Application Concept: Term Structure
The yield curve guides investors in understanding how the value of investments changes over time with the term structure of interest rates.
Bootstrapping: A Step-by-Step Guide
Understanding the term structure of interest rates is crucial for making informed investment decisions. Bootstrapping is a method used to derive implied interest rates for different maturities based on observed market prices. Let's walk through the process step by step using 1, 2, and 3-year bonds.
Step 1: 1-year Bond
Implied Interest Rate = (Future Value - Present Value) / Present Value
For a 1-year bond:
- Future Value is the amount the bond will be worth in one year, which is $1000 (the face value of the bond).
- Present Value is the cost of the bond today, which is $980.
= ($1000 - $980) / $980
= $20 / $980
≈0.0204 or 2.04%
Step 2: 2-year Bond
Implied Interest Rate = ((Future Value - Present Value) / Present Value) / Time
For a 2-year bond:
- Future Value is the amount the bond will be worth in two years, which is $1000 (the face value of the bond).
- Present Value is the cost of the bond today, which is $950.
= (($1000 - $950) / $950) / 2
= ($50 / $950) / 2
≈0.0263 or 2.63%
Step 3: 3-year Bond
Implied Interest Rate = ((Future Value - Present Value) / Present Value) / Time
For a 3-year bond:
- Future Value is the amount the bond will be worth in three years, which is $1000 (the face value of the bond).
- Present Value is the cost of the bond today, which is $900.
= (($1000 - $900) / $900) / 3
= ($100 / $900) / 3
≈0.0370 or 3.70%
Conclusion
By following these steps, we have successfully bootstrapped implied interest rates for 1, 2, and 3-year bonds. This method allows investors to create a term structure that aligns with market prices, providing valuable insights for decision-making in the dynamic world of fixed-income securities.
This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.