Debt Capital Markets puzzles, solved step by step
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009Quick maths: what is the accrued coupon on Rs 350 crore of a 7.25% bond for 73 days, on an actual/365 basis?Private credit
Try it first
Before multiplying: what fraction of a year is 73 days on an actual/365 basis?
Show the worked solution
Rs 5.075 crore. The annual coupon is 7.25% of Rs 350 crore, Rs 25.375 crore. On actual/365, 73 days is exactly one fifth of a year, because 73 times 5 is 365. One fifth of Rs 25.375 crore is Rs 5.075 crore, which a buyer settling on day 73 pays the seller on top of the clean price.
What do you look for before you multiply?
A friendly fraction. Mental maths on a desk is mostly spotting which number makes the rest easy. 73 is exactly a fifth of 365, so the whole calculation collapses to one fifth of the annual coupon. It is like splitting a Rs 25,375 bill between five friends: nobody reaches for a calculator once they see it is a clean fifth. Say the fraction out loud first, so the interviewer hears the shortcut rather than watching you grind through 7.25 times 350 times 73.
Seventy three days is exactly one fifth of a 365 day year, so the accrued coupon is one fifth of the Rs 25.375 crore annual coupon on Rs 350 crore at 7.25%, which is Rs 5.075 crore. How do you get the annual coupon quickly?
Split the rate. 7% of 350 is 24.5 and a quarter per cent of 350 is 0.875, so the annual coupon is Rs 25.375 crore. Breaking an awkward rate into a round rate plus a small piece keeps each multiplication in your head. Then divide by five: 25 divided by 5 is 5, and 0.375 divided by 5 is 0.075, so Rs 5.075 crore. Another route is 350 divided by 5 first, which is 70, and 7.25% of 70 is 5.075. Either way, two steps.
The relationshipAI accrued interest, Rs crore F face value held, Rs 350 crore c annual coupon rate, 7.25% d days since the last coupon, 73 What it says in wordsAccrued interest is the annual coupon times the share of the year that has passed since the last payment.Why does accrued interest matter on a trade?
Because the seller has earned 73 days of coupon but the buyer will receive the whole next coupon. The buyer pays the accrued interest to the seller at settlement, so the cash that changes hands is the clean price plus accrued, the dirty price. On Rs 350 crore, Rs 5.08 crore is real money. Also say the limit: the day count convention varies by market and by instrument, and actual/365, actual/actual and 30/360 give slightly different answers, so check the bond's terms before you settle.
Where candidates lose it
The loss here is speed, not knowledge. Candidates multiply 350 by 7.25% by 73 and divide by 365 the long way, drop a decimal somewhere, and give 50.75 or 0.5075 instead of 5.075.
The second slip is quietly switching to a 360 day year, which gives about 5.145. The question said actual/365; repeat the convention back as you answer so the interviewer knows you heard it.
What the interviewer asks next
- What is the accrued interest after 146 days on the same holding?
- The bond is quoted at a clean price of 101.20. What does the buyer pay in total per Rs 100 of face?
- Why do markets quote bonds on a clean price rather than a dirty price?
034What is 1 basis point worth on Rs 2,500 crore for a year, for a quarter and for one day?Syndicate desks
Try it first
One basis point on Rs 2,500 crore for a year is:
Show the worked solution
Rs 25 lakh a year, Rs 6.25 lakh a quarter and about Rs 6,850 a day. A basis point is 0.0001, so Rs 2,500 crore times 0.0001 is Rs 0.25 crore, Rs 25 lakh a year. Divide by four for a quarter. Divide by 365 for a day, which gives Rs 6,849 on an actual/365 basis, or Rs 6,944 on a 360-day basis.
Why would a desk ask something this simple?
A shopkeeper who knows that one rupee off a product's price costs her Rs 3,000 a month in margin negotiates very differently from one who has to work it out after the customer leaves. Every pricing conversation in debt markets is in basis points, and the listener has to turn them into rupees on the deal in front of them instantly. An issuer who hears that 5 basis points is on the table wants to know that means Rs 1.25 crore a year, not to wait for a spreadsheet.
