Introduction

The yield curve is a critical tool in understanding the relationship between bond yields and their respective maturities. In the context of interest rate futures, particularly Treasury bond futures, the yield curve plays a significant role in determining the cheapest-to-deliver (CTD) Treasury bond. The choice of the CTD bond is crucial as it directly influences the final contract price and market participants’ trading decisions. This chapter delves into how the level and shape of the yield curve impact the selection of the CTD Treasury bond.

Impact of Yield Curve Level

The level of the yield curve, often referred to as the “flatness” or “steepness,” refers to the difference in yields between short-term and long-term bonds. In a steep yield curve, the difference between short and long-term yields is substantial, while in a flat yield curve, this difference is minimal. The level of the yield curve affects the CTD decision as follows:

• Steep Yield Curve: When the yield curve is steep, long-term bonds tend to have higher yields than short-term bonds. In this scenario, the CTD bond is more likely to be a long-term bond with a higher yield. This is because delivering a high-yield bond results in a more favorable final contract price.

• Flat Yield Curve: In a flat yield curve environment, the yield differentials between short and long-term bonds are narrower. Here, the CTD decision might lean towards a short-term bond due to its relatively higher liquidity and ease of trading.

Impact of Yield Curve Shape

The shape of the yield curve refers to its overall curvature, which can be upward-sloping (normal), downward-sloping (inverted), or flat. The shape influences the CTD decision in the following ways:

• Normal Yield Curve: An upward-sloping yield curve implies that longer-term bonds have higher yields than shorter-term bonds. In this case, the CTD decision may favor longer-term bonds since their higher yields can provide a better final contract price.

• Inverted Yield Curve: A downward-sloping yield curve suggests that short-term bonds have higher yields than long-term bonds. Here, market participants might opt for short-term bonds as the CTD, expecting that their higher yields will result in a more advantageous final contract price.

• Flat Yield Curve: In a flat yield curve scenario, the differences in yields between various maturities are minimal. This can lead to a more nuanced CTD decision, where other factors like liquidity and deliverability play a larger role.

Formula

The formula for calculating the implied yield on the CTD bond is:

$$\text{Implied Yield on CTD = } \frac{F V-P}{P} \times \frac{1}{T}$$

Where:

• $FV=$ Face value of the bond
• $P=$ Price of the bond
• $T=$ Time to maturity of the bond in years

Example: Consider a situation where the yield curve is steep, indicating higher yields for long-term bonds. If Bond A (10-year maturity) has a yield of 4% and Bond B (2-year maturity) has a yield of 2%, it might be advantageous to choose Bond A as the CTD bond due to its higher yield.