Fixed-Income Instruments, Issuance and Trading

Finance-Plus Ring · Branch FI (Fixed Income Analytics) · Node FI1.05 · ~14 focused hours, mastery gate ≥ 85%

Two desks agree that a listed Indian corporate bond is worth 97.337659 per 100. Same bond, same settlement date, same ₹10 crore of face value, same screen. One of them wires ₹9,98,00,124.64. The other wires ₹9,97,87,658.89.

Neither has made an arithmetic mistake. The gap of ₹12,465.75 is entirely a difference in how many days each desk thinks have accrued since the last coupon, and the two answers are 107/365 of a year and 105/360 of a year on exactly the same pair of dates. One of those conventions is what the regulator of Indian listed corporate debt specifies; the other is what the government-securities market uses. A trader who reaches for the wrong one has not mispriced anything. They have simply misread the contract.

That is the shape of everything here. A bond is a document before it is a cash flow, and most of the money careful people lose in fixed income is lost between the document and the spreadsheet.

A coupon that steps up in a year they modelled flat. A floating-rate note whose margin is fixed while the index is not. A call schedule with a make-whole formula they read as a par call. An index-linked principal that a deflation floor rescues at maturity but not in the coupons along the way.

Everything else in the Fixed Income branch assumes you have already read the document. Pricing off a discount curve assumes you know what the cash flows are. Duration assumes you know when they arrive. Bootstrapping assumes you know which bond is a par bond. Option-adjusted spread assumes you know the call schedule. Each of those is a genuine analytical skill and each of them is downstream of an act of reading.

The numbering here is misleading, and it is worth saying plainly. Study this before FI1.01, not after. The fixed-income audit that proposed the branch wanted it as the branch's opening node, and the id it carries is an artefact of when it was written rather than where it sits. The rest of the branch will make more sense once you can look at a term sheet and say what the instrument does.

Three things are being built here. The first is fluency with coupon structures, so that a step-up, a payment-in-kind, a floater and a linker each produce a cash-flow table you can write out without hesitation. The second is settlement arithmetic done properly: the day count, the accrued interest, the full price, the flat price, and the reason a screen shows you one while your bank debits the other.

The third is a working knowledge of how bonds actually get sold and traded, from a Reserve Bank of India auction on a Friday morning to a dealer's bid-ask on an off-the-run Treasury. The price you can transact at is not the price a model produces.

One honest limit, stated at the front. Almost every convention in this node is set by a market body, a regulator or a circular, and every one of them drifts. The arithmetic is permanent; the conventions are not. Wherever a figure or a rule is the kind of thing that changes, it carries a verify flag and names the source you should check it against.

Learning objectives

By the end you can:

1. Read a bond term sheet or offer document and extract the fourteen fields that determine every subsequent calculation, naming the clause each one comes from.
2. Build the cash-flow table for a fixed, step-up, deferred, payment-in-kind, floating or index-linked structure, and state for each one where the issuer's cash strain sits.
3. Compute an index ratio, an inflation-adjusted principal and a real coupon across a stated inflation path, and apply the deflation floor to the right quantity at the right date.
4. Set a floating-rate note's coupon from a reference rate and a quoted margin, compute the discount margin implied by a market price, and state the two conditions under which its price equals par.
5. Compute an accrual fraction under 30/360, actual/actual and actual/360 on the same pair of dates, and say in rupees or dollars what the choice is worth on a stated position.
6. Decompose a settlement amount into full price, accrued interest and flat price, and explain why the market quotes the flat price and settles the full one.
7. Matrix-price a new or illiquid issue by interpolating a comparable-bond yield matrix across rating and maturity, and state the comparability assumptions the answer rests on.
8. Allocate a sovereign auction under both a uniform-price and a multiple-price rule, computing the stop-out, the pro-rata fill, the weighted-average accepted price and the proceeds difference between the two rules on the same bid book.
9. Describe how corporate debt reaches investors through underwritten, best-efforts, private-placement and shelf routes in India and the United States, and say who bears which risk in each.
10. Price the liquidity of a secondary market: convert a bid-ask into a round-trip cost, into basis points of yield, and into the holding period an off-the-run concession must survive to pay for itself.

Prerequisites & connections

Builds on. M0.02 gave you the map of who issues securities and who buys them, and this node fills in the debt half of that map with the actual mechanics. M1.08 gave you liabilities and financing from the issuer's books, including effective-interest amortisation, which is the accounting mirror of every accretion schedule below. M3.01 gave you time value of money, and nothing here needs more mathematics than that: every price in the node is a discounted cash flow, and the difficulty is entirely in knowing which cash flows and on which dates. FI1.05 opens the Fixed Income branch, and it unlocks once you pass M3.01.

Feeds forward. FI1.01 takes the instruments described here and prices them off a discount curve, and owns the whole yield family including the four money-market yield conventions this node deliberately stops short of. FI1.02 takes the same cash flows and measures their rate sensitivity. FI1.03 takes the sovereign issues described here and bootstraps a curve out of them. FI1.04 takes the contingency provisions read off a document here and values them on a tree. FI1.06 (Fixed-Income Portfolio Management I: Liability-Driven and Index-Based) builds portfolios out of these instruments against a liability schedule or a benchmark, and FI1.07 (Active Fixed Income: Yield-Curve and Credit Strategies) trades them; both assume you can already read what you are holding. E11.01 supplies the credit opinion that decides which row of the matrix an issuer belongs in.

The non-overlaps are deliberate and worth stating field by field. FI1.01 owns pricing off a discount curve, yield to maturity, yield to call, yield to worst, the total-return decomposition and the four money-market yield measures (bank discount, holding period, add-on and bond-equivalent), so this node describes money-market instruments as contracts and hands the conversion chain forward untouched. FI1.02 owns duration, convexity and DV01; where a duration appears below it is an input borrowed to price liquidity, never a thing being taught. FI1.03 owns bootstrapping, spot and forward rates and swap spreads. FI1.04 owns the valuation of every embedded option: this node reads call schedules, put schedules, sinking funds and make-whole clauses off the document and computes their contractual cash amounts, and stops exactly where option value begins. E11.01 owns covenants, ratings methodology and recovery analysis. MS1.03 owns repo, the collateral chain and money-market plumbing. FI1.06 owns liability-driven and index-based mandates; FI1.07 owns active curve and credit strategies, including the carry-and-roll-down arithmetic that turns a liquidity concession into a position.

Core teaching content

4.14 Money-market instruments, described here and priced elsewhere

Anything with an original maturity of a year or less is a money-market instrument, and almost all of them are zero-coupon in form. Four types cover the market.

Treasury bills are the sovereign's short-dated paper. India issues 91-day, 182-day and 364-day bills through weekly auctions; the United States issues bills across a similar range. Both are sold at a discount to face.

Commercial paper is a corporate or non-bank finance company's unsecured short-term promise, issued at a discount, and it is the instrument whose rollover risk turns a funding squeeze into a solvency event. A borrower funding long assets with paper that must be resold every 90 days has a maturity mismatch, and the paper does not fail gradually.

