Fisher Real Yield
Inflation-adjusted real yield via the Fisher equation: (1 + nominal) = (1 + real)(1 + inflation). The exact relationship between stated nominal yields and inflation-adjusted purchasing-power yields.
When to use: Use to convert a nominal Treasury yield into an inflation-adjusted real yield given an inflation expectation, or to compare nominal bonds against TIPS. The formula is the bridge between cash-return yields and purchasing-power returns.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Real | Real Yield | Inflation-adjusted real yield as a decimal | % |
| Nominal | Nominal Yield | Nominal annual yield as a decimal | % |
| Inflation | Inflation Rate | Expected annual inflation rate as a decimal | % |
Real-Life Examples
Example 1: 5% Nominal, 3% Inflation
A 10-year Treasury yields 5% nominal; expected inflation over the same horizon is 3%.
Given
Step-by-Step
Real yield is 1.94%, slightly below the simple "nominal − inflation" approximation (2.00%). The exact form differs by ~6 bps at these levels; the gap grows with inflation level.
Frequently Asked Questions
The simple subtraction is a first-order approximation: real ≈ nominal − inflation, accurate when both are small. The full Fisher equation accounts for the cross-product (nominal × inflation), which matters once inflation exceeds ~3-5%.
It's the cleanest bridge between nominal bond yields and inflation-protected yields (TIPS). A nominal bond + an inflation swap (or short an inflation-linked bond) creates a synthetic real-yield exposure. Real yields drive long-term equity discount rates too.
For ex-ante real-yield analysis (forecasting), use expected inflation. For ex-post (looking back), use realized inflation over the same horizon. They typically differ — the gap is what nominal bondholders gain or lose to inflation surprise.