Cheapest to deliver: Meaning, Criticisms & Real-World Uses

What Is Cheapest to Deliver?

Cheapest to Deliver (CTD) refers to the specific underlying security within a futures contract that a seller, holding a short position, can deliver at the lowest cost to satisfy the contract's obligations. This concept is a crucial element within derivatives trading, particularly prevalent in the market for U.S. Treasury bonds and notes futures, where a range of diverse financial instruments can qualify for delivery. Because multiple Treasury securities can be delivered against a single futures contract, identifying the Cheapest to Deliver allows the short position to optimize their profit by selecting the most economically advantageous security to deliver to the buyer, who holds the long position.

History and Origin

The concept of Cheapest to Deliver arose with the development of exchange-traded interest rate futures, particularly those on government debt. Unlike futures contracts on commodities, where the underlying asset is typically standardized, bond futures contracts often allow for the delivery of various bonds that meet certain criteria (e.g., maturity range, coupon rate). This flexibility provides the short position with a "delivery option," allowing them to choose which bond to deliver. The Chicago Board of Trade (CBOT), now part of the CME Group, introduced the first U.S. Treasury bond futures contract in 1977. This innovation necessitated a mechanism for determining the most economical bond for delivery among the eligible basket of securities. The calculation of the Cheapest to Deliver bond became fundamental for pricing and trading these contracts. CME Group provides extensive resources explaining how the Cheapest to Deliver is determined and its significance in the Treasury futures market.⁶

Key Takeaways

Cheapest to Deliver (CTD) is the most cost-effective bond or security that a seller can deliver to fulfill a futures contract obligation.
It is particularly relevant for Treasury bond and note futures, where a "basket" of eligible securities can be delivered.
The determination of the CTD bond significantly impacts the pricing and trading strategies for these futures contracts.
Factors like coupon rates, maturities, market prices, and conversion factor influence which bond is the CTD.
Traders on the short side of the futures contract aim to identify and deliver the CTD to maximize profitability or minimize costs.

Formula and Calculation

The Cheapest to Deliver bond is determined by calculating the implied cost of delivering each eligible bond. The general approach involves comparing the invoice price of each deliverable bond to its current market price. The invoice price is what the long position pays to the short position upon delivery.

The formula for the invoice price is:

\text{Invoice Price} = (\text{Futures Settlement Price} \times \text{Conversion Factor}) + \text{Accrued Interest}

Where:

Futures Settlement Price: The price at which the futures contract settled.
Conversion Factor: A multiplier set by the exchange (e.g., CME Group) for each eligible bond. It adjusts the futures price to account for differences in coupon rates and maturities relative to a notional bond specified by the exchange. The conversion factor is the price of the delivered note (with a $1 par value) to yield 6 percent, as specified by exchanges like the CBOT for certain Treasury notes.⁵
Accrued Interest: The interest earned on the bond since its last coupon payment, which the buyer must pay to the seller.

To find the Cheapest to Deliver, traders calculate the "net basis" or "implied repo rate" for each eligible bond. The bond with the lowest net basis or the highest implied repo rate is typically the CTD.

The net basis is generally calculated as:

\text{Net Basis} = \text{Cash Price of Bond} - (\text{Futures Price} \times \text{Conversion Factor}) - \text{Carry}

Where:

Cash Price of Bond: The current market price of the deliverable bond.
Carry: The financing cost (or income) of holding the bond until the delivery date, typically involving the repo market and the bond's coupon income.

The bond with the lowest net basis is the Cheapest to Deliver.

Interpreting the Cheapest to Deliver

Understanding the Cheapest to Deliver is vital for participants in fixed income markets, particularly those trading Treasury futures. The CTD bond effectively becomes the de facto underlying asset of the futures contract because its price movements often dictate the futures contract's price. When the CTD bond changes, the futures contract's pricing characteristics can shift.

Traders continuously monitor the basket of eligible bonds to identify the CTD because changes in interest rates or the yield curve can cause a different bond to become the Cheapest to Deliver. This is known as a "CTD switch." A CTD switch can lead to significant price adjustments in the futures contract as market participants re-evaluate its value based on the new underlying security. Academic research has explored the complexities of CTD determination, noting that the CTD bond may not always be the one with extremal duration, challenging common misconceptions.⁴

Hypothetical Example

Consider a scenario involving a hypothetical 10-year Treasury note futures contract. There are three eligible bonds for delivery:

Bond A: 2.00% coupon, 9 years to maturity, current market price $102, conversion factor 0.950
Bond B: 3.50% coupon, 10 years to maturity, current market price $110, conversion factor 1.050
Bond C: 1.50% coupon, 8.5 years to maturity, current market price $98, conversion factor 0.900

Assume the futures settlement price is 120 and the carry cost for all bonds until delivery is equivalent.

To find the Cheapest to Deliver, we calculate the implied invoice price for each bond and then determine which bond offers the short seller the greatest profit (or smallest loss) by comparing the invoice price to the bond's cash market price. A simpler method, when ignoring carry for illustrative purposes, is to find the bond that provides the most cash from delivery relative to its market cost.

Let's simplify and consider the cash bond's cost relative to the proceeds from selling the futures contract:

Proceeds from futures (for short seller) = Futures Price × Conversion Factor

Bond A: Proceeds = 120 × 0.950 = $114.00. Cost to acquire = $102. Profit/Loss (Proceeds - Cost) = $12.00
Bond B: Proceeds = 120 × 1.050 = $126.00. Cost to acquire = $110. Profit/Loss = $16.00
Bond C: Proceeds = 120 × 0.900 = $108.00. Cost to acquire = $98. Profit/Loss = $10.00

In this simplified example, Bond B offers the highest profit margin (\$16.00) for the short seller, making it the Cheapest to Deliver. In real-world scenarios, carry costs and the precise calculation of net basis or implied repo rate would be critical to this determination.