Certificates of deposit are a bank's negotiable time deposit. The form differs by market in a way that matters: Indian certificates of deposit are issued at a discount to face value, while large negotiable American certificates are conventionally interest-bearing on an add-on basis, meaning the investor pays face and receives face plus interest. Practice Problem 16 computes both on comparable terms, and the two forms produce different cash flows from the same headline rate.

Repurchase agreements are the fourth, and MS1.03 owns them entirely: the collateral, the haircut, the rehypothecation chain and the role of the central bank's repo window in setting the policy rate. What belongs here is only the observation that a repo is economically a collateralised loan wearing a sale-and-repurchase document, and that the document form is the reason it behaves differently in a bankruptcy from the loan it resembles.

The reason each of these needs its own yield convention is that they are quoted on incompatible bases: a discount rate computed on face value, an add-on rate computed on price, a 360-day year in one market and a 365-day year in another. Converting between them, and knowing which measure belongs next to a coupon bond's yield to maturity, is a self-contained skill with its own worked examples, and FI1.01 owns it.

Describe the instrument here. Convert the yield there.

4.15 What a term sheet has to tell you before you compute anything

Fourteen fields decide every number in this node, and a term sheet that leaves one of them silent is telling you something.

The issuer's exact legal entity and the security's seniority and any security interest come first, because they decide which credit you are analysing. Face value per unit and total issue size come next; the second one is a liquidity variable as much as a size one. Then the coupon rate and its type, the frequency and the payment dates, which together produce the cash-flow table.

The day-count convention and the business-day convention come next and are the two most often skipped. A business-day convention says what happens when a payment date falls on a holiday: following moves it to the next business day, modified following does the same unless that crosses a month end, in which case it moves backward, and adjusted conventions recompute the accrual for the moved date while unadjusted ones do not. The difference is a few days of interest, every period, forever.

The first coupon date matters separately from the frequency, because a first period that is not a whole period produces a short or long first coupon whose amount has to be computed from the actual dates rather than from the annual rate divided by the frequency. Then the maturity date and the redemption amount, then the call schedule, the put schedule, the sinking-fund schedule and the make-whole formula with its named reference security and spread.

Read the ranking of payments and the events of default alongside those, and hand them to the credit analysis rather than to the pricing.

Where the document is silent, write silent. A market default is a guess, and a guess recorded as a fact is how a modelling error becomes an unexplained profit-and-loss line six months later.

Common mistakes & how experts think differently

1. Using the flat price as the settlement amount. The screen shows the flat price and the bank debits the full price, and on a bond three months into a coupon period the difference is most of a coupon. The error survives because it produces a number in the right neighbourhood. An experienced settlement check runs the other way: take the amount actually wired, subtract accrued computed under the document's own convention, and confirm the residual matches the quoted price to the last paisa. On the module's Indian debenture the full price is ₹998,001.246417 and the flat price is ₹973,376.588882, so accrued interest is 2.467397% of the amount actually wired.

1. Porting a day-count convention across markets by habit. An analyst who learned on Indian government securities reaches for 30/360; one who learned on dollar floaters reaches for actual/360. On the same pair of dates those two produce ₹24,500.00 and ₹24,966.67 on a single debenture. The expert habit is to treat the day count as a field to be read rather than a default to be assumed, and to write it into the model as an explicit parameter so that changing it is a one-line change rather than an archaeology exercise.

1. Believing a floating-rate note always prices at par. The identity is true at a reset date and only when the required margin equals the quoted margin. Between resets the fixed current coupon and a moving stub rate pull the price off par, and a change in the issuer's credit pulls it off par permanently. The module's note sits 0.1055352746 per 100 below par thirty days into a period after a 60 basis point move, and would price at 99.35 rather than 100 at a reset if the required margin has widened to 103.7766 basis points. An expert asks two questions before using the identity: is today a reset date, and has the credit moved.

1. Applying the deflation floor to the coupons. The floor protects principal at maturity. Coupons in the deflation years are computed on the unfloored inflation-adjusted principal, and treating them otherwise overstates the module's five-year linker by $1,232.89 on $1,000,000. The tell that you have made this error is a linker whose cash coupon never falls, which is not a property any real linker has.

1. Reading a make-whole call as a par call. The two produce opposite conclusions about who is hurt. On the module's utility notes a par call would take $14,370,216.64 of market value from holders; the make-whole call instead costs the issuer $10,235,239.45 more than the notes are worth. An analyst who models a make-whole as a call at 100 will build a redemption assumption backwards and will treat as likely an event that is deliberately made uneconomic.

1. Treating a matrix price as an observation. It is a construction resting on an evenly spaced rating ladder, a locally linear curve and a set of comparables that match on seniority, sector, optionality and liquidity. Moving one assumption, from AA sitting halfway between AA+ and AA- to sitting 60% of the way toward AA-, moves the module's six-year issue by 0.232356 per 100, which is ₹232,356.13 on ₹10 crore. An expert reports the price with its two load-bearing assumptions named in the same sentence.

1. Ignoring the auction rule when reading a cut-off. Under a uniform-price rule the stop-out is what everybody paid; under a multiple-price rule it is only what the marginal bidder paid, and the weighted-average price is the number that describes the auction. On the module's Indian book the cut-off is ₹99.41 and the weighted average is ₹99.5262828947, and quoting the first as though it were the second understates proceeds by ₹37.210526 crore.

1. Confusing deferral with capitalisation. A deferred-coupon bond postpones cash and leaves the principal alone. A payment-in-kind coupon converts cash interest into more principal, which compounds. Over five years at 11%, capitalising for three of them turns ₹100 crore of principal into ₹136.7631 crore, so the refinancing task at maturity is 36.763100% larger. The cash saved in the early years is real, and so is the wall at the end.

1. Pricing liquidity as though it were free. A yield pickup on an off-the-run or a less liquid issuer is compensation for a cost you pay twice, on the way in and on the way out. The module's off-the-run Treasury needs 1.82291667 years of a 6 basis point pickup to cover the extra round trip. Experts hold the breakeven period in mind before buying the concession, and hold it again before assuming they can exit at the quoted spread in size.

1. Assuming the stated maturity is the cash-flow horizon. A sinking fund shortens the average life without moving the maturity date, a put schedule can end the bond early at the holder's choice, and a call schedule can end it early at the issuer's. The module's sinking-fund example has an average life of 5.33333333 years against a stated seven, and any duration or reinvestment analysis built on the stated maturity is measuring an instrument that does not exist.

Worked examples

Every figure below was computed rather than quoted, and each example states its market and currency in the heading. Where a synthetic entity is used it is labelled synthetic and no real security is being described. The Verify block at the end of the section restates every headline figure at full precision so that a reader rebuilding these can see immediately where a divergence begins.

Worked example 1: Settlement and matrix pricing on an Indian debenture (India, ₹)

Girnar Ispat Ltd (synthetic) has a listed senior unsecured non-convertible debenture outstanding: face value ₹10,00,000 per unit, coupon 8.40% payable annually on 15 June, maturity 15 June 2031. A trade settles on 30 September 2026 in 100 units, so ₹10 crore of face value. The market yield for the credit at that tenor is 9.10% annual. The last coupon was paid on 15 June 2026 and the next falls on 15 June 2027.