The relationship0.0001 one basis point, a hundredth of one per cent 0.25 crore a quarter of Rs 1 crore, which is Rs 25 lakh What it says in wordsMultiply the deal size by one ten-thousandth, then convert crore to lakh by multiplying by 100.One basis point on Rs 2,500 crore is Rs 25 lakh a year, Rs 6.25 lakh a quarter and Rs 6,849 a day on an actual/365 basis, and five years of it discounted at 8% is worth about Rs 99.8 lakh today. What changes when the basis point is on price instead of coupon?
The numbers above are one basis point of coupon or spread, paid each year. A basis point of yield on a bond's price is a different quantity. A one basis point move in yield changes a bond's value by roughly its duration times the notional times 0.0001, so on a five-year bond with duration near 4 it is about Rs 1 crore, not Rs 25 lakh. The two agree once you see why: five years of Rs 25 lakh, discounted at 8%, is worth about Rs 99.8 lakh today. Duration is roughly the present value of a stream of basis points.
Day counts are the last detail worth a sentence. Many rupee bonds count actual days over 365, while money market instruments and many floating rate loans elsewhere use 360; confirm the convention in the term sheet rather than assume it. The difference on one day is about Rs 95 here, trivial on a day and material over a large book, which is why the convention is always named in the documents.
Where candidates lose it
The common slip is a zero: Rs 2.5 lakh or Rs 2.5 crore, because crore, lakh and 0.0001 are three unit changes in one line. Say the steps aloud: 0.0001 of 2,500 crore is 0.25 crore, which is 25 lakh.
The second loss is treating a basis point of yield and a basis point of coupon as the same thing. On a five-year deal they differ by a factor of about four, and a syndicate desk will ask which one you mean.
What the interviewer asks next
- An issuer saves 7 basis points on a Rs 2,500 crore, 5-year deal. What is that worth today at 8%?
- What is the price value of a basis point on Rs 2,500 crore of a bond with modified duration 6.5?
- Why do money market instruments often use a 360-day year?
051A bond's yield moves from 7.20% to 7.38%. By how many basis points has it moved, and by what percentage? Which number does a bond desk quote?Fixed income asset management
Try it first
How would a DCM banker describe this move on a call?
Show the worked solution
The yield has moved 18 basis points, a 2.5% relative change, and the desk quotes the 18 basis points. 7.38 minus 7.20 is 0.18 percentage points, and one basis point is one hundredth of a point. The relative change is 0.18 over 7.20, or 2.5%. Saying the yield rose 2.5% invites a listener to hear 9.70%, so rate moves are quoted as absolute changes in basis points.
Why are there two different answers to one move?
Think of a batting side's run rate going from 6 an over to 9. You can say it rose by 3 runs an over or by 50%, and both are true. Yields work the same way, except the thing being measured is already a percentage. An absolute change in a yield is measured in percentage points; a relative change is a percentage of a percentage, and spoken aloud the two sound alike. Here the absolute change is 0.18 points and the relative change is 0.18 over 7.20, or 2.5%.
The yield moved from 7.20% to 7.38%, which is 0.18 percentage points or 18 basis points, and also a 2.5% relative change; said carelessly, a 2.5% rise can be heard as a move to 9.70%, a 250 basis point error. Why does a bond desk insist on basis points?
A basis point is one hundredth of a percentage point, a unit small enough to price with and impossible to confuse with a relative change. Say 18 basis points and nobody on the call can hear 9.70%. The unit also makes the money easy to see: on a Rs 500 crore issue, 18 basis points of extra coupon is 0.0018 x 500 crore, Rs 90 lakh a year. Spreads, new issue premiums and fee cuts are all quoted in basis points for the same reason.
