Conversion factor
Also written CF · Conversion factor for deliverable grade security
The multiplier that scales a futures settlement price into a fair invoice price for each bond in the deliverable basket, by valuing that bond at the notional 7% yield.
In plain language
A physically settled bond future is written on a notional bond — a 10-year GOI security with a notional coupon of 7%, which does not exist. What the seller actually delivers is a real bond out of an eligible basket, and no two of those bonds are worth the same.
The conversion factor is the adjustment that makes the choice fair. Each deliverable bond gets its own factor, computed so that delivering a high-coupon bond earns the seller proportionately more and delivering a low-coupon bond earns proportionately less. In theory it should leave the seller indifferent between them.
In practice it does not, and that is the interesting part — which is why the cheapest-to-deliver bond exists.
How it works
For the 10-year notional coupon-bearing GOI security future, the workbook's rule is precise:
The remaining term to maturity is calculated in complete three-month quarters, always rounded down. If after rounding the bond lasts an exact number of six-month periods, the first coupon is assumed to be paid after six months. If there is an extra three months, the first coupon is assumed after three months and accrued interest is subtracted.
The deliverable basket itself is GOI securities maturing at least 7.5 years but not more than 15 years from the first day of the delivery month, with a minimum total outstanding stock of Rs 10,000 crore.
Because the factor is fixed for the whole delivery month while bond prices move every minute, the seller's economics keep shifting. One bond becomes the cheapest to buy in the market relative to what the invoice pays for it, and every seller converges on that bond. The futures price then tracks the cash price of the CTD bond rather than the notional bond it was written on.
The formula
Invoice Amount (IA) = (SP × CF + AI) × CA / 100
SP = Final settlement price, per 100 of face value
CF = Conversion factor for that deliverable bond
AI = Accrued interest, per 100 of face value, on that bond
CA = Contract amount (market lot) = 2,00,000
A bond carrying a coupon above the notional 7% prices above par at a 7% yield, so its conversion factor exceeds 1. A bond with a coupon below 7% has a factor below 1.
A worked example
A seller holds one lot of the 10-year notional GOI security future into delivery. The final settlement price is Rs 96.50 per 100 of face value, and the contract amount is Rs 2,00,000.
Two bonds in the basket:
| Bond A (high coupon) | Bond B (low coupon) | |
|---|---|---|
| Conversion factor | 1.0250 | 0.9420 |
| Accrued interest per 100 | Rs 1.75 | Rs 2.10 |
| SP × CF | 96.50 × 1.0250 = 98.9125 | 96.50 × 0.9420 = 90.9030 |
| Invoice per 100 | 100.6625 | 93.0030 |
| Invoice amount received | Rs 2,01,325 | Rs 1,86,006 |
The factor has done its work: the seller is paid Rs 15,319 more for delivering the richer bond.
Now bring in the market. What matters is the invoice received against the cost of buying that bond:
| Bond A | Bond B | |
|---|---|---|
| Dirty market price per 100 | Rs 101.20 | Rs 92.50 |
| Cost of Rs 2,00,000 face | Rs 2,02,400 | Rs 1,85,000 |
| Invoice received | Rs 2,01,325 | Rs 1,86,006 |
| Net to the seller | −Rs 1,075 | +Rs 1,006 |
Delivering Bond A costs the seller Rs 1,075; delivering Bond B earns him Rs 1,006. Bond B is the cheapest-to-deliver, and every rational short will deliver it — so the futures price will track Bond B's cash price, not the notional bond's.
Why NISM asks about it
Chapter 7 (Clearing, Settlement and Risk Management of IRD) sets out the conversion factor, the invoice price formula and the cheapest-to-deliver logic in the physical settlement section; Chapter 3 carries the matching contract specification for the 10-year notional coupon-bearing GOI security future, including the deliverable grade criteria.
Questions are usually one of three: state the yield to which the conversion factor prices a bond (7%, semi-annual); compute an invoice amount from SP, CF and AI; or explain why a CTD bond exists despite the conversion factor being designed to prevent one. Section 3.1 also asks it historically — the 2009 contract failed partly because of cheapest-to-deliver.
Common exam traps
- The conversion factor prices the bond to yield 7%, not to its own coupon and not to the market yield. The 7% is the notional coupon of the contract.
- The factor is frozen for the delivery month; prices are not. That mismatch is the whole reason a cheapest-to-deliver bond emerges — not a flaw in the arithmetic.
- Invoice price includes accrued interest. Futures are quoted on the clean price, so the AI term has to be added back at delivery.
- CA is 2,00,000 and the formula divides by 100, because SP, CF and AI are all quoted per 100 of face value. Skip the division and every answer is 100 times too large.
- The remaining term is rounded down to complete quarters, never to the nearest quarter.
- None of this is live in India today. Exchanges may introduce physically settled IRD contracts, but no ETIRD contract currently settles by delivery — so the conversion factor is examinable theory, not market practice.
Where this is taught
Free preparation for NISM Series IVRelated terms
- Accrued interestCoupon earned from the last coupon date up to settlement, paid by the buyer to the seller on top of the negotiated price, because the issuer will pay the whole coupon to whoever holds the bond next.
- Cheapest-to-deliverThe bond in the deliverable basket that costs a futures seller least to deliver — and, because the seller chooses, the bond whose cash price the futures contract actually tracks.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- Deliverable grade securitiesThe government securities a seller is permitted to deliver against a physically settled bond futures contract — GOI bonds of 7.5 to 15 years from the delivery month with at least Rs 10,000 crore outstanding.
- Interest Rate FuturesA standardised exchange-traded contract to buy or sell a notional government security, or an interest rate itself, at a price agreed today for settlement on a future date.
- Invoice priceThe cash a buyer pays the seller on physical delivery: the futures settlement price multiplied by the delivered bond's conversion factor, plus its accrued interest, scaled by the contract amount.
- Clean priceThe quoted price of a coupon bond, excluding interest accrued since the last coupon date. Bonds trade at the clean price and settle at the dirty price, which adds accrued interest.
- Notional bondA theoretical bond with a fixed coupon and maturity that no one has issued — used as a futures underlying so the contract does not depend on the liquidity of any single security.