Solution. Step 1, the accrual fractions, all three of them. From 15 June 2026 to 30 September 2026 the American 30/360 rule counts 30 × 3 + (30 − 15) = 105 days against a 360-day year, a fraction of 0.2916666667. Actual days elapsed are 15 + 31 + 31 + 30 = 107, and the actual coupon period runs 365 days, so actual/actual gives 0.2931506849. Actual/360 gives 107/360 = 0.2972222222.

Step 2, accrued interest under each. The annual coupon is ₹10,00,000 × 8.40% = ₹84,000.00.

Actual/actual exceeds 30/360 by ₹124.657534 per unit, which is ₹12,465.75 on the trade and 0.508806% of the accrued amount. Actual/360 exceeds 30/360 by ₹466.666667 per unit, ₹46,666.67 on the trade.

Step 3, the full price. Five coupons of ₹84,000 remain, on 15 June 2027 through 15 June 2031, with ₹10,00,000 of principal alongside the last. The first is 1 − 0.2931506849 = 0.7068493151 of a year away and the rest follow at annual intervals.

Step 4, decompose it. Full price ₹998,001.246417 minus accrued ₹24,624.657534 gives a flat price of ₹973,376.588882, which is 97.337659 per 100 and is what the screen shows. Had the desk computed accrued on a 30/360 basis while agreeing the same flat quote, it would have wired ₹997,876.588882 per unit rather than ₹998,001.246417, and the trade would have settled ₹12,465.75 light.

Step 5, cross-check by a second route. On 15 June 2026, ex-coupon, the same five cash flows discount to ₹972,842.941357. Growing that at 9.10% for 0.29315068 of a year gives ₹998,001.246417, matching the direct calculation to 2 × 10⁻¹⁰. Two routes, one number.

Step 6, matrix-price a new issue. Girnar now wants to place a new six-year debenture, unlisted and untraded, rated AA. The comparable matrix, all senior unsecured bullets in the same broad sector:

Treating AA as the midpoint of the notch ladder gives 8.100000% at five years and 8.330000% at seven. Interpolating linearly to six years gives 8.215000%. A ₹10,00,000 face, 8.00% annual-coupon six-year bond at that yield prices at ₹990,125.304359, which is 99.012530 per 100; the coupon that would have priced it at par is 8.21500000%.

Read it. The 8.215000% is not a market observation and should never be reported as one.

Two assumptions carry it. The first is that the rating ladder is evenly spaced in yield, which no agency claims: place AA 60% of the way toward AA- instead and the yield becomes 8.266000%, the price 98.780174, and the answer moves ₹232,356.13 on ₹10 crore of face. The second is that the four comparables match the target on seniority, sector, callability and issue size, because a callable comparable would hand the target an option premium it never sold. Report the price with both assumptions in the same sentence or do not report it.

Worked example 2: A floating-rate note and a Treasury auction (US, $)

Cascade Ridge Funding Corp (synthetic) has a three-year floating-rate note outstanding: $10,000,000 face, quarterly coupons, reference rate plus a quoted margin of 80 basis points, actual/360.

Solution. Step 1, two coupons from a stated rate path. The reference sets at 4.8500% for a 91-day period and at 5.1000% for the following 92-day period.

The 5.6500% is an actual/360 rate. Restated on a 365-day basis it is 5.728472%, and an analyst comparing it to a bond yield without that step understates the note by 7.8 basis points.

Step 2, the discount margin from a market price. The note now has twelve quarterly periods left, the current reference is 4.8000% and the market price is 99.35. Assuming the reference holds at 4.8000% for all remaining periods, the quarterly coupon is 1.4000000000 per 100, and solving for the spread that discounts those cash flows plus par to 99.35 gives a discount margin of 103.7766 basis points. Feeding 103.7766 basis points back through the pricer returns 99.3500000000, a residual of 3 × 10⁻¹³.

Step 3, the price-at-reset identity, and its qualifier. Set the discount margin equal to the quoted margin of 80 basis points on the same note and the price is exactly 100.0000000000. At 40 basis points it is 101.1044637403 and at 120 basis points it is 98.9092494793, so the note moves about 0.0274 per 100 for each basis point of margin near par.

Now break the second condition. Thirty days into the 91-day period the coupon is already fixed at 5.6500%, worth 1.4281944444 per 100 for the full period, while the reference for the remaining 61-day stub has risen 60 basis points to 5.4500%. Discounting 100 plus the fixed coupon at 6.2500% over 61/360 of a year gives a full price of 100.3652980588. Accrued on an actual/360 basis for 30 days is 0.4708333333. The flat price is 99.8944647254, which is 0.1055352746 below par, or $10,553.53 on the position. Had the reference not moved, the flat price would have been 99.9955351693.

Step 4, a uniform-price Treasury auction. The Treasury offers $40.0 billion of a ten-year note. Non-competitive tenders total $2.0 billion and are filled in full, leaving $38.0 billion for competitive bidders.

The book fills to $38.0 billion at D's bid, so the stop-out yield is 4.210% and D receives 7.00/8.00 of its bid. Total tenders of $47.0 billion against $40.0 billion accepted give a bid-to-cover of 1.175000. The coupon is set at 4.125%, the highest eighth of a percent that prices the issue at or below par, and at the stop-out yield the price is 99.3120545725 per 100. Every accepted bidder pays that price, including the non-competitive tranche, so total proceeds are $39,724,821,828.99.

Step 5, the counterfactual that shows what the rule does. Charge each accepted bidder its own bid instead. A would pay 99.5542166939, B 99.4330482804, C 99.3523664136 and D 99.3120545725, and the non-competitive tranche would pay the weighted-average accepted price of 99.4299148121. Proceeds become $39,771,965,924.85, which is $47,144,095.85 more, or 11.8677 basis points of proceeds.

Read it. The multiple-price rule raises more on this particular book, which is exactly what it should look like on a book taken as given.

The book, though, is not a given. What the static comparison cannot show is the behavioural response: under a multiple-price rule the aggressive bidder pays its own aggression, so bidders shade, and the observed book would not have looked like this one. The static gain of 11.8677 basis points is an upper bound on the rule's benefit, not an estimate of it, and treating it as an estimate is the standard error made with this comparison.

Worked example 3: An index-linked bond with the deflation floor binding (US, $)

A five-year inflation-linked note has original principal of $1,000,000 and a real coupon of 1.500%, paid annually for clarity; real securities of this type pay semi-annually and the mechanics per period are identical. The reference index stands at 300.000 at issue.

Solution. Step 1, the index path and the ratios.

Each coupon is the real rate applied to that year's adjusted principal: 1.5000% × $987,564.000000 = $14,813.460000 confirms the year-three row.

Step 2, redemption and the floor. The adjusted principal at maturity is $972,306.136200, below the original $1,000,000. The deflation floor pays the greater of the two, so redemption is $1,000,000.00 and the floor is worth $27,693.863800, which is 2.769386% of original principal.

