A cheapest-to-deliver bond is a bond that can be delivered to fulfill a futures contract at the lowest cost for the seller. It is relevant for futures contracts that allow different bonds to be delivered, such as Treasury bond futures. The seller can choose the bond that has the lowest price relative to the invoice price, which is the price that the buyer pays for the bond. The invoice price is calculated using a conversion factor, which is a number that adjusts the bond’s price to match the notional bond in the contract. The notional bond is a hypothetical bond with a 6% coupon rate and a certain maturity range. The conversion factor is based on the bond’s coupon rate and maturity, and it is usually different from the bond’s actual market price. Therefore, the seller can benefit from delivering a bond that has a lower market price than the conversion factor implies. This bond is the cheapest-to-deliver bond.
To determine the cheapest-to-deliver bond, the seller can use two methods. The first method is to find the bond that has the highest implied repo rate, which is the rate of return that the seller can earn by buying the bond in the spot market and selling it in the futures market. The second method is to find the bond that has the lowest basis, which is the difference between the bond’s spot price and futures price. The bond with the lowest basis usually has the highest implied repo rate and is the cheapest to deliver.
Cheapest-to-deliver bonds are important for pricing futures contracts, as they reflect the lowest cost of delivery for the seller. The futures price is usually based on the cheapest-to-deliver bond, as it is assumed that the seller will deliver this bond. However, the cheapest-to-deliver bond can change over time, depending on the market conditions and the bond characteristics. Therefore, the seller needs to monitor the bond market and the conversion factors to identify the optimal bond to deliver.
Basic Theory:
Cheapest-to-Deliver refers to the bond that, when delivered to fulfill a futures contract, minimizes the cost for the party delivering the bond. In the context of bond futures, the seller of the futures contract has the obligation to deliver a specific bond on the settlement date. The idea is to deliver the bond with the lowest cost, considering factors such as yield, accrued interest, and any other associated costs.
Procedures:
- Identify Eligible Bonds:
- Determine the eligible bonds that can be delivered to fulfill the futures contract.
- Bonds need to meet the criteria specified in the futures contract, including maturity, coupon rate, and other relevant features.
- Calculate Conversion Factor:
- Each eligible bond has a conversion factor, representing the present value of future cash flows of the bond relative to the futures contract.
- The formula for the conversion factor is:
Conversion Factor = (1 - (1 + Yield)^(-Time to Maturity)) / Yield
- Determine the Cheapest-to-Deliver:
- Multiply the conversion factor by the clean price of each eligible bond.
- The bond with the lowest resulting value is the Cheapest-to-Deliver.
Scenario with Real Numbers:
Let’s consider a bond futures contract with three eligible bonds: Bond A, Bond B, and Bond C.
| Bond | Coupon Rate | Maturity | Yield to Maturity | Clean Price | Conversion Factor | Cost (Clean Price * Conversion Factor) |
|---|---|---|---|---|---|---|
| Bond A | 5% | 5 years | 3% | $950 | 4.4724 | $4,248.78 |
| Bond B | 4% | 4 years | 2.5% | $980 | 3.9152 | $3,839.04 |
| Bond C | 6% | 6 years | 3.8% | $920 | 4.8616 | $4,482.05 |
In this scenario, Bond B is the Cheapest-to-Deliver, as it has the lowest cost.
Result:
The Cheapest-to-Deliver bond is Bond B.
Other Approaches:
- Yield-to-Worst Approach:
- Instead of using the yield to maturity, consider the worst-case scenario yield, which can provide a more conservative estimate.
- Total Cost Analysis:
- Include all costs associated with delivering the bond, such as transaction costs, taxes, and any other fees.
