Debt Capital Markets puzzles, solved step by step

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

Showing 31–39 of 39 · filtered from 100Clear filters

071You hold Rs 100 crore face of a 5-year corporate bond with a DV01 of 0.043 per Rs 100 of face. You want to hedge its interest rate risk by shorting a 10-year government bond whose DV01 is 0.068 per Rs 100. How much face value of the government bond do you short?Duration and convexityCoreFixed income asset managementSyndicate desks
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How much of the government bond do you short?
Show the worked solution
Short about Rs 63.2 crore face of the government bond. The corporate position moves Rs 100 crore x 0.043%, Rs 4.3 lakh, for each basis point. Each Rs 1 crore of the 10-year government bond moves Rs 6,800 per basis point. Matching the two takes 4.3 lakh over 6,800, about 63.2 lots of Rs 1 crore. The hedge ratio is the ratio of the DV01s, 0.043 over 0.068, not one for one on face value.
What exactly are you trying to balance?
Two children on a seesaw balance when weight times distance from the pivot matches on both sides, not when they weigh the same. A rate hedge balances when the rupee change per basis point matches on both sides, so you hedge DV01 against DV01, not face value against face value. The corporate bond's DV01The change in a bond position value for a one basis point change in yield, in rupees. is 0.043 per Rs 100, so Rs 100 crore of it gains or loses Rs 4.3 lakh for every basis point. That is the number the short has to offset.
Rs 100 crore of the corporate bond at a DV01 of 0.043 balances Rs 63.2 crore of the government bond at a DV01 of 0.068, both carrying Rs 4.3 lakh per basis point, while shorting a matching Rs 100 crore would over-hedge by Rs 2.5 lakh per basis point.
The relationship
$F_{hedge} = F \times \frac{DV01_{corp}}{DV01_{gov}} = 100 \times \frac{0.043}{0.068} = 63.2\ \text{crore}$
F the face value you hold, Rs 100 crore
DV01_corp the corporate bond's price change per basis point, per Rs 100
DV01_gov the government bond's price change per basis point, per Rs 100
What it says in wordsScale the hedge so that its rupee move per basis point equals the position's.
Why do you need less of the government bond than you hold?
The 10-year government bond has a longer duration, so each rupee of it moves more when rates move: 0.068 per Rs 100 against 0.043. A smaller position in the more sensitive bond carries the same rupee risk. Check the balance: Rs 63.2 crore x 0.068% is Rs 4.3 lakh a basis point, the same as the corporate position. If rates fall 20 basis points in parallel, the corporate bond gains about Rs 86 lakh and the short loses about Rs 86 lakh.
Then say what the hedge does not cover, because that is the follow-up. A DV01 hedge removes the risk of a parallel move in rates, but it leaves you exposed to the curve twisting between 5 and 10 years and to the corporate bond's credit spread moving. If 5-year yields rise while 10-year yields stay put, the hedge does nothing for you. Desks often hedge with a bond or swap closer in maturity for exactly this reason, and rebalance as DV01s drift with time and rates.
Where candidates lose it
The instinctive answer is Rs 100 crore, shorting the same face value you hold. With a longer, more sensitive hedging bond that over-hedges by more than half and turns a long rate position into a short one.
The second slip is inverting the ratio and shorting Rs 158 crore. Check the direction with intuition: the hedging bond is more sensitive, so you need less of it, not more.
What the interviewer asks next
Rates fall 20 basis points in a parallel move. What is the profit or loss on each leg?
The 5-year yield rises 10 basis points and the 10-year is unchanged. What happens to the hedged position?
Why might you hedge with a 5-year interest rate swap instead?
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?
078A 3-year bond pays a 10% annual coupon and yields 10%, so it prices at par. Work out its Macaulay duration from a table of present values, and explain why the answer is less than 3 years.Duration and convexityCoreFixed income asset management
Try it first
Before building the table: roughly where does the duration land?
Show the worked solution
The Macaulay duration is about 2.74 years. Discount each cash flow at 10%: 9.09 at year 1, 8.26 at year 2 and 82.64 at year 3, adding to the price of 100. Weight each year by its share of the price: 1 x 9.09 plus 2 x 8.26 plus 3 x 82.64 is 273.55, over 100. It is below 3 because the coupons are paid before maturity and pull the average in.
What is duration actually averaging?
Suppose a friend owes you money and pays a little next month, a little the month after, and most of it in the third month. Asked when, on average, you got paid, you would not say the third month: some of the money came earlier. Macaulay duration is the average time until you are paid, with each payment weighted by its present value as a share of the bond's price. Present values rather than face amounts, because a rupee that arrives later is worth less today and should carry less weight.
Year Cash flow Discount factor at 10% Present value Share of price Year x share
1 10 0.9091 9.09 9.09% 0.0909
2 10 0.8264 8.26 8.26% 0.1653
3 110 0.7513 82.64 82.64% 2.4793
Total 130 100.00 100.00% 2.7355
The present values add to the price of 100, and the year-weighted shares add to a duration of 2.7355 years.
Placed as weights on a time line, the present values 9.09, 8.26 and 82.64 balance at 2.74 years, a little inside the 3 year maturity, because the two early coupons pull the balance point towards today.
The relationship
$D_{Mac} = \sum_t t\,\frac{PV_t}{P} = \frac{1(9.09) + 2(8.26) + 3(82.64)}{100} = 2.74$
t the year a cash flow arrives