Step 3, what the floor does and does not cover. Total coupons paid are $74,976.108243. Applying the floor to the coupons as well would have paid $76,209.000000, a difference of $1,232.891757 the holder does not receive. Total cash to the holder is $1,074,976.108243.

Step 4, the yield the floor is worth. Buying at original principal, the actual cash flows give an internal rate of return of 1.50045230% in money terms. Strip the floor out and pay the unfloored $972,306.136200 at maturity and the return falls to 0.95673684%. The clause is worth 54.3715 basis points of yield on this path.

Read it. The floor is not what delivers the real return. Indexation does that, and on this path the holder's real return is the stated 1.500% before the floor is applied at all. What the floor adds is nominal, and it adds it once. It hands back the $27,693.86 of principal that five years of net deflation had taken, which lifts the money return from 0.95673684% to 1.50045230% and the real return from 1.50000000% to 2.04680618%. The coupons keep the deflation. Each was computed on the unfloored adjusted principal and the floor does not reach back to collect them. And the whole calculation is conditional on one path. Feed an inflationary path through the same table and the floor is worth zero, which is the usual case and is why the clause is easy to forget until the year it matters.

Worked example 4: A step-up and a payment-in-kind, side by side (India, ₹)

Meghna Roadways Finance Ltd (synthetic), a non-bank finance company, is choosing between two five-year ₹100 crore private placements. The step-up pays 8.00% in years one and two, 9.00% in year three and 10.00% in years four and five, all in cash. The payment-in-kind alternative carries 11.00% capitalised for three years and paid in cash thereafter, with the accreted principal repaid at maturity. Both are priced at par.

Solution. Step 1, the step-up's table.

Discounting those flows to ₹100 crore gives an internal rate of return of 8.89807933%, and discounting the same flows at 8.89807933% returns 100.0000000000.

Step 2, the payment-in-kind's table.

The accreted principal is ₹136.763100 crore, which is 100 × 1.11³ to fourteen decimal places, and the internal rate of return is 11.00000000% exactly, as it must be for an instrument whose every cash flow accrues at 11%.

Step 3, read the two against each other. Over the first three years the step-up pays ₹25.000000 crore of cash and the payment-in-kind pays nothing, so the borrower's early liquidity is ₹25 crore better under the second structure. Over the full five years the step-up hands over ₹145.000000 crore and the payment-in-kind ₹166.850982 crore. At maturity the step-up must refinance ₹100.00 crore and the payment-in-kind ₹136.763100 crore, a wall 36.763100% higher.

Read it. Neither structure is cheaper or dearer in the abstract. They price different things. The step-up sells a fixed, known deferral and is what an issuer uses when it expects its own credit to improve on a schedule. The payment-in-kind sells an unfunded compounding claim and is what an issuer uses when its cash is genuinely absent, which is why the coupon is higher and why a lender agreeing to it should be modelling the refinancing at maturity rather than the yield to it. A credit analyst who compares the two on coupon alone will read 11.00% against 8.00% and conclude the second borrower is riskier, which is true but is not what the numbers said: the numbers said the second borrower will owe 36.763100% more principal on a date it has not yet arranged to meet.

Worked example 5: A make-whole call, priced and interpreted (US, $)

Blue Harbor Utilities Inc (synthetic) has $500,000,000 of 5.25% senior notes outstanding, semi-annual coupons, and is considering a make-whole redemption with exactly five years, meaning ten semi-annual periods, remaining. The indenture sets the redemption price at the greater of par and the present value of remaining scheduled interest and principal discounted at the yield of a comparable Treasury security plus 25 basis points.

Solution. Step 1, the present value at the formula's discount rate. The reference Treasury yields 3.90%, so the discount rate is 4.1500%, or 2.075% per semi-annual period. Ten coupons of 2.625 per 100 plus 100 at period ten discount to 104.9210912177 per 100. That exceeds par, so the formula binds rather than the floor, and the redemption amount is $524,605,456.09, a premium over par of $24,605,456.09.

Step 2, what the notes were actually worth. The credit trades 70 basis points over the same Treasury, so its market yield is 4.6000% and its market price is 102.8740433271 per 100, or $514,370,216.64. Calling therefore costs the issuer $10,235,239.45 more than the notes are worth. An open-market repurchase at the market price would cost that much less, but no holder can be forced to sell into it.

Step 3, the same formula when rates have risen. Hold everything else and move the reference Treasury to 6.00%. The discount rate becomes 6.2500% and the present value of the identical remaining cash flows is 95.7619781172, below par, so the par floor binds and the redemption price is exactly 100.0000000000.

Step 4, the par-call counterfactual. Had these notes carried an ordinary par call rather than a make-whole, the issuer would have paid $500,000,000.00 for notes worth $514,370,216.64, transferring $14,370,216.64 from holders. The make-whole premium over a par call is 4.9210912177 per 100, or $24,605,456.09.

Read it. The redemption price implies a yield to the holder of exactly 4.15000000%, which is 45 basis points below what the same credit yields in the market, and that gap is the whole reason the price sits above market value. A make-whole clause is a deterrent priced as a formula. It exists so that the issuer can redeem, for a merger, a covenant clean-up or a liability-management exercise, not so that it profitably will. The name is also misleading in one specific way worth stating: it makes the holder whole against the government curve, and if the reference yield has risen enough the floor pays par on a bond the holder would rather have kept, which is not whole by any definition the holder would choose.

Worked example 6: A multiple-price government auction (India, ₹)

The Reserve Bank of India offers a reissue of ₹32,000 crore of an existing 7.10% dated security with exactly ten years remaining, semi-annual coupons. The auction is price-based, because it is a reissue, and multiple-price. Five percent of the notified amount, ₹1,600 crore, is reserved for non-competitive bidders who receive the weighted-average accepted price (check the current reservation under the RBI's non-competitive bidding scheme).

Solution. Step 1, rank and fill. Price-based bids rank from highest to lowest, and ₹30,400 crore is available to competitive bidders.

The cut-off price is ₹99.41, D is filled at 98.333333%, and E is rejected. Total tenders of ₹37,100 crore against ₹32,000 crore notified give a bid-to-cover of 1.159375.

Step 2, the weighted-average price. Weighting each accepted allotment by its own price gives ₹99.5262828947, which is what the non-competitive tranche pays.

Step 3, proceeds, both rules. Under the multiple-price rule the government raises ₹31,848.410526 crore. Under a uniform-price rule at the cut-off it would raise ₹31,811.200000 crore. The difference is ₹37.210526 crore, or 11.6973 basis points.

Step 4, translate the price ladder into yields. At exactly ten years and a 7.10% semi-annual coupon:

The accepted book spans 2.9870 basis points of yield, and the rejected bid was 1.5679 basis points cheap to the cut-off. Inverting the cut-off yield back through the pricer returns ₹99.4100000000, which is the check that the two directions agree.

Read it. Three numbers describe this auction, and they answer different questions. The cut-off tells you where the marginal bid cleared, which is what a secondary trader will mark against. The weighted average tells you what the government actually received and what the non-competitive tranche paid. The bid-to-cover tells you how much demand stood behind the clearing level, and a thin cover on a wide book is a different market from a thin cover on a tight one. Quoting the cut-off as though it were the auction result understates proceeds here by ₹37.210526 crore, and quoting the weighted average as though it were the clearing level misleads anyone trying to mark a position.

