Introduction

Understanding the profit and loss (P&L) components of a bond position or portfolio is crucial for bond investors and traders. In this chapter, we will delve into the decomposition of the P&L for bond positions, breaking it down into distinct factors. By the end of this chapter, you will be able to identify and analyze the individual components that contribute to the P&L, including carry roll-down, rate change, and spread change effects. This knowledge is invaluable for making informed investment decisions in the fixed-income market.

Decomposing the P&L

When assessing the performance of a bond position or portfolio, it’s essential to understand the various factors that contribute to changes in its value. The P&L can be decomposed into three primary components:

Carry Roll-Down Effect

• The carry roll-down effect, often referred to simply as “carry”, represents the income generated by holding a bond position over time.
• It is the result of earning the bond’s coupon payments and is also influenced by the yield curve’s shape.
• Formula for Carry (C): $C = \sum \text{(Coupon Payments)} - \sum \text{(Yield Changes)}$

For example, suppose you hold a bond with a coupon rate of 5% in an environment where yields are expected to remain stable. The carry would be the 5% coupon payment you receive annually.

Rate Change Effect

• The rate change effect reflects the impact of changes in interest rates on bond prices.
• When interest rates rise, bond prices typically fall, leading to a negative rate change effect.
• Conversely, when rates decline, bond prices tend to rise, resulting in a positive rate change effect.
• Formula for Rate Change Effect (R): R = Price Change Due to Rate Change

For instance, if market interest rates increase by 1%, causing your bond’s price to decrease by 2%, the rate change effect would be -2%.

Spread Change Effect

• The spread change effect relates to adjustments in the yield spread between a bond and a benchmark, often a government bond.
• When the spread narrows (bond yield decreases compared to the benchmark), it contributes positively to the P&L.
• Conversely, when the spread widens (bond yield increases relative to the benchmark), it negatively impacts the P&L.
• Formula for Spread Change Effect (S): S = Price Change Due to Spread Change

For example, if the yield spread of your corporate bond narrows compared to a government bond, causing your bond’s price to increase, the spread change effect would be positive.