Invoice price

A bond futures contract is written on a notional bond, but a seller delivers a real one. The two cannot be worth the same, so the payment has to be adjusted before money changes hands.

The conversion factor does the first adjustment. It restates the delivered bond in notional-bond terms — the price it would fetch, per rupee of principal, if it were priced to yield the notional 7%. Multiply the futures settlement price by it and you have what the buyer owes for the bond itself.

The second adjustment is accrued interest. The seller has held the bond since the last coupon date and is entitled to that interest, exactly as in any cash-market G-Sec trade.

Add the two and scale by the contract amount — Rs 2,00,000 of face value — and you have the invoice amount, the actual rupees that settle.

The clearing corporation computes it, not the parties. When a selling clearing member gives notice of intention to deliver, the notice carries the notional face value, the security ISIN, the coupon, the maturity and issuance dates and the coupon convention. From those details the CC calculates the invoice price, allocates the delivery to long position holders by vintage — oldest first, random within a vintage — and tells the identified longs by 8 pm the same day what they will receive and what they will pay.

The invoice price then does duty beyond the payment itself. It is the base for the delivery margin: positions marked for delivery attract a margin equal to the VaR of the futures on the invoice price, plus 5% of face value, plus mark-to-market adjustments, charged to both buyer and seller from the intention day until settlement completes. Where no intention has been given between the last trading day and the last intention day, the same margin is computed on the invoice price of the costliest security in the deliverable basket.

It is also the reference for failure. On an unsuccessful buy-in auction the defaulting member is debited the invoice price plus a 5% penalty on the face value short delivered.

                                       CA
Invoice amount  =  [ (SP × CF) + AI ] × ───
                                       100

   SP = final settlement price, per Rs 100 of face value
   CF = conversion factor of the bond actually delivered
   AI = accrued interest on that bond, per Rs 100 of face value
   CA = contract amount (market lot) = Rs 2,00,000

so CA ÷ 100 = 2,000 units per contract

The conversion factor itself is the price of the deliverable security, per rupee of principal, on the first calendar day of the delivery month, priced to yield 7% with semi-annual compounding.

One contract, delivered. The futures settle at Rs 98.50. The seller delivers a GOI security whose published conversion factor is 0.9642, carrying Rs 2.1500 of accrued interest per Rs 100 of face value.

SP × CF          = 98.50 × 0.9642      = Rs 94.9737
plus AI                                = Rs  2.1500
Invoice price per Rs 100 face          = Rs 97.1237

Invoice amount = 97.1237 × (2,00,000 ÷ 100)
               = 97.1237 × 2,000
               = Rs 1,94,247.40

Delivering a different bond changes the bill. Against the same Rs 98.50 settlement, a second eligible security with a conversion factor of 1.0316 and accrued interest of Rs 0.8400:

(98.50 × 1.0316) + 0.84 = 101.6126 + 0.84 = Rs 102.4526
Invoice amount          = 102.4526 × 2,000 = Rs 2,04,905.20

Rs 10,658 more for the same contract — because a higher-coupon bond converts at above par and carries its own accrued interest. Neither buyer nor seller is better or worse off, because the bond received is correspondingly more valuable. That is what the conversion factor is for.

Scaled to a real delivery. A clearing member short 25 contracts delivering the first security:

Notional face value = 25 × Rs 2,00,000    = Rs 50,00,000
Invoice amount      = 25 × Rs 1,94,247.40 = Rs 48,56,185

And the margin it drives. Delivery margin on those positions is the VaR of the futures on the invoice price plus 5% of face value:

5% of Rs 50,00,000 = Rs 2,50,000, before the VaR component and MTM

Chapter 7, section 7.9 (Delivery Under Physical Settlement), gives the invoice price formula with its SP, CF, AI and CA definitions, immediately after the conversion factor definition and immediately before the cheapest-to-deliver discussion. The same section uses the invoice price in the delivery margin, in the costliest-security margin between last trading day and last intention day, and in the auction and close-out penalties. Chapter 1, section 1.8, is where "invoice price" first appears, as another name for the dirty price.

Questions hand you a settlement price, a conversion factor and an accrued interest figure and ask for the invoice amount — which makes the CA ÷ 100 = 2,000 step the one that decides the mark.

• The conversion factor multiplies only the settlement price. Accrued interest is added after the multiplication, never before it — SP × (CF + AI) is wrong.
• Scale by CA ÷ 100, which is 2,000. Multiplying by Rs 2,00,000 gives an answer a hundred times too large; the price is already quoted per Rs 100 of face.
• The accrued interest is on the delivered bond, computed on its own coupon and dates, not on the notional bond's 7%.
• A different deliverable produces a different invoice amount, and that is correct — the bonds are not identical, so the payments should not be.
• The clearing corporation computes it from the delivery notice. It is not negotiated, and the longs are told the figure by 8 pm on the notice day.
• The workbook uses "invoice price" in three places for three things: another name for the dirty price in Chapter 1, section 1.8; a name for the clean price in the valuation steps of section 1.11.3; and this delivery amount in Chapter 7. Take the meaning from the chapter.