Worked example 7: The price of liquidity (US, $, with an India tail)

A portfolio manager can buy $50,000,000 of either the current on-the-run ten-year Treasury or an off-the-run issue of similar maturity that yields 6 basis points more. The on-the-run is quoted 99-14+ / 99-15; the off-the-run is quoted 96-08 / 96-12. Both have a modified duration of about 8.0, borrowed here as an input rather than computed.

Solution. Step 1, decode the quotes. Treasury prices are quoted in thirty-seconds, with a trailing plus meaning a further half of a thirty-second. The on-the-run bid is 99 + 14.5/32 = 99.4531250000 and the ask is 99 + 15/32 = 99.4687500000, a spread of 0.0156250000 per 100, or one sixty-fourth. The off-the-run bid is 96.2500000000 and the ask 96.3750000000, a spread of 0.1250000000, or four thirty-seconds and eight times as wide.

Step 2, the round-trip cost in money.

The yield conversion divides the spread by the DV01, which at a modified duration of 8.0 is 0.07956875 per 100 for the on-the-run and 0.07705000 for the off-the-run.

Step 3, the breakeven holding period. The extra round-trip cost is $54,687.50. A 6 basis point pickup on $50,000,000 is $30,000.00 a year. The concession therefore takes 1.82291667 years, about twenty-two months, to pay for the cost of capturing it. The same answer arrives from the yield side: the extra cost is 10.937500 basis points of face, and 10.937500 divided by 6.0 is 1.82291667 years.

Step 4, the India tail. On ₹100 crore of face, a benchmark government security quoted 2 paise wide costs ₹2,00,000 to round-trip; a state development loan quoted 15 paise wide costs ₹15,00,000. The extra ₹13,00,000 against a 35 basis point pickup worth ₹35,00,000 a year gives a breakeven of 0.37142857 years, about four and a half months.

Read it. The Indian breakeven is far shorter than the American one because the yield concession on the less liquid instrument is much larger relative to the wider bid-ask. That is a real and persistent feature of that market rather than an accident of these numbers.

What neither calculation captures is the thing that actually goes wrong. Both breakevens assume the quoted spread is available in the size you need on the day you need it, and the state loan quoted 15 paise wide in ₹5 crore may be quoted 60 paise wide in ₹100 crore, or not quoted at all in a bad week. A liquidity premium earned in calm markets and paid back in one exit is a negative-carry trade with a positive-carry disguise.

Verify: every figure above at full precision

Worked example 1. Accrual fractions 0.2916666667 (30/360), 0.2931506849 (actual/actual), 0.2972222222 (actual/360). Accrued ₹24,500.000000, ₹24,624.657534, ₹24,966.666667. Full price ₹998,001.246417, computed two ways with a residual of 2.328 × 10⁻¹⁰. Flat price ₹973,376.588882. Matrix yield 8.215000%; price ₹990,125.304359; alternative ladder spacing 8.266000% and ₹987,801.743073.

Worked example 2. Coupons $142,819.444444 and $150,777.777778, total $293,597.222222. Discount margin 1.0377661634%, repricing to 99.3500000000 with a residual of 2.558 × 10⁻¹³. Price at a discount margin equal to the quoted margin, 100.0000000000. Between-reset full price 100.3652980588, accrued 0.4708333333, flat 99.8944647254. Stop-out 4.210%, price 99.3120545725, inverted back to 4.2100000000%. Uniform-price proceeds $39,724,821,828.99; multiple-price proceeds $39,771,965,924.85; difference $47,144,095.85. Allotments sum to $40.000000 billion exactly.

Worked example 3. Index ratios 1.030000000, 1.050600000, 0.987564000, 0.957937080, 0.972306136. Coupons $15,450.000000, $15,759.000000, $14,813.460000, $14,369.056200, $14,584.592043, totalling $74,976.108243. Redemption $1,000,000.00; floor worth $27,693.863800. Internal rate of return 1.50045230% with the floor and 0.95673684% without, a gap of 54.3715 basis points. Real return, meaning the same cash flows deflated by the index ratio, 1.50000000% without the floor and 2.04680618% with it.

Worked example 4. Step-up cash coupons ₹45.000000 crore, total cash ₹145.000000 crore, internal rate of return 8.89807933%, repricing to 100.0000000000. Payment-in-kind accreted balance ₹136.763100 crore against 100 × 1.11³ = 136.7631000000, residual 2.842 × 10⁻¹⁴; cash coupons ₹30.087882 crore; total cash ₹166.850982 crore; internal rate of return 11.00000000%.

Worked example 5. Make-whole price 104.9210912177 at 4.1500%, redemption $524,605,456.09, premium $24,605,456.09. Market price 102.8740433271 at 4.6000%, value $514,370,216.64. Excess cost $10,235,239.45. Present value at 6.2500% is 95.7619781172, so the floor pays 100.0000000000. Sanity check: discounting the same schedule at the coupon rate of 5.25% returns 100.0000000000.

Worked example 6. Cut-off ₹99.41, weighted average ₹99.5262828947, bid-to-cover 1.159375. Proceeds ₹31,848.410526 crore and ₹31,811.200000 crore, difference ₹37.210526 crore. Yields 7.15384730%, 7.16716766%, 7.18371766% and 7.19939623%; the cut-off yield reprices to ₹99.4100000000. Allotments sum to ₹32,000.0000 crore exactly.

Worked example 7. Spreads 0.0156250000 and 0.1250000000 per 100. Round trips $7,812.50 and $62,500.00, a ratio of exactly 8. DV01 0.07956875 and 0.07705000 per 100. Yield-equivalent spreads 0.196371 and 1.622323 basis points. Breakeven 1.82291667 years, cross-checked as 10.937500 / 6.0. India tail: ₹2,00,000, ₹15,00,000, ₹35,00,000 a year, breakeven 0.37142857 years.

Practice set

Work each problem before reading its solution; the whole value of the set is in the attempt. A calculator is assumed and a spreadsheet is fine. Answers within 0.5% of the stated figure count as correct except where a problem names a tighter band, and any answer whose sign or order of magnitude differs is wrong however close the digits look. The first three carry scaffolding and the rest do not. Markets alternate deliberately, because carrying a convention across a border is the error this set is built to catch.

P1 (guided). Three conventions on one pair of dates. An Indian corporate debenture of ₹10,00,000 face pays 7.75% annually on 15 February. Settlement is 31 August 2026; the last coupon was 15 February 2026 and the next is 15 February 2027. Compute the accrual fraction under 30/360 (American), 30E/360, actual/actual and actual/360, then the accrued interest under three of them, and state which convention Indian listed corporate debt is required to use.

