Accrued interest

A bond pays its coupon twice a year to whoever owns it on the coupon date. The issuer keeps no record of who owned it in between.

So if you sell a bond four months into a six-month coupon period, the buyer collects the full six months' coupon two months later — including the four months you earned. Accrued interest fixes that. The buyer pays it to you at settlement as an add-on, and recovers it from the issuer on the next coupon date.

This is why every G-Sec has two prices. The clean price is what the two parties negotiate and what gets quoted on the screen. The dirty price — clean plus accrued interest — is what actually settles in the bank account. Dirty price is always the higher of the two.

The obvious question is why not simply quote one price and be done with it. The workbook answers it properly, and the answer is examinable.

If accrued interest were built into the market price, the price would climb smoothly every single day by the daily accrual and then drop by the full coupon on the coupon date — a saw-tooth repeating every six months. That movement is deterministic: it is known in advance and tells a trader nothing.

Bond prices also move for two reasons that are stochastic — interest rates changing, and the issuer's credit standing changing. Those are the moves a trader needs to watch. Stripping the known saw-tooth out of the quoted price leaves the clean price carrying only the unknown moves.

The arithmetic depends entirely on the day count convention: Actual/Actual for Indian corporate bonds, 30/360 European for Indian government securities. The market convention includes the first day of the period and excludes the last.

The equity market has no equivalent. The workbook notes that "accrued dividend" could in principle be computed between announcement and ex-date, but dividends are a negligible part of equity return, whereas coupons can be 50–100% of the return on a bond.

Accrued interest = Coupon per period × (Days from last coupon date to settlement
                                          ÷ Days in the full coupon period)

Dirty price = Clean price + Accrued interest

For a semi-annual G-Sec on 30/360 European, the coupon per period is Coupon ÷ 2 and the denominator is 180.

The workbook's pair, showing why the convention matters. A 6.90% semi-annual bond, previous coupon 13-Jan-2021, next coupon 13-Jul-2021, settling 5 March.

On a clean price of Rs 101.50, the 30/360 dirty price is Rs 102.4967. The two conventions differ by 2.46 paise per Rs 100 of face — which on Rs 100 crore of face value is Rs 2,45,680 settling to the wrong party.

A full G-Sec settlement. 5.79% GOI 2030, last coupon 11-May-2020, trade settling 12-Aug-2020, 30/360E, so 91 days have accrued:

Accrued interest = 5.79 × (91 ÷ 360) = Rs 1.4636 per Rs 100 face

Quoted (clean) price       Rs  99.1828
Accrued interest           Rs   1.4636
Dirty price (settles)      Rs 100.6464

On one futures-lot equivalent of Rs 2,00,000 face — 2,000 units — the buyer hands over an extra Rs 2,927.20 of accrued interest beyond the negotiated price.

And at the scale of a hedging desk. The Chapter 5 short-hedge example holds Rs 5 crore of 6.10% G-Sec 2031 at a clean price of Rs 100 with 69 days accrued on a 30/360 basis:

Accrued interest  = Rs 1.169167 per Rs 100
Total consideration = Rs 5,05,84,583.33

The accrued interest alone is Rs 5,84,583 — larger than the entire tick-by-tick profit on most days of trading.

Chapter 1, section 1.8 (Accrued Interest) defines it and gives both day-count computations; section 1.11.3 (Valuing Bonds at Non-Coupon Dates) repeats it inside a full discounted-cash-flow valuation. It then appears wherever money actually changes hands: the Chapter 3 futures pricing model treats accrued interest as the income on the cash position, Chapter 5 uses it in the hedging scenarios, and Chapter 7 puts it into the invoice price for physical delivery.

Expect to be handed a coupon, two coupon dates, a settlement date and a day count and asked for the accrued interest or the dirty price. Expect also the concept question: why is accrued interest excluded from the quoted price?

• Dirty price is never below clean price. Accrued interest is added, not subtracted. If your dirty price is lower, you have the direction reversed.
• Use the periodic coupon, not the annual one. A 6.90% semi-annual bond accrues on 3.45 per period, not 6.90 — unless, as in the 5.79% example, the fraction is already expressed over a 360-day year.
• Include the first day and exclude the last. The convention is fixed and it changes the day count by one, which on a large book is real money.
• The seller receives accrued interest; the buyer recovers it on the next coupon date. It is a reimbursement, not a profit for either party.
• Quotation is clean, settlement is dirty — and modified duration, PV01 and the convexity correction all act on the dirty price.
• The workbook uses "invoice price" for two different things. Section 1.8 calls the dirty price "also known as invoice price", while section 1.11.3 lists "invoice price" among the names for the clean price, and Chapter 7 defines invoice price as a delivery amount built from the settlement price, conversion factor and accrued interest. Read the chapter before you read the term.