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Application Concept: Term Structure

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Textbook ELI8 Bootstrapping Bootstrap Coupon Bond

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.