Solution. From 15 February to 31 August the American 30/360 rule gives 30 × 6 + (31 − 15) = 196 days, because the start day is 15 rather than 30 and so the end day is not truncated; the fraction is 196/360 = 0.5444444444. The European rule caps the end day at 30, giving 195 days and 0.5416666667. Actual days are 13 + 31 + 30 + 31 + 30 + 31 + 31 = 197, over a 365-day coupon period, so actual/actual is 0.5397260274. Actual/360 is 197/360 = 0.5472222222. The annual coupon is ₹77,500.00, so accrued interest is ₹42,194.444444 under 30/360, ₹41,828.767123 under actual/actual and ₹42,409.722222 under actual/360; the actual/360 answer exceeds the 30/360 answer by ₹215.277778 per debenture. Listed Indian corporate debt securities compute interest on an actual/actual basis under SEBI's uniform methodology (check against the current circular), so ₹41,828.767123 is the contractual figure and the other two are what you would get by importing the government-securities or money-market habit.

P2 (guided). Decompose a settlement amount. A US corporate bond settles at a full price of 103.4812 per 100. Its coupon is 4.75% semi-annual, the day count is 30/360, and 48 days of a 180-day period have elapsed. Compute the accrued interest, the flat price, and all three amounts on $25,000,000 of face value.

Solution. The period coupon is 2.375 per 100 and the accrual fraction is 48/180, so accrued interest is 2.375 × 48/180 = 0.6333333333 per 100; the same answer arrives as 100 × 4.75% × 48/360. The flat price is 103.4812 − 0.6333333333 = 102.8478666667, and that is the number a screen shows. On $25,000,000 of face the full price is $25,870,300.00, accrued is $158,333.33 and the flat amount is $25,711,966.67. The buyer wires the full price; the quote never mentions it.

P3 (guided). Two floating coupons. A $20,000,000 floating-rate note pays the reference rate plus a quoted margin of 65 basis points, actual/360, quarterly. The reference sets at 5.0500% for a 90-day period and at 4.7000% for the following 92-day period. Compute both cash coupons and the total, and say when each rate was known.

Solution. Period one: (5.0500% + 0.65%) = 5.7000% on 90/360 of $20,000,000 = $285,000.000000. Period two: (4.7000% + 0.65%) = 5.3500% on 92/360 = $273,444.444444. Total $558,444.444444. Each rate was fixed at the start of its own period and paid at the end of it, so a mid-period move in the index changes nothing about the coupon then accruing; it changes the price of the note and the coupon of the next period.

P4. Discount margin from a price. A five-year quarterly floating-rate note has twenty periods remaining, a quoted margin of 95 basis points and a current reference rate of 4.20%, and trades at 98.10. Compute the discount margin and the gap to the quoted margin.

Solution. Assuming the reference holds at 4.20%, the quarterly coupon is 100 × (4.20% + 0.95%)/4 = 1.2875 per 100. Solving for the spread that discounts twenty such coupons plus par to 98.10 gives a discount margin of 1.3881879875%, or 138.8188 basis points. That is 43.8188 basis points above the quoted margin, which is why the note trades 1.90 points below par: the market now demands more than the contract pays, and the discount makes up the difference over the remaining five years.

P5. The price at a reset. Take the note from P4 and price it at a discount margin of 95, 60 and 150 basis points. State the two conditions under which a floater prices at par.

Solution. At a discount margin of 95 basis points, equal to the quoted margin, the price is 100.0000000000. At 60 basis points it is 101.5476385525 and at 150 basis points it is 97.6217660539. A floating-rate note prices at par only when both conditions hold: the valuation date is a reset date, so no coupon is already fixed for a period still running, and the required margin equals the quoted margin, so the market is content with the spread the contract pays. Fail the first and the price moves with the remaining stub; fail the second and it moves permanently.

P6. An index-linked bond with the floor binding. A four-year linker has original principal of $2,000,000, a real coupon of 2.125% paid annually, and a reference index of 250 at issue. The index moves +4.5%, +1.0%, −8.0% and −4.0%. Build the cash-flow table, compute the redemption amount and state what the deflation floor is worth.

Solution.

Coupons total $170,154.591200. The adjusted principal at maturity is $1,864,346.880000, so the floor binds and redemption is $2,000,000.00, making the floor worth $135,653.120000. The years-three and years-four coupons were computed on the unfloored principal and stay where they are; the floor reaches the principal at maturity and nothing else.

P7. Matrix-price an unrated gap. An Indian issuer wants a four-year private placement rated A+. The comparable matrix holds AA- paper at 8.55% for three years and 8.80% for five, and A paper at 9.30% and 9.62% at the same tenors. Interpolate to A+ at four years and price a ₹10,00,000 face, 9.25% annual-coupon bond at that yield.

Solution. A+ sits between AA- and A on the notch ladder, so the midpoint at three years is (8.55 + 9.30)/2 = 8.925000% and at five years (8.80 + 9.62)/2 = 9.210000%. Interpolating linearly to four years gives 9.067500%. Pricing a four-year 9.25% annual bond at 9.067500% gives ₹10,05,903.739452, which is 100.590374 per 100. The bond prices above par because its coupon exceeds the interpolated yield. Both interpolations are conveniences: the notch ladder is not evenly spaced in yield and the curve between three and five years is not straight.

P8. Allocate a uniform-price auction. The Treasury offers $24.0 billion of a seven-year note. Non-competitive tenders total $1.5 billion. Competitive bids are $7.0bn at 3.880%, $6.5bn at 3.895%, $6.0bn at 3.900% and $5.5bn at 3.915%. Find the stop-out yield, the pro-rata fill, the bid-to-cover, the price at a 3.750% coupon, and the proceeds.

Solution. Competitive bidders share $24.0 − $1.5 = $22.5 billion. Filling from the lowest yield: 7.0, then 13.5, then 19.5 cumulative, leaving $3.0 billion for the 3.915% bid, which is filled at 54.545455% of its $5.5 billion. The stop-out yield is 3.915% and it is the yield every accepted bidder pays, including the non-competitive tranche. Total tenders are $25.0 + $1.5 = $26.5 billion against $24.0 billion accepted, a bid-to-cover of 1.104167. A 3.750% coupon seven-year note at 3.915% prices at 98.9982405719 per 100, so the marginal bidder pays $2,969,947,217.16 and total proceeds are $23,759,577,737.25.

P9. Allocate a multiple-price auction. The Reserve Bank of India offers ₹19,000 crore of a reissue, with ₹950 crore reserved for non-competitive bidders. Competitive price bids are ₹6,000 crore at ₹100.15, ₹5,500 crore at ₹100.08, ₹5,000 crore at ₹99.97 and ₹4,000 crore at ₹99.90. Find the cut-off price, the weighted-average accepted price and the proceeds under both rules.

Solution. Competitive bidders share ₹18,050 crore. Filling from the highest price: 6,000, then 11,500, then 16,500 cumulative, leaving ₹1,550 crore for the ₹99.90 bid, a 38.750000% fill. The cut-off price is ₹99.90 and the weighted-average accepted price is ₹100.0573407202, which is what the non-competitive tranche pays. Proceeds under the multiple-price rule are ₹19,010.894737 crore; under a uniform-price rule at the cut-off they would be ₹18,981.000000 crore, a difference of ₹29.894737 crore. Reporting the cut-off as the auction's price understates what the government received.