PV_t the present value of that cash flow at the 10% yield
P the bond price, the sum of the present values
What it says in wordsWeight each payment date by how much of today's price arrives on that date.
Why is it always below maturity for a coupon bond?
Any payment before the final date pulls the balance point towards today, so only a zero-coupon bond has a duration equal to its maturity. Raise the coupon and the pull grows: the same 3-year bond with a 15% coupon, still discounted at 10%, has a duration of 2.65 years. Divide by one plus the yield and you get the modified durationMacaulay duration divided by one plus the yield. It gives the approximate percentage price change for a one point change in yield., 2.49: a 1 point rise in yield should take about 2.49% off the price. The exact price at 11% is 97.56, a fall of 2.44%, close to the estimate.
Where candidates lose it
The common error is weighting the years by the raw cash flows, 10, 10 and 110, instead of their present values. On this bond it gives 2.77 years: close enough to look right and wrong enough to fail the first follow-up, because it ignores that later money is worth less.
The other loss is saying duration equals maturity for any bond. It does only for a zero. Say that once, with the reason, and you have answered the why before it is asked.
What the interviewer asks next
What is the modified duration, and what price change does it predict for a 50 basis point rise in yield?
Without calculating, is the duration of a 3-year zero-coupon bond higher or lower than this one?
What happens to this bond's duration if its yield rises to 15%, and why?
081A Rs 1,000 crore 5-year bond is priced at 100 and trades at 100.40 on the break. Its modified duration is 4.5. How many basis points did the issuer leave on the table, what is that in rupees, and was a 10 basis point new issue premium too generous?Issuance and refinancing arithmeticCoreSyndicate desks
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How many basis points of yield is a 0.40 point price rise on this bond?
Show the worked solution
About 8.9 basis points, or roughly Rs 4 crore, and yes, 10 basis points looks generous. A 0.40 point rise on a duration of 4.5 is 0.40 / 4.5 = 8.9 basis points of tightening. On Rs 1,000 crore, 0.40 points is Rs 4.0 crore of value that went to investors. Almost all of the premium came back on the first trade, so the book would probably have cleared tighter.
How do you turn a price jump into basis points?
A shop that sells out of a new phone in an hour, and then sees it resold online for more, has learned that it priced too low. A bond's first trades tell the issuer the same thing. Modified durationThe approximate percentage price change for a one point change in yield. is the exchange rate between price and yield: here a 1 basis point move in yield moves the price by about 4.5 hundredths of a point. So a price rise of 0.40 points means the market is valuing the bond about 8.9 basis points tighter than where it was priced.
A 0.40 point rise on a duration of 4.5 is 8.9 basis points of tightening and Rs 4.0 crore of value, which is nearly all of the 10 basis point premium the issuer paid, leaving only 1.1 basis points that the market still required.
The relationship
$\Delta y \approx \frac{\Delta P / P}{D_{mod}} = \frac{0.40\%}{4.5} = 0.089\% \approx 8.9\text{ bp}$
Delta P / P the percentage price change on the break, 0.40%
D_mod modified duration, 4.5
Delta y the implied change in yield
What it says in wordsDivide the percentage price move by duration to get the yield move that caused it.
What does the Rs 4 crore actually cost the issuer?
It is paid through the coupon, not written as a cheque. Pricing about 8.9 basis points too wide costs Rs 0.89 crore a year on Rs 1,000 crore, for five years: Rs 4.4 crore in total, or about Rs 3.6 crore in today's money at an assumed 7.5% yield, the same order as the Rs 4.0 crore jump in the bond's price. The first trade after pricing tells you how much of the premium was needed, because it shows where investors will buy the bond once the allocation is done.
So was 10 basis points too much?
On these numbers, most of it. But say two things before you convict the syndicate desk. First, strip out the market: if benchmark yields fell 3 basis points during the same session, only 5.9 basis points of the move belongs to the deal. Second, some positive performance is deliberate. Investors who were allocated want to see the bond trade well, and a flat or weak break makes the issuer's next deal harder to fill. A generous premium is a cost this time and an investment in the next book; the judgement is whether nearly the whole premium needed to be spent.
Where candidates lose it
The fast wrong answer treats 0.40 points as 40 basis points. Points are price, basis points are yield, and duration converts one into the other. Say the division out loud so the interviewer hears the method.
The second loss is a one-sided verdict. Calling the premium wasted without adjusting for the market move, or without mentioning why desks want some aftermarket performance, sounds like arithmetic without judgement.
What the interviewer asks next
The bond had instead traded at 99.80 on the break. What does that tell you, and who is unhappy?
How would you separate the deal's own performance from a market rally on the same day?
Why might an issuer accept paying a premium it does not strictly need?
085You have two ropes. Each takes exactly 60 minutes to burn from one end to the other, but they burn unevenly, so half a rope does not take 30 minutes. With a lighter and nothing else, how do you measure exactly 45 minutes?Logic and brainteasersCoreSyndicate desks
Try it first
What is the one move that makes this possible?
Show the worked solution
