Introduction

The US Treasury bond futures market plays a crucial role in risk management and speculation for market participants. Understanding the concept of the conversion factor is vital to effectively trade these futures contracts. In this chapter, we delve into the explanation and calculation of a US Treasury bond futures contract conversion factor, shedding light on its significance and usage.

Explanation of Conversion Factor

A conversion factor is a key parameter in the US Treasury bond futures market that facilitates the delivery process. It represents the approximate price relationship between the underlying Treasury bond and the futures contract. The conversion factor is designed to equalize the value of different Treasury bonds to ensure a standardized contract size for trading.

The conversion factor takes into account the bond’s coupon rate, maturity, and yield-to-maturity. Higher coupon bonds tend to have lower conversion factors, as the higher coupon payments compensate for the lower market value of the bond. Similarly, longer maturity bonds have lower conversion factors due to the longer period over which the coupon payments are received.

Calculation of Conversion Factor

The conversion factor (CF) can be calculated using the following formula:

$$CF=\frac{P}{B} \times\left(1-\frac{C P N}{(1+YTM)^T}\right)$$ Where:

• $P=$ Clean price of the bond
• $B=$ Bond’s face value
• $CPN=$ Annual coupon payment
• $YTM=$ Yield to maturity as a decimal
• $T=$ Number of semi-annual periods until bond maturity

Example: Let’s consider a US Treasury bond with a clean price of USD 1,200, a face value of USD 1,000, an annual coupon payment of USD 50, a yield to maturity of 3%, and 8 semi-annual periods remaining until maturity.

$$CF=\frac{1200}{1000} \times\left(1-\frac{50}{(1+0.03)^8}\right) \approx 1.185$$

This calculated conversion factor indicates that for every 1.185 change in the bond’s clean price, the futures contract price changes by one point.