon?

Where candidates lose it

What the interviewer asks next

Try it first

Why divide by the loss, not the default rate?

What does the number leave out?

Where candidates lose it

What the interviewer asks next