Light rope A at both ends and rope B at one end at the same moment. Rope A burns out after exactly 30 minutes. At that instant, light the other end of rope B, which has 30 minutes of burn left. With two flames it finishes in 15 minutes, so rope B goes out at exactly 45 minutes.
Why does lighting both ends always give 30 minutes?
Two people painting a fence from opposite ends meet when the whole fence is painted, whatever the pace on each stretch; if the job is one hour for one painter, together they finish in half an hour. A rope's burn time behaves the same way: two flames consume the rope's 60 minutes of burn between them, so they must meet after 30 minutes, even though the meeting point is not the middle of the rope. Unevenness changes where they meet, never when.
Rope A, lit at both ends, burns out at 30 minutes; that is the signal to light rope B's other end, and the 30 minutes of burn left in rope B then finish in 15 minutes, at the 45 minute mark.
Why does rope B have exactly 30 minutes left?
Rope B has burned from one end for 30 minutes, so 30 of its 60 minutes of burn are gone and 30 remain, spread unevenly along whatever length is left. Lighting its other end applies the same halving trick to what remains: 30 minutes of burn with two flames takes 15. 30 plus 15 is 45. The trick works on any remaining burn time, not just a whole rope.
The relationship
$t_{\text{both ends}} = \frac{t_{\text{one end}}}{2} \qquad 30 + \frac{30}{2} = 45$
t one end burn time with one flame
t both ends burn time with two flames, always half
What it says in wordsTwo flames halve whatever burn time is left, so a half followed by a half of a half gives 45 minutes.
Say what the puzzle is testing, briefly: separating what you know (total burn time) from what you do not (where along the rope that time sits). A desk reading a bond's cash flows faces the same split: the total is fixed, the timing can be lumpy.
Where candidates lose it
The common wrong move is cutting a rope in half and assuming each half burns for 30 minutes. The question tells you the burn is uneven precisely to rule that out, and an interviewer will stop you there.
The second loss is lighting both ropes at both ends at once and then being stuck with two 30 minute timers. Keep one flame on rope B back until rope A tells you 30 minutes have passed.
What the interviewer asks next
How would you measure exactly 15 minutes with the same two ropes?
With only one rope, which times can you measure?
Using both ropes, list every time you can measure exactly.
088The yield on a 10-year zero-coupon bond doubles from 3% to 6%. Does its price halve? Work out the old and the new price per Rs 100 of face value.Bond pricing and yieldCoreFixed income asset management
Try it first
Roughly how much does the price fall?
Show the worked solution
No. The price falls from about 74.41 to 55.84 per Rs 100, a fall of 25.0%, not 50%. A zero's price is 100 divided by one plus the yield, compounded for ten years. Doubling the yield moves one plus the yield only from 1.03 to 1.06, so the price is divided by (1.06/1.03) to the tenth, about 1.33. Halving the price would need a yield near 10.4%.
Why is doubling the yield not doubling the discount?
A shop that raises its markup from 3% to 6% has doubled the markup, but the price tag only goes from 103 to 106. The thing that multiplies through is one plus the rate, not the rate. A bond's price depends on (1 + y) compounded over its life, so doubling y from 3% to 6% changes the base only from 1.03 to 1.06, about 2.9% a year. Ten years of that is a factor of 1.333, which takes about a quarter off the price.
A 10-year zero priced at 74.41 at a 3% yield falls to 55.84 at 6%, a 25.0% drop, well short of the 37.20 that halving would need, which would take a yield of about 10.4%.
The relationship
$P = \frac{100}{(1+y)^{10}}: \quad \frac{100}{1.03^{10}} = 74.41, \quad \frac{100}{1.06^{10}} = 55.84$
P price per Rs 100 of face value
y the annual yield
10 years to maturity, with nothing paid before then
What it says in wordsDiscount the single Rs 100 payment back ten years at each yield.
How does duration check the answer?
The modified duration of a 10-year zero at 3% is 10 / 1.03, about 9.71. Multiplied by a 3 point rise that predicts a fall of about 29.1%, against the true 25.0%. The straight-line estimate overshoots on a large move because the price curve bends: each extra point of yield takes off less than the one before. That bend is convexity, and a 3 point move is big enough to show it. For small moves duration is close; for large ones, reprice the bond directly.
Where candidates lose it
The trap is answering yes, because doubling feels proportional. Price is not inversely proportional to yield; it is inversely proportional to one plus the yield, compounded.
The second loss is getting 25% right and then being unable to say why duration gave 29%. One sentence on convexity turns a correct number into an understood one.
What the interviewer asks next
What yield would halve the price from 74.41?
If the yield falls from 3% to 0%, what happens to the price, and is the move bigger or smaller than the fall you just computed?
Would a 10-year bond paying a 6% coupon fall by more or less than the zero for the same move?
091A fund wants to buy Rs 5,000 crore of a bond segment where average daily trading is Rs 1,000 crore, and it will not take more than 2% of each day's volume. How long does it take to build the position, and what does that say about liquidity?Estimation and market sizingCoreFixed income asset managementSyndicate desks
Try it first
Roughly how long does the fund need?
Show the worked solution