P10. A step-up's true yield. An Indian ₹50 crore four-year step-up pays 7.00%, 7.50%, 8.50% and 9.50% in cash, and repays principal at maturity. Priced at par, what yield does the investor earn, and what flat coupon would be equivalent?

Solution. Cash coupons are ₹3.500000, ₹3.750000, ₹4.250000 and ₹4.750000 crore, with ₹50 crore of principal alongside the last. Solving for the rate that discounts ₹3.50, ₹3.75, ₹4.25 and ₹54.75 crore to ₹50 crore gives 8.04331789%. A flat-coupon bullet of the same maturity paying ₹4.021659 crore a year would be equivalent. The step-up's headline range of 7.00% to 9.50% brackets the answer, and neither endpoint is it: the early low coupons are discounted least and the late high ones most, so the internal rate of return sits below the simple average of 8.125%.

P11. Payment-in-kind accretion. An Indian mezzanine lender provides ₹250 crore at 12.50%, capitalised for four years with no cash interest. What is the balance at the end of year four, by how much has the principal at risk grown, and what has the lender received in cash?

Solution. The balance compounds: ₹281.250000, ₹316.406250, ₹355.957031 and ₹400.451660 crore at the end of years one to four. The principal at risk has risen by ₹150.451660 crore, or 60.180664%, and the lender has received nothing in cash. The accrued return is real accounting income and entirely unrealised, which is why a payment-in-kind position's carrying value tells you very little about whether it will be repaid, and why the first cash-pay date is the date that matters in the credit file.

P12. Make-whole, both directions. A US issuer has $300,000,000 of 6.00% semi-annual notes with three years, meaning six periods, remaining. The make-whole formula discounts remaining cash flows at the comparable Treasury plus 35 basis points. Compute the redemption price and amount when the Treasury yields 4.40%, then again when it yields 7.00%.

Solution. At a Treasury of 4.40% the discount rate is 4.7500%, and six coupons of 3.00 per 100 plus 100 discount to 103.4570164792 per 100, which exceeds par, so the redemption price is 103.4570164792, the amount is $310,371,049.44 and the premium over par is $10,371,049.44. At a Treasury of 7.00% the discount rate is 7.3500% and the same cash flows discount to 96.4238106847, below par, so the par floor binds and the redemption price is exactly 100.0000000000. The formula never pays the holder less than par and never protects them against the issuer's own credit spread, which is the asymmetry the clause encodes.

P13. Sinking-fund average life. A $300 million issue matures in seven years and retires $50 million of principal in each of years three, four, five and six, with $100 million at maturity. Compute the average life and compare it to a bullet of the same maturity.

Solution. Weighting each principal payment by its year gives (3 × 50) + (4 × 50) + (5 × 50) + (6 × 50) + (7 × 100) = 150 + 200 + 250 + 300 + 700 = 1,600, and dividing by the $300 million total gives an average life of 5.33333333 years. A bullet of the same maturity has an average life of exactly 7.00000000 years, so the sinking fund shortens it by 1.66666667 years without moving the maturity date. Principal ties out: 50 + 50 + 50 + 50 + 100 = $300 million.

P14. Buy the concession or not. An Indian fund can hold ₹200 crore of a benchmark government security quoted 3 paise wide, or a state development loan quoted 20 paise wide that yields 42 basis points more. Compute both round-trip costs and the breakeven holding period, then state the assumption the answer depends on.

Solution. Round-trip cost is the face value times the spread: ₹200 crore × 0.03/100 = ₹6,00,000 for the government security and ₹200 crore × 0.20/100 = ₹40,00,000 for the state loan, an extra ₹34,00,000. A 42 basis point pickup on ₹200 crore is ₹84,00,000 a year, so the breakeven is 34/84 = 0.40476190 years, a little under five months. The answer assumes the 20 paise quote is available in ₹200 crore on the day you sell, which is exactly the assumption that fails in a stressed market; a realistic exit spread of 60 paise would push the breakeven past a year.

P15. Read a term sheet and compute the next accrual. An Indian debenture of ₹10,00,000 face pays 8.95% semi-annually on 5 May and 5 November. Settlement is 20 January 2027. Compute the accrued interest under 30/360 and under actual/actual, and the difference on 100 debentures.

Solution. The period coupon is ₹44,750.00. From 5 November 2026 to 20 January 2027 the 30/360 rule counts 360 + 30 × (1 − 11) + (20 − 5) = 75 days of a 180-day period, a fraction of 0.4166666667, giving ₹18,645.833333. Actual days are 25 + 31 + 20 = 76 of the 181-day period from 5 November to 5 May, a fraction of 0.4198895028, giving ₹18,790.055249. The difference is ₹144.221915 per debenture and ₹14,422.19 on a hundred of them. Under SEBI's uniform methodology the actual/actual figure is the contractual one (check the current circular).

P16. Discount form against add-on form. An Indian company issues ₹5,00,00,000 of 91-day commercial paper at an implied yield of 7.20% on a 365-day basis. An American bank issues a $5,000,000 91-day negotiable certificate of deposit at 5.10% on an add-on, actual/360 basis. Compute what each investor pays and receives, and the holding-period return on each.

Solution. The commercial paper is a discount instrument, so the investor pays face divided by (1 + 0.0720 × 91/365) = ₹4,91,18,292.998019, a discount of ₹8,81,707.001981, and receives ₹5,00,00,000 at maturity; the holding-period return is 1.7950684932%. The certificate is an add-on instrument, so the investor pays face of $5,000,000.00 and receives $5,000,000 × (1 + 0.0510 × 91/360) = $5,064,458.333333, of which $64,458.333333 is interest; the holding-period return is 1.2891666667%. Two instruments of the same tenor, two entirely different cash-flow shapes from the same kind of headline rate. Annualising these two returns onto a common basis so they can be compared is the money-market yield chain, and FI1.01 owns it.

Applied mini-project

Read two real documents, and make them settle.

Three artefacts, each with a numbered test it must pass before it counts. Use a spreadsheet or Python. Every convention must be cited to the document it came from, with a page or clause reference.

A convention you cannot cite is a convention you have assumed, and an assumed convention scores zero on the row that depends on it.

Label any invented entity synthetic. Where a real issuer's document is used, take facts only from that document or from the issuer's own filings, and record the date you retrieved it.

Artefact 1, the instrument descriptions (2 tests). Choose one real Indian debenture with a published information memorandum or key information document, and one real United States corporate bond with a published prospectus or offering memorandum. Extract each into the same fourteen-field table, using the fields listed in section 4.15: legal issuer, seniority and security, face value and issue size, coupon rate and type, frequency and payment dates, day-count and business-day conventions. Then the first coupon date with any short or long first period, the maturity date and redemption amount, and the four contingency schedules: call, put, sinking fund, and the make-whole formula with its reference security and spread. Test 1: every populated cell carries a clause reference. Test 2: every field the document does not state is marked silent rather than filled from market practice, and you can say for each silent field what a wrong default assumption would have cost.

