Introduction

Understanding the spread of a bond is crucial in fixed income markets. It provides valuable insights into a bond’s relative value and risk compared to a benchmark, typically a government bond. In this chapter, we will define and interpret the spread of a bond and explain how it is derived from a bond’s price and the term structure of interest rates.

Spread of a Bond

The spread of a bond, often referred to as the yield spread, is the additional yield that investors demand for holding a bond compared to a benchmark bond with a similar maturity. It reflects the compensation investors require for taking on additional credit risk associated with the bond issuer.

Spread helps in assessing the creditworthiness of the bond issuer. A wider spread indicates that investors perceive higher credit risk, while a narrower spread suggests lower perceived risk.

Deriving Spread from Bond Price

To derive the spread from a bond’s price, you can use the following formula:

$$\text{Spread} = \text{Yield of the Bond} - \text{Yield of the Benchmark Bond}$$

Where:

• Yield of the Bond: The yield-to-maturity (YTM) of the bond in question
• Yield of the Benchmark Bond: The YTM of a similar-maturity benchmark bond, often a government bond

Deriving Spread from Term Structure of Rates

The spread can also be derived from the term structure of interest rates, specifically from the yield curve. The yield curve represents the relationship between interest rates (or yields) and the time to maturity of bonds.

To calculate the spread using the term structure, follow these steps:

1) Obtain the yields of bonds with different maturities on the yield curve.
2) Identify a benchmark bond with a similar maturity to the bond in question.
3) Subtract the yield of the benchmark bond from the yield of the bond in question.

Example: Let’s say you have a corporate bond with a YTM of 5%, and the yield on a comparable government bond with the same maturity is 3%. The spread for this corporate bond would be:

$$Spread=5\%−3\%=2\%$$

This indicates that investors require a 2% higher yield to compensate for the additional risk associated with the corporate bond compared to the government bond.