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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.

Textbook ELI8 Bootstrapping Bootstrap Coupon Bond
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Bootstrapping Coupon Bonds: A Step-by-Step Guide

Understanding the term structure of interest rates is crucial for making informed investment decisions, especially when dealing with coupon bonds. 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 practical examples of 1, 2, and 3-year coupon bonds.

Step 1: 1-year Coupon Bond

Implied Interest Rate = (Face Value + Coupon Payment - Cost of Bond Today) / Cost of Bond Today

For a 1-year coupon bond:

  • Face Value is $1000 (the face value of the bond).
  • Coupon Payment, let's assume, is $50.
  • Cost of Bond Today is $980.

Calculate the implied interest rate by adding the face value and coupon payment, subtracting the cost of the bond today, and dividing by the cost of the bond today.

This gives us an implied interest rate of approximately 7.14%.

Step 2: 2-year Coupon Bond

Implied Interest Rate = (Face Value + 2 * Coupon Payment - Cost of Bond Today) / Cost of Bond Today

For a 2-year coupon bond:

  • Face Value is still $1000.
  • Coupon Payment remains $50.
  • Cost of Bond Today is now $950.

Calculate the implied interest rate similarly by incorporating the face value, coupon payment, and cost of the bond today.

This gives us an implied interest rate of approximately 7.89%.

Step 3: 3-year Coupon Bond

Implied Interest Rate = (Face Value + 3 * Coupon Payment - Cost of Bond Today) / Cost of Bond Today

For a 3-year coupon bond:

  • Face Value is once again $1000.
  • Coupon Payment remains $50.
  • Cost of Bond Today is $920.

Calculate the implied interest rate using the provided formula, involving the face value, coupon payment, and cost of the bond today.

This gives us an implied interest rate of approximately 7.28%.

Conclusion

By following these steps, we have successfully bootstrapped implied interest rates for 1, 2, and 3-year coupon 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.