Determine the expense of handing over a given bond to settle a Treasury bond futures contract.
The idea
The short party in a Treasury bond futures contract chooses which eligible bond to deliver. The cash it receives is the invoice price. Invoice price = settlement futures price × conversion factor + accrued interest on the delivered bond. The cost of buying that bond is its quoted price plus the same accrued interest, so the accrued interest cancels. Delivery cost = quoted bond price − settlement futures price × conversion factor. This is per 100 of face value. The bond with the lowest cost is the cheapest to deliver (CTD). A negative cost means that buying and delivering the bond produces a gain. Typical errors are multiplying the bond price by the conversion factor instead of the futures price, dividing by the factor, and forgetting to scale by face value. Exam questions give prices, factors and a settlement price and ask which bond is cheapest and by how much.
Formulas
Cost of delivering a bond into Treasury futures
cost of delivery = quoted bond price − futures price × CF
- quoted bond price
- the clean price of the bond, per 100
- futures price
- the latest settlement futures price
- CF
- the bond's conversion factor
Accrued interest cancels. The bond with the lowest cost is cheapest to deliver; multiply by the futures price, never by the bond price.
Invoice price received by the short
invoice price = futures price × CF + accrued interest
- futures price
- the settlement futures price
- CF
- the delivered bond's conversion factor
- accrued interest
- accrued interest on the delivered bond, per 100
Per 100 of face; scale by the face value delivered. Dividing by CF is the classic error.
A practice question
In a Treasury bond futures contract, the cost to the short party of delivering a particular bond, per 100 of face value, is calculated as:
- quoted bond price - (settlement futures price x conversion factor) - correct
- quoted bond price - (settlement futures price / conversion factor)Why not: Divides by the conversion factor; the factor multiplies the futures price in the invoice.
- (quoted bond price x conversion factor) - settlement futures priceWhy not: Applies the conversion factor to the bond price instead of the futures price.
- settlement futures price - quoted bond priceWhy not: Ignores the conversion factor altogether and reverses the sign.
The short receives futures price x CF (plus accrued interest) and pays the quoted price (plus the same accrued interest), so the cost = quoted price - futures price x CF.
A harder one
The settlement futures price is 98.00. A deliverable bond has a quoted price of 142.50 and a conversion factor of 1.4000. Accrued interest is the same on the invoice and in the market. The cost of delivering this bond per 100 of face value is:
- 44.50Why not: Ignores the conversion factor in the invoice amount.
- 5.30 - correct
- 3.79Why not: Divides the bond price by the conversion factor instead of multiplying the futures price by it.
- -5.30Why not: Reverses the sign: cost is the bond price less the invoice amount, not the invoice less the bond price.
Cost = 142.50 - 98.00 x 1.4000 = 142.50 - 137.20 = 5.30.
The hardest tier
The latest settlement futures price is 101.00. The table lists four deliverable bonds as (quoted price, conversion factor): Bond A (97.34, 0.9400), Bond B (119.80, 1.1500), Bond C (132.30, 1.3000), Bond D (151.59, 1.4900). Which bond is cheapest to deliver?
- Bond A, with a cost of 2.40Why not: Ranks bonds by quoted price instead of by price less futures price x conversion factor.
- Bond C, with a cost of 1.00 - correct
- Bond D, with a cost of 1.10Why not: Ranks by price divided by conversion factor, which scales the cost by each bond's factor and misorders the close pair C and D.
- Bond B, with a cost of 3.65Why not: Picks the bond with the highest delivery cost; the short wants the lowest cost.
Costs = price - 101.00 x CF: A 2.40, B 3.65, C 1.00, D 1.10. Bond C has the lowest cost and is cheapest to deliver.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Interest Rate Futures
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