About 250 trading days, roughly a year. The fund may buy 2% of Rs 1,000 crore, which is Rs 20 crore a day, and Rs 5,000 crore divided by Rs 20 crore is 250. The position is five full days of the whole market's trading, which makes it illiquid for this fund: it would take about as long to sell as to buy.
Why is the answer not five days?
Imagine wanting to buy 500 kilos of tomatoes from a village market that sells 100 kilos a day. In theory it is five days of the market's supply; in practice, if you take everything, prices jump and the regular buyers go home empty handed. So you decide to take no more than a couple of kilos a day. The limit on your share of daily volume, not the market's total volume, sets how fast you can trade, and here that limit is Rs 20 crore a day. Rs 5,000 crore at Rs 20 crore a day is 250 days.
At 2% of Rs 1,000 crore a day the fund buys Rs 20 crore daily and needs 250 trading days, about a year, while a 10% share of volume would take 50 days and a segment ten times as liquid 25 days.
The relationship
$\text{Days} = \frac{\text{Position}}{\text{ADV} \times \text{participation}} = \frac{5{,}000}{1{,}000 \times 2\%} = 250$
Position the amount to buy, Rs 5,000 crore
ADV average daily volume, Rs 1,000 crore
participation the most of each day's volume the fund will take, 2%
What it says in wordsDivide what you want to trade by what you are allowed to trade each day.
What does this tell you about liquidity?
Liquidity belongs to a position, not to a market: the same bonds are liquid for a Rs 50 crore holder and illiquid for a Rs 5,000 crore holder. Days to trade is the simplest honest measure. At 250 days, the fund carries a year of market risk while it builds, and faces the same year if it ever needs to sell, which matters most exactly when others are selling too. Daily volume also falls in a stressed market, so the exit could take longer than the entry. A desk would size the position down, accept a higher participation rate and more price impact, or look for a block trade or a new issue where it can take size in one go.
Where candidates lose it
The fast wrong answer is five days, dividing the position by the whole market's volume. It ignores the participation limit that the question hands you.
The second loss is giving 250 days and stopping. The interviewer wants the implication: this position is illiquid for this fund, the exit is the real risk, and there are ways to get size faster, each with a cost.
What the interviewer asks next
If the fund accepts 5% of daily volume, how long does it take, and what does it give up?
Daily volume halves in a sell-off. How long would it take to exit the full position at 2%?
Why might a new issue be a better way to build this position than the secondary market?
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
Try it first
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?
099At initial price thoughts of 150 basis points over the benchmark, a bond's order book is 4 times covered. Each 5 basis points of tightening loses 10% of the original demand. How far can you tighten and still keep the book at least 2 times covered?Issuance and refinancing arithmeticCoreSyndicate desks
Try it first
Where does the book hit 2 times cover?
Show the worked solution
You can tighten 25 basis points, to 125, and still be 2 times covered. Each 5 basis point step loses 10% of the original demand, which is 0.4x of cover. Going from 4.0x to 2.0x gives up 2.0x, or five steps, so 5 x 5 = 25 basis points. On a Rs 500 crore deal the book falls from Rs 2,000 crore to Rs 1,000 crore, and the issuer saves Rs 1.25 crore a year.
What is actually being traded off?
A shopkeeper with a queue of forty customers for twenty items can raise the price, and some customers will walk away; the question is how high to go before the queue gets too short to be comfortable. Book-building trades cover for price: each step tighter saves the issuer money and costs orders, and cover is the buffer against a weak aftermarket. Here every 5 basis points costs 0.4x, because the loss is 10% of the original book each time.
Starting at 4.0x cover at 150 basis points, each 5 basis points of tightening removes 0.4x, so the book reaches the 2.0x floor at 125 and any further tightening leaves it under-covered.
The relationship
$\text{cover}(s) = 4.0 - 0.4 \times \frac{150 - s}{5} \ge 2.0 \;\Rightarrow\; 150 - s \le 25$
s the final spread in basis points
0.4 the cover lost per 5 bp step, 10% of the original 4.0x
2.0 the minimum cover you want to keep
What it says in wordsCover falls by the same amount every step, so divide the cover you can spare by the cover each step costs.
Would you really go all the way to 125?
Not automatically. The linear rule is a model of the book; real books drop in lumps, because price-sensitive orders carry limits and the orders that leave first are often the highest quality long-term investors. Landing exactly on the 2.0x floor leaves no margin if a few orders drop after the final terms. A syndicate desk might stop one step short, at 130 with 2.4x cover, giving up Rs 0.25 crore a year of saving on Rs 500 crore for a safer book and a better chance of a positive break. The arithmetic sets the limit; the judgement picks the point inside it.
Where candidates lose it
The common slip is treating 10% as 10% of the remaining book, which makes each step smaller and the answer wider than 25 basis points. The question says original demand, so the steps are equal.
The second loss is stopping at the number. The interviewer wants to hear what cover is for, why the real book is lumpier than the model, and why a desk might leave some tightening unused.
What the interviewer asks next
If each step lost 10% of the remaining book instead, how far could you tighten?
What else in the book, besides its size, would you look at before tightening?
Why might an issuer prefer a larger deal at 130 to the planned size at 125?

