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# Cheapest to Deliver (CTD): Definition and Calculation Formula

## Definition

“Cheapest to Deliver (CTD)” in finance refers to the least expensive security that can be delivered to the long position to satisfy a futures contract. It is often used in bond or futures contracts that allow varieties of a commodity to fulfill contract obligations. The calculation formula commonly involves comparing the gross basis (futures price minus the spot price) for all deliverable bonds, with the one having the lowest cost being designated as the CTD.

### Phonetic

The phonetics for “Cheapest to Deliver (CTD): Definition and Calculation Formula” are:Cheapest – /ˈtʃiːpɪst/to – /tuː/ Deliver – /dɪˈlɪvər/ CTD – /ˌsiː tiː ˈdiː/Definition – /ˌdɛfɪˈnɪʃ(ə)n/and – /ænd/Calculation – /ˌkælkjuˈleɪʃn/Formula – /ˈfɔːrmjʊlə/

## Key Takeaways

1. Definition: In the context of futures contracts involving tangible commodities like bonds or grains, the term “Cheapest to Deliver (CTD)” refers to the least expensive security or commodity that can be delivered to the contract buyer to satisfy the requirements of the futures contract. Essentially, it is the asset that is least costly for the seller to deliver on the contract date.
2. Relevance and Application: When it comes to futures contracts, each contract specifies the product that is to be delivered, but it doesn’t always specify the particular commodity or security. Hence, the seller has the advantage when it comes the physical delivery. The seller can choose from many securities that are acceptable for delivery and will typically choose the cheapest. The CTD security is relevant in determining the futures contract’s theoretical fair value.
3. Calculation Formula: The Cheapest to Deliver is calculated by comparing the Future Value (FV) of each deliverable grade of security (for bond futures for example). It is essentially calculated by incorporating considerations of rates, times, and conversion factors. The CTD bond is the bond for which this difference, also referred to as the implied repo rate, is the largest.

## Importance

The term Cheapest to Deliver (CTD) is crucial in finance and business particularly in the bond and futures market. It refers to the least expensive underlying security (often a bond) that can be delivered to the long position holder to fulfill a futures contract. The calculation formula involves identifying the bond that can be bought in the market and then delivered at the lowest possible cost in order to fulfil the futures commitment. Understanding which instrument is the CTD in a future contract is important as it holds direct relevance to the pricing of the contract and provides insights into potential future trading strategies. Consequently, its knowledge can be used to predict how the price of the futures contract will behave, thus enabling more informed investment decisions.

## Explanation

Cheapest to Deliver (CTD) is a crucial concept used in the futures market, particularly pertaining to bond futures contracts. Essentially, the term denotes the least expensive security or commodity that can be delivered to the futures contract buyer to fulfill the delivery requirements of the contract and close out a futures position. The purpose of identifying the Cheapest to Deliver option is to minimize cost and maximize gain for the seller of the futures contract. Therefore, it inherently holds explicit economic appeal to the seller, allowing them to fulfill their contractual obligation at the lowest possible cost, while still adhering to the contract terms.

The precise determination of which asset is the Cheapest To Deliver involves a specific calculation formula. It primarily factors in the price of the security, the interest earned on the security until the delivery date, and the deliverable price (the price received by the contract holder upon delivery). Therefore, the CTD is not necessarily the bond with the lowest price, but rather the bond which ultimately provides the greatest net return considering the above factors. This information can be critical when negotiating the terms and prices of futures contracts, and it also provides traders with useful insight into the future direction of bond prices.

## Examples

Cheapest to Deliver (CTD) refers to the least expensive underlying asset that can be delivered to fulfil a derivatives contract. This concept is predominantly used in futures contracts, where the seller has the choice of several different assets to deliver to the buyer upon the contract’s maturity. Here are three real-world examples that illustrate this concept:

1. Government Bond Futures: A seller who has a futures contract for US Government Treasury bonds will consider the CTD when it’s time to deliver. Assuming the seller possesses a variety of Treasury bonds that come with varying yields and maturities, the bond with the lowest relative cost (yield, duration) would be the “Cheapest to Deliver.” In this case, the seller will deliver the Treasury bond that is least valuable in the market to fulfil the futures contract.

2. Mortgage-Backed Securities: Consider the scenario of a futures contract on mortgage-backed securities. The seller could deliver one out of a variety of different mortgage-backed securities when the contract matures. They would calculate the CTD and deliver the mortgage-backed security that would cost the least. In this case, variables like interest, maturity date, and the creditworthiness of the underlying mortgages would factor in to find the CTD.

3. Commodity Futures: In a gold futures contract, for example, the seller has the option to deliver gold bullion from various mines. The quality of the gold, transportation costs, and other factors would differ across these mines. The seller will perform a CTD calculation considering all these factors and deliver the gold which is cheapest for them to deliver – hence fulfilling the contract at the lowest possible cost. The calculation formula for CTD hugely depends on the specifics of each situation, but broadly it involves comparing the current market value of each potential deliverable asset, less any income that would be received during the delivery period, plus the cost of financing the acquisition of that asset until the delivery date. The asset with the lowest such value is considered the ‘cheapest to deliver.’

What is Cheapest to Deliver (CTD)?

Cheapest to Deliver, often abbreviated as CTD, is a term used in the futures market. Essentially, it’s the cheapest bond or other deliverable security that can be delivered to the futures contract buyer to fulfill the contract obligations, by the seller, whilst minimizing the cost.

What are the factors considered while determining the CTD?

The determination of the CTD involves several factors such as the price of the bond, interest rate, time to maturity, and the financing cost.

How does the CTD affect the futures contract?

The CTD, being the most cost-effective option, often underlies a futures contract and therefore significantly impacts the pricing and related strategies in the futures market.

How is the delivery option of a bond influential in the concept of CTD?

The contract specifications of the futures generally allow several bonds to be delivered. Thus, the delivery option of the bond plays a crucial role as the holder of the short futures position generally chooses the most economical or ‘Cheapest to Deliver’ bond.

What is the calculation formula for Cheapest to Deliver (CTD)?

The formula for calculating the CTD is:CTD = Bond price – (Bond price x Conversion factor).Where the conversion factor is the price of the deliverable bond to that of the bond future.

Can other securities besides bonds be CTD?

Yes, while the concept is most commonly associated with bond futures, CTD can relate to any futures contract where multiple deliverable assets might exist – such as different grades of oil in an oil future contract.

Does the Cheapest to Deliver (CTD) change over time?

Yes, the CTD can change over the life of the futures contract due to factors such as changes in interest rates, time to maturity, and shifts in the yield curve.

## Related Finance Terms

• Future Contract: A legal agreement to buy or sell a particular commodity asset, or security at a predetermined price at a specified time in the future. Frequently associated with Cheapest To Deliver as it allows the seller to deliver the least expensive commodity.
• Bond Yield: The return an investor realizes on a bond. The calculation of bond yield plays a crucial role in determining the Cheapest To Deliver bond in terms of cost-effectiveness.
• Delivery Option: The options available to the seller regarding what, when, and where to deliver under a futures contract. An important term to understand in connection with Cheapest To Deliver as it directly affects the cost of delivery.
• Conversion Factor: A scaling factor used to equalize the differences among various bonds. It is used in the calculation of Cheapest To Deliver to normalize the price differences due to varying coupon rates and time to maturity.
• Notional Amount: The total amount of a security’s underlying asset. In terms of Cheapest to Deliver, it represents the face value of the bond to be delivered under a futures contract.

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