The relationshippp percentage points, the absolute gap between two yields bp basis points, one hundredth of a percentage point 0.18 / 7.20 the relative change, the move as a share of the starting yield What it says in wordsThe absolute move is the gap between the two yields; the relative move is that gap divided by where the yield started.The relative figure is not useless. It compares moves in proportion: a 3.00% yield rising to 3.18% is also 18 basis points, but it is a 6% relative jump against 2.5% here. In the room, give the basis point number first, give the relative number only if asked, and label each one.
Where candidates lose it
The trap is answering 2.5% and stopping, or saying the yield rose 2.5% without saying relative to what. On a desk that sentence gets corrected at once, because the natural hearing is that the yield went up 2.5 percentage points, to 9.70%.
The second loss is a slip in the conversion: 0.18 points is 18 basis points, not 1.8 and not 180. Say one basis point is one hundredth of a point as you convert, and the number checks itself.
What the interviewer asks next
- A spread tightens from 250 to 210 basis points. What is the relative change, and when would a credit investor quote that instead?
- On Rs 750 crore of issuance, what is 12 basis points of coupon worth each year?
- A yield doubles from 0.50% to 1.00%. How many basis points is that, and why does the relative change mislead here?
083If a given date is a Monday this year, what day of the week will the same date be one year from now? When does the answer change?Oaktree Capital ManagementLos Angeles · 2022
Try it first
Answer inside five seconds.
Show the worked solution
Tuesday, or Wednesday if 29 February falls in between. A normal year is 365 days, which is 52 weeks and 1 day, so every date moves on one weekday. When the year you step across contains 29 February, it is 366 days, 52 weeks and 2 days, and the date moves on two. The remainder after dividing by 7 does all the work.
Why does the weekday move by exactly one?
A clock that runs for 25 hours ends up one hour past where it started, because 24 of those hours bring it round in a full circle. Weeks are the same circle with seven stops. Only the remainder after dividing the day count by 7 moves the weekday, and 365 divided by 7 leaves a remainder of 1. The 52 full weeks bring you back to Monday; the one extra day carries you to Tuesday.
A normal year of 365 days is 52 full weeks plus one day, so a Monday date falls on a Tuesday the next year; a year containing 29 February has 366 days and moves the same date to a Wednesday. When exactly does the answer become Wednesday?
When 29 February sits between the two dates. That depends on the date as well as the year. 15 March 2027 is a Monday, and 15 March 2028 is a Wednesday, because 29 February 2028 falls in between: 366 days. Step on again and 15 March 2029 is a Thursday, only 365 days later, because the next 29 February is still years away. Ask whether 29 February lies inside the year you are stepping across, not whether either year is a leap year. Leap years are those divisible by 4, except century years, which count only when divisible by 400.
The relationship52 x 7 364 days, which leaves the weekday unchanged +1, +2 the leftover days that move the weekday on What it says in wordsDivide the day count by seven and the remainder is how far the weekday moves.Why would a credit interviewer bother with this?
Because bonds and loans live on calendars. A coupon due on the 15th of March lands on a different weekday every year, and when it lands on a weekend or holiday the documents say whether it moves to the next business day and whether interest accrues for the extra days. Day count conventions such as actual/365 turn the leap day into a slightly larger coupon in some years. Quick calendar arithmetic is how you catch a payment schedule that has been rolled wrongly.
Where candidates lose it
The instinctive answer is Monday, because it is the same date. It takes one sentence about 52 weeks being 364 days to fix, but candidates who say Monday first rarely recover the room.
The second loss is the leap-year rule stated too broadly. What matters is whether 29 February falls between the two dates, so a date in January of a leap year and a date in March of the year before can both move by two.
What the interviewer asks next
- If today is a Monday, what day is it 100 days from now?
- A 5-year bond pays annual coupons on 15 March. How many of those five coupon dates can fall on a weekend?
- Why was 1900 not a leap year but 2000 was?
Asked at Oaktree Capital Management, Generalist, Los Angeles, 2022 (Wall Street Oasis):
If [a date] is a Monday what week of the day would [same date] be a year from now?
