Interpolated Treasury Rate Calculator
Understanding the Interpolated Treasury Rate
The Interpolated Treasury Rate (often referred to as the I-Rate) is a derived yield calculated by using linear interpolation between the yields of two benchmark Treasury securities with different maturities. This is essential when valuing financial instruments that do not align perfectly with the standard "on-the-run" Treasury maturities (e.g., 2, 3, 5, 7, 10, 20, or 30 years).
The Linear Interpolation Formula
To find the yield for a specific target maturity, the calculator uses the following mathematical formula:
Where:
T = Target Maturity (in years)
T1 = Shorter Benchmark Maturity (in years)
T2 = Longer Benchmark Maturity (in years)
R1 = Yield of the Shorter Benchmark
R2 = Yield of the Longer Benchmark
Example Calculation
Suppose you need to find the interpolated yield for a 4-year Treasury bond, but you only have data for the 2-year and 5-year benchmarks:
- 2-Year Yield (R1): 4.10%
- 5-Year Yield (R2): 4.55%
- Target (T): 4 Years
The calculation would be: 4.10 + [(4 – 2) * (4.55 – 4.10) / (5 – 2)] = 4.40%.
Why Use Interpolated Yields?
Interpolated rates are vital for fixed-income analysis and corporate finance. They are commonly used for:
- Bond Valuation: Pricing private placements or corporate bonds by adding a spread to the interpolated treasury rate.
- Loan Pricing: Establishing benchmarks for commercial loans with non-standard durations.
- Yield Curve Construction: Creating a smooth yield curve from discrete data points provided by the Treasury Department.
- Hedging: Calculating precise hedge ratios for specific interest rate exposures.