What it means
Bond futures do not name a single bond. The exchange publishes a basket of eligible issues and the seller chooses which to deliver, so the contract behaves as though the seller holds a valuable option.
Conversion factors exist to make bonds with different coupons and maturities roughly comparable. They are calculated by pricing each bond to a standard notional yield, but the adjustment is never exact, and those residual differences are what create a cheapest to deliver bond.
The calculation compares the cost of buying a bond in the market with the invoice amount received on delivery, which is the futures price multiplied by that bond's conversion factor plus accrued interest. The smallest net cost, or equivalently the highest implied repo rate, identifies the winner.
This matters well beyond the delivery process itself, because hedgers use these contracts to manage interest rate risk. The futures contract behaves like the cheapest to deliver bond, so a hedge sized against a different bond will not move as expected.
The identity of the cheapest to deliver bond is not fixed. It shifts as yields move, generally favouring longer, lower coupon bonds when yields rise and shorter, higher coupon bonds when yields fall, which is why the delivery option has genuine value.
In practice
Real-world examples.
Example
A bank holding $50,000,000 of government bonds hedges with futures and sizes the hedge using the duration of the cheapest to deliver bond rather than the average duration of the basket. Using the wrong bond would have left roughly a tenth of the position unhedged.
Example
A pension fund trader notices that after a sharp fall in yields the cheapest to deliver has switched from a 30 year bond to a shorter, higher coupon issue. The hedge ratio has to be recalculated, and the fund adds contracts to keep the same interest rate exposure.
Example
A proprietary trader buys the cheapest to deliver bond and sells futures against it, earning an implied repo rate of 4.6% while funding the position at 4.2%. On $10,000,000 of bonds held for 90 days, the 0.4 percentage point spread is worth $10,000,000 x 0.004 x 90 / 360 = $10,000.
Formula
Calculation
Net cost of delivery = market price of the bond - (futures price x conversion factor)
The cheapest to deliver bond is the one with the lowest net cost.
A bond futures contract settles at a price of 98.00 and three bonds are eligible for delivery, all quoted per $100 of face value.
Bond A trades at 102.50 with a conversion factor of 1.0450, so the seller receives 98.00 x 1.0450 = 102.41 and the net cost is 102.50 - 102.41 = 0.09. Bond B trades at 105.20 with a factor of 1.0700, giving 98.00 x 1.0700 = 104.86 and a net cost of 105.20 - 104.86 = 0.34. Bond C trades at 96.40 with a factor of 0.9820, giving 98.00 x 0.9820 = 96.236 and a net cost of 96.40 - 96.236 = 0.164.
Bond A is the cheapest to deliver at 0.09 per $100 of face value. On a contract covering $100,000 of face value that is $90, against $340 for Bond B and $164 for Bond C, so a trader short the future would buy and deliver Bond A.Case study
Seen in the real world.
The following is an illustrative and fictional example. Corvid Capital, an invented fixed income fund, was short 200 bond futures contracts into a delivery month, each covering $100,000 of face value, a total of $20,000,000.
Its analyst priced all three eligible bonds on the morning of the delivery notice using a futures settlement price of 98.00. Bond A came out at a net delivery cost of 0.09 per $100, Bond B at 0.34 and Bond C at 0.164. Delivering Bond A rather than Bond B saved 0.34 - 0.09 = 0.25 per $100, which on $20,000,000 of face value was 0.25% x $20,000,000 = $50,000 for a decision that took an hour to check.
The fictional fund had learned the lesson two months earlier. Yields had risen by around 80 basis points, the cheapest to deliver had quietly shifted to a longer, lower coupon bond with greater sensitivity to rate moves, and a hedge left sized against the old bond had drifted badly out of line before anyone noticed.
Watch out
Common mistakes.
- Assuming a bond futures contract tracks one specific bond, when the seller may deliver any issue from an eligible basket.
- Treating conversion factors as a perfect equaliser, which would mean every bond costs the same to deliver and no cheapest to deliver bond exists.
- Setting a hedge ratio once and leaving it, even after yields have moved enough to change which bond is cheapest to deliver.
Questions
People also ask.
Why does a cheapest to deliver bond exist at all?
Because conversion factors are calculated against a standard notional yield, so they only approximate the real price relationships between bonds in the basket.
Who benefits from the delivery choice?
The seller of the contract, who holds the option of which bond to deliver, and that option value is reflected in a slightly lower futures price.
What happens when yields move sharply?
The cheapest to deliver bond can switch to a different issue with a different duration, which changes how the futures contract behaves and how large a hedge needs to be.
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