# Cheapest to Deliver CTD Definition and Calculation Formula

## Cheapest to Deliver (CTD) Definition

The Cheapest to Deliver (CTD) is a concept used in the financial industry, particularly in the bond market, to determine the most cost-effective bond that can be delivered to fulfill a futures contract. It is an important concept for traders and investors who participate in futures trading.

The determination of the CTD bond involves several factors, including the bond’s price, yield, and the conversion factor. The conversion factor is a measure of the bond’s value relative to the futures contract. It takes into account the bond’s coupon rate, maturity date, and other factors.

The calculation of the CTD bond involves complex mathematical formulas and analysis. Traders and investors often rely on specialized software and tools to perform these calculations accurately and efficiently.

### Importance of the CTD

Furthermore, the CTD is used as a benchmark for pricing other bonds in the market. It serves as a reference point for determining the value of similar bonds, and it helps investors and traders make informed decisions about buying and selling bonds.

### Factors Affecting CTD Selection

Several factors can influence the selection of the CTD. These factors include the bond’s yield, duration, and liquidity. Bonds with higher yields and longer durations are generally more attractive as CTDs because they offer higher returns. Additionally, bonds that are more liquid and actively traded are preferred as CTDs because they are easier to buy and sell in the market.

Market conditions and investor preferences can also play a role in the selection of the CTD. For example, if interest rates are expected to rise, bonds with shorter durations may be preferred as CTDs to mitigate interest rate risk.

## CTD Calculation Formula

The calculation of the Cheapest to Deliver (CTD) is an important concept in the financial market. It helps determine which bond is the most cost-effective to deliver when settling a futures contract. The CTD calculation formula takes into account several factors to determine the cheapest bond.

### Factors Considered in CTD Calculation Formula:

• Conversion Factor: Each bond has a conversion factor that represents the price of the bond relative to the futures contract. The conversion factor is determined by the bond’s coupon rate, yield, and time to maturity.
• Invoice Price: The invoice price is the price at which the bond is delivered in the futures contract. It is calculated by multiplying the futures price by the conversion factor of the bond.
• Accrued Interest: Accrued interest is the interest that has accumulated on the bond since the last coupon payment. It is calculated based on the number of days since the last coupon payment and the bond’s coupon rate.
• Clean Price: The clean price is the price of the bond without considering accrued interest. It is calculated by subtracting the accrued interest from the invoice price.
• Yield: The yield is the return on the bond, expressed as a percentage. It is calculated based on the bond’s coupon rate, clean price, and time to maturity.

The CTD calculation formula combines these factors to determine the cheapest bond. The formula is as follows:

By calculating the CTD, traders and investors can identify the bond that offers the most cost-effective delivery option for settling a futures contract. This information is crucial in making informed decisions in the financial market.

## How to Calculate the Cheapest to Deliver (CTD)

Calculating the Cheapest to Deliver (CTD) is an important step in bond trading. The CTD is the bond that is most cost-effective to deliver when a futures contract expires. It is crucial to understand how to calculate the CTD to make informed trading decisions.

To calculate the CTD, you need to consider several factors:

1. Conversion Factor: Each bond has a conversion factor that represents the relationship between the bond’s price and the futures price. The higher the conversion factor, the more valuable the bond is as a delivery option.
2. Yield: The yield of each bond in the basket is also a crucial factor. The bond with the highest yield is typically the CTD.
3. Delivery Date: The delivery date is the date on which the futures contract expires. The CTD is the bond that can be delivered and settled on this date.

Once you have gathered this information, you can use the following formula to calculate the CTD:

CTD = (Conversion Factor * Bond Price) / Yield

By plugging in the values for the conversion factor, bond price, and yield, you can determine which bond in the basket is the cheapest to deliver.

It is important to note that the CTD can change over time as bond prices and yields fluctuate. Traders need to stay updated on market conditions and regularly recalculate the CTD to ensure they are making the most cost-effective trading decisions.