Artefact 2, the settlement calculation (3 tests). Pick a settlement date for each bond that falls between coupon dates, and a market yield you can justify. Compute, for each, the accrual fraction under the document's own convention and under one wrong convention, the accrued interest, the full price and the flat price. Test 3: the full price minus the accrued interest equals the flat price to the last unit of currency. Test 4: the full price computed by discounting each remaining cash flow from the settlement date matches the full price computed by discounting to the last coupon date and growing forward, to at least eight significant figures. Test 5: the cost of the wrong convention is stated in currency on a position size you name.

Artefact 3, the matrix price (2 tests). Build a comparable-bond yield matrix of at least four cells for one of the two issuers, by rating and maturity, from quotes or valuation data you cite. Matrix-price a hypothetical new issue from the same issuer at a maturity that is not in your matrix. Test 6: the interpolation refuses to extrapolate, and you say so if the target sits outside the grid. Test 7: you re-run the price with one interpolation assumption changed, name which assumption, and state the price difference in currency on a stated size.

Deliverable. One workbook or notebook and a two-page memo carrying the two instrument tables, the two settlement decompositions, the matrix price with its sensitivity, the seven test results, and a closing paragraph naming the single convention your answers are most sensitive to with that sensitivity quantified.

Rubric (18 points; pass at 14 with no zero on any row).

Two points for a row met at the "2" standard and three at the "3" standard. Any artefact whose test fails scores zero on the rows that depend on it, however well the memo is written. The point of that rule is the point of the whole node: a settlement that does not tie is not a presentation problem.

Reading & resources

Use the list below as a set of anchors to check your own work against. None of it is a source to copy a convention from without confirming that the convention still applies to the specific instrument in front of you.

Instruments and conventions:

• Frank J. Fabozzi (ed.), The Handbook of Fixed Income Securities. The desk reference; its chapters on bond features, day counts, corporate issuance and the money markets cover most of the ground here at greater depth. [Paid] [Intermediate to Advanced]
• Frank J. Fabozzi, Bond Markets, Analysis and Strategies. A gentler ramp, with worked accrual and settlement arithmetic and a clear treatment of floating-rate note margins. [Paid] [Beginner to Intermediate]
• Bruce Tuckman and Angel Serrat, Fixed Income Securities: Tools for Today's Markets. The most careful published treatment of accrued interest, day-count conventions and the mechanics of Treasury auctions. [Paid] [Advanced]
• Moorad Choudhry, The Bond and Money Markets. Strong on the London-market conventions that shape a great deal of international documentation. [Paid] [Intermediate]
• CFA Institute Level I and Level II Fixed Income readings on instrument features, issuance and markets. Exam-shaped coverage of the same conventions, useful for checking that you have not invented one. [Paid] [Beginner to Intermediate]

India, primary sources:

• FIMMDA, Government Securities Market in India: A Primer, and the association's valuation guidelines. The source for the 30/360 accrual convention on government securities and for how illiquid corporate bonds are valued off a matrix. [Free] [Beginner to Intermediate]
• Reserve Bank of India, FAQs on Government Securities and the auction notifications on its own site. Auction method, notified amounts, the non-competitive bidding scheme and primary-dealer underwriting, all of which change and all of which must be read current. [Free] [Beginner to Intermediate]
• Clearing Corporation of India (CCIL) and the NDS-OM daily reports. Where Indian government securities actually trade, and the closest thing that market has to a public tape. [Free] [Intermediate]
• Financial Benchmarks India (FBIL) methodology documents. Who administers which rupee benchmark, and how each is computed; the reference-rate half of any rupee floater. [Free] [Intermediate]
• SEBI, the Issue and Listing of Non-Convertible Securities Regulations, and the circular prescribing a uniform methodology for computing interest on debt securities. The actual/actual requirement for listed corporate debt and the electronic-book rules for private placements live here. [Free] [Intermediate]
• RBI Master Directions on Commercial Paper and on Certificates of Deposit. Eligibility, tenor limits and the discount form of both instruments. [Free] [Intermediate]

United States, primary sources:

• The Treasury's Uniform Offering Circular for the sale and issue of marketable book-entry securities. The auction rules themselves, including the single-price rule, the non-competitive cap and how coupons are set. [Free] [Intermediate]
• TreasuryDirect auction announcements and results. Real bid-to-cover ratios, stop-out yields and allotment percentages to test your allocation code against. [Free] [Beginner]
• SEC EDGAR, specifically prospectus supplements and the description-of-notes section. Where a real call schedule, make-whole formula and day-count convention are written down. [Free] [Beginner to Advanced]
• FINRA's trade reporting facility for corporate bonds and the MSRB's disclosure portal for municipals. Actual transaction prices, which is how you find out that a matrix price was 40 basis points off. [Free] [Beginner]
• The Treasury's published inflation index ratios for inflation-protected securities. The reference-index arithmetic of section 4.3, computed and published daily by the issuer. [Free] [Beginner]

One exercise is worth more than the whole list above. Download one real prospectus supplement and one real Indian information memorandum, and fill in the fourteen-field table from section 4.15 by hand, timing yourself. The first will take an hour and the second forty minutes. Then find the issuer's own first interest payment notice and check that your accrued-interest figure for that period matches it to the currency unit. Almost everyone's first attempt is wrong in exactly one field, and finding out which field is yours is worth more than any amount of reading about conventions.

Teach it back & journal

Feynman prompt. Take a colleague who prices bonds off a curve and has never settled one. Put the module's Indian debenture in front of them and ask for the amount to wire on 100 units at a quoted price of 97.337659. They will say ₹9,73,37,658.89. Let them, then show them the ₹9,98,00,124.64 that actually leaves the account, and make them tell you where the other ₹24,62,465.75 came from and whose money it was before the trade. Once they have the three prices straight, hand them the same trade with a 30/360 accrual and ask which of the two wires is correct and how they would find out. The answer is not in either spreadsheet; it is in a SEBI circular and a term sheet, and the moment they reach for the document rather than the model, the habit has installed.

Then the second half, which is harder. Give them a floating-rate note and ask whether it is worth par. Most people answer yes without qualification, because the identity is taught without its conditions. Walk them to the two conditions, then show them the note sitting 0.1055352746 below par thirty days into a period, and make them say out loud why a coupon that was fixed last month cannot protect a price this month.

Journal prompt. For two weeks, write down four things about every bond you meet in a pitch, a rating report or a portfolio statement, before you use any number attached to it. Record the coupon structure, the day-count convention, whether the price in front of you is flat or full, and whether any provision can end the instrument before its stated maturity. Then answer in writing at the end of the fortnight. Count how many of the four you could find without opening the offer document, and how many times a number reached you with no statement of which convention produced it. Where the convention was missing, what did you assume, and what would that assumption have cost you on a ₹10 crore or $10 million position?

Then write a paragraph on the following. The whole of this node is a claim that reading is an analytical skill rather than a preliminary to one, and that claim is easy to accept and hard to act on when a deadline is close. Which of the fourteen term-sheet fields are you most likely to skip when you are in a hurry, and what specifically goes wrong when you skip it? Write down one change to how you work, this month, that makes skipping it harder than doing it. A checklist that lives in the model file rather than in your head is the usual answer, and the reason it works is that it fails loudly.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.