F	the face value you hold, Rs 100 crore
DV01_corp	the corporate bond's price change per basis point, per Rs 100
DV01_gov	the government bond's price change per basis point, per Rs 100

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%

Expected recovery	Loss given default	Implied annual PD
0%	100%	3.0%
40%	60%	5.0%
70%	30%	10.0%

Year	Cash flow	Discount factor at 10%	Present value	Share of price	Year x share
1	10	0.9091	9.09	9.09%	0.0909
2	10	0.8264	8.26	8.26%	0.1653
3	110	0.7513	82.64	82.64%	2.4793
Total	130		100.00	100.00%	2.7355

Try it first

What exactly are you trying to balance?

Why do you need less of the government bond than you hold?

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

What is duration actually averaging?

Why is it always below maturity for a coupon bond?

Where candidates lose it

What the interviewer asks next

Try it first

How do you turn a price jump into basis points?

What does the Rs 4 crore actually cost the issuer?

So was 10 basis points too much?

Where candidates lose it

What the interviewer asks next

Try it first

Why does lighting both ends always give 30 minutes?

Why does rope B have exactly 30 minutes left?

Where candidates lose it

What the interviewer asks next

Try it first

Why is doubling the yield not doubling the discount?

How does duration check the answer?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the answer not five days?

What does this tell you about liquidity?

Where candidates lose it

What the interviewer asks next

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Why divide by the loss, not the default rate?

What does the number leave out?

Where candidates lose it

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What is actually being traded off?

Would you really go all the way to 125?

Where candidates lose it

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