Cheapest-to-deliver

A physically settled bond futures contract lets the seller deliver any security in the eligible basket. Each one carries a conversion factor meant to make the choice neutral: in theory the seller should be indifferent.

In practice he never is. The conversion factors are fixed for the whole delivery month, published upfront, while the prices and yields of the deliverable bonds move every second of every trading day. Once the two drift apart, one bond becomes cheaper to buy in the cash market than the invoice it earns on delivery, and every rational seller will deliver that one.

That bond is the cheapest-to-deliver. And because the market knows the seller will choose it, the futures price tracks the cash price of the CTD, not the notional bond it was supposedly written on.

The comparison is between what the seller pays for a bond in the cash market and what he receives for delivering it.

Net cost of delivery = Cash price of the bond − (Futures settlement price × its CF)

Accrued interest sits on both sides — the seller pays it when buying the bond and receives it inside the invoice amount — so it cancels, and the comparison can be made on clean prices. The bond with the smallest net cost is the CTD.

The choice is not static. As yields move, conversion factors stay put, and the CTD can switch from one bond to another mid-month. That is precisely the uncertainty the design introduces.

Why this killed a product. The workbook records three attempts at exchange-traded interest rate futures in India. The second, in August 2009, launched bond futures on a notional 7% 10-year GOI bond, and "as the settlement for the futures was on the basis of a cheapest-to-deliver methodology, this was also not adopted by the market." The verdict is stated plainly: the product design prior to December 2013 suffered from drawbacks including cheapest to deliver, physical settlement and the zero coupon yield curve, and those drawbacks led to failure. The contracts that finally worked, from December 2013, were cash settled on a named on-the-run bond — no basket, no conversion factors, no CTD.

For each bond i in the deliverable basket:

   Net delivery cost(i) = Clean price(i) − [ Final settlement price × CF(i) ]

   CTD = the bond with the LOWEST net delivery cost

Invoice amount actually received = [ (SP × CF) + AI ] × 2,000

The conversion factor is the price of that security per rupee of principal on the first calendar day of the delivery month, priced to yield 7% semi-annually — computed once, then frozen while the market moves.

Choosing the delivery. The December contract settles at Rs 98.50. Three bonds sit in the basket, with conversion factors published at the start of the delivery month:

The 7.18% GS 2037 is cheapest-to-deliver at 23.74 paise per Rs 100 of face.

What the choice is worth. On a short position of 50 contracts — Rs 1 crore of face value:

Delivering the CTD    : 0.2374 × 2,000 × 50 = Rs 23,740
Delivering the 2033   : 1.2263 × 2,000 × 50 = Rs 1,22,630
Difference                                  = Rs 98,890

Nearly Rs 1 lakh on a Rs 1 crore position, turning entirely on which bond the seller hands over. No seller leaves that on the table.

Why the buyer objects. The long has no say in what arrives. He may need the 2033 for his own book and receive the 2037 instead, with a different duration and a different yield — so his hedge is against a bond he did not choose and may have to sell. Meanwhile the futures price has been tracking the 2037 all month, so a hedger using the contract against the 2033 has been carrying an unmeasured basis all along.

And why the CTD moves. If the 2037 sells off 80 paise while the others hold, its net cost rises to Rs 1.0374 and the 6.79% GS 2034 becomes the CTD at Rs 0.3025. The conversion factors did not move — the market did.

Chapter 7, section 7.9, defines the CTD bond at the close of the physical delivery material: the seller can deliver any of the deliverable bonds, theory says the conversion factor should make him indifferent, practice says otherwise because conversion factors are fixed while prices move, and consequently the futures price tracks the cash price of the CTD. Chapter 3, section 3.1, supplies the history — the August 2009 contract failed on a cheapest-to-deliver settlement methodology, and pre-December-2013 designs are listed as suffering from CTD, physical settlement and the zero coupon yield curve.

Questions are conceptual: why the seller is not indifferent, what the futures price tracks, and which design flaw is blamed for the failure of India's earlier bond futures contracts.

• The seller chooses, not the buyer. The delivery option belongs to the short, which is why it is the short who benefits from it.
• Conversion factors are frozen; prices are not. That mismatch is the entire cause — a question that has conversion factors updating during the month has the mechanism wrong.
• The futures price tracks the CTD, not the notional bond. This is what turns an apparently clean hedge into a basis-risk position.
• Cheapest means lowest net cost of delivery, not lowest market price. A cheap-looking bond with a low conversion factor is often not the CTD.
• The CTD can change during the delivery month. It is a running comparison, re-made as yields move.
• India's live bond futures have no CTD. The successful December 2013 design is cash settled on a named on-the-run security; CTD belongs to the physically settled notional contract, which the workbook presents for study and reference only.