Practical Applications

The Cheapest to Deliver concept has several critical practical applications in financial markets:

Futures Pricing: The price of a Treasury futures contract is not simply the price of a single bond but is heavily influenced by the Cheapest to Deliver bond. Traders and analysts often refer to the futures price as the price of the CTD bond, adjusted by its conversion factor. This relationship is crucial for basis trading strategies, which involve simultaneously buying (or selling) the futures contract and selling (or buying) the underlying CTD bond.
Hedging Strategies: Portfolio managers and financial institutions use Treasury futures to hedge interest rate risk. Accurate identification of the CTD is essential for constructing effective hedge ratios, ensuring that the futures position appropriately offsets the risk of the underlying bond portfolio.
Arbitrage Opportunities: Discrepancies between the theoretical value of a futures contract (derived from its CTD bond) and its market price can create arbitrage opportunities. Sophisticated traders actively seek these mispricings.
Market Analysis: Tracking the CTD bond provides insights into the prevailing market conditions and expectations. A change in the CTD can signal shifts in the yield curve or relative value of different Treasury securities, impacting broader market sentiment. The Federal Reserve Bank of New York regularly analyzes the U.S. Treasury market's market liquidity and functioning, which are directly impacted by factors influencing the CTD.

##³ Limitations and Criticisms

While the Cheapest to Deliver is a cornerstone of Treasury futures trading, it has certain limitations and criticisms:

Dynamic Nature: The CTD can change frequently due to shifts in interest rates, changes in the shape of the yield curve, or supply and demand dynamics for specific bonds. This dynamic nature means that the "underlying" asset of the futures contract is not static, complicating long-term portfolio management and analysis.
Complexity: The calculation of the CTD involves multiple variables and can be complex, especially when considering the nuances of accrued interest and various financing costs. This complexity can make it challenging for less experienced market participants to accurately identify the CTD.
Model Dependence: Determining the CTD often relies on financial models that make assumptions about future interest rates and market behavior. If these assumptions are flawed, the identified CTD may not truly be the most economical choice. Research has indicated that the CTD determination is not always straightforwardly characterized by bond duration and can involve scenarios with complex combinations of coupons and maturities.
² Market Illiquidity: While the overall Treasury market is highly liquid, specific bonds within the deliverable basket might experience periods of reduced liquidity. If the theoretically Cheapest to Deliver bond becomes illiquid, it can be difficult or costly for the short position to acquire and deliver, undermining the theoretical advantage.
¹ Delivery Options and Risk: The flexibility provided by delivery options means that the short seller, not the long buyer, controls the choice of bond. This introduces an element of uncertainty for the long position regarding the exact bond they will receive, though the contract specifications ensure the bond is within a defined grade and quality.

Cheapest to Deliver vs. Implied Repo Rate

The Cheapest to Deliver (CTD) and the Implied Repo Rate are two intimately related concepts in futures markets, particularly for bonds. While the CTD identifies the most economically advantageous bond for delivery, the implied repo rate is a key metric used in that determination.

The Cheapest to Deliver is the outcome—it is the specific bond within the eligible basket that a short position will choose to deliver because it minimizes their cost or maximizes their profit. It's the bond that provides the best return when purchased in the cash market and simultaneously sold through the futures contract for delivery.

The Implied Repo Rate (IRR) is a calculation that helps identify the CTD. It represents the hypothetical interest rate or return an arbitrageur would earn by simultaneously buying an eligible bond in the cash market, selling a futures contract, and then lending the bond out in the repo market until the futures delivery date. The bond with the highest implied repo rate is generally the Cheapest to Deliver. A higher implied repo rate indicates a more attractive return for performing this "cash and carry" trade, signaling that the bond is relatively undervalued in the cash market compared to the futures market, making it the most profitable for the short position to deliver. Therefore, while CTD is the ultimate selection, IRR is a crucial analytical tool for making that selection.

FAQs

What types of futures contracts commonly involve the Cheapest to Deliver concept?

The Cheapest to Deliver concept is most commonly associated with Treasury futures contracts, such as those for U.S. Treasury bonds and notes, which allow for a basket of different but similar securities to be delivered. It can also appear in other fixed income or commodity futures where the underlying asset has a range of deliverable grades or maturities.

Why is the Cheapest to Deliver important for futures traders?

For futures traders, particularly those on the short side, identifying the Cheapest to Deliver (CTD) is critical for maximizing profit or minimizing loss. The CTD dictates the effective underlying asset of the futures contract, influencing its pricing and providing a benchmark for arbitrage and hedging strategies.

Can the Cheapest to Deliver bond change over time?

Yes, the Cheapest to Deliver bond can change, or "switch," over time. This typically happens due to movements in interest rates, changes in the shape of the yield curve, or shifts in the supply and demand for specific deliverable bonds. Traders continuously monitor market conditions to identify potential CTD switches.

How do exchanges like the CME Group facilitate the Cheapest to Deliver process?

Exchanges like the CME Group define the basket of eligible securities for each futures contract and publish the conversion factors for each bond. These factors standardize the value of different deliverable bonds relative to the futures contract's notional bond, making it possible for market participants to calculate and identify the Cheapest to Deliver.

Does the Cheapest to Deliver benefit the buyer or seller of a futures contract?

The Cheapest to Deliver primarily benefits the seller (the short position) of a futures contract, as they have the option to choose which bond to deliver from the eligible basket. Their goal is to select the bond that is most cost-effective for them to acquire and deliver, thereby maximizing their profit on the short futures position.