Inferring Real Yields and Inflation from Nominal Rates

Summary

The note addresses whether nominal spot rates alone can determine both real interest rates and expected inflation through the Fisher relationship. Its proposed market-based route is to use inflation-linked government bonds. Their quoted prices can account for inflation already accrued, while prices excluding that uplift can be used to derive real yields. Bootstrapping those yields produces a real zero-coupon curve, which can then be compared with nominal rates to estimate market-implied inflation.

The result is an implied expectation rather than a uniquely determined forecast from nominal rates alone. The answer cautions that similar inflation-linked instruments can imply different inflation expectations across markets, even when they reference the same inflation index. Such differences indicate that the subtraction can reflect market-specific pricing conditions as well as inflation expectations. The note gives a practical curve-construction outline but does not specify instruments, adjustments, or a full method for isolating those effects.

Key ideas

• Nominal spot rates alone do not identify real rates and expected inflation separately.
• Inflation-linked bond prices can be used to estimate real yields.
• Bootstrapping real yields produces a real zero-coupon curve for comparison with nominal rates.
• The difference between nominal and real rates gives a market-implied inflation measure.
• Markets referencing the same inflation index may still imply different expectations.

Tags

# How to get real interest rate from Nominal spot rates?


# How to get real interest rate from Nominal spot rates?












I have the nominal spot rates. Based on the Fisher equation , how to get the real interest rate ($r$) and the "expected inflation" ($\pi$) ?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/22305

There is a market for inflation linked government bonds (some countries e.g. US,CA,UK,FR,Germany,...). There are various prices quoted. The price with inflation lift (the inflation that has accumulated since the inception of the bond) and the price without the lift reflecting future nominal interest and inflation. You can calculate the real yield to maturity of inflation linked bonds (using the price without the lift) you get a coupon/yield curve. If you bootstrap this curve then you get a real zero curve. You can subtract nominal rates to get some kind of implied inflation expectation.

But note that for example Germany and France issue bonds linked to EMU inflation and I would be surprised if you get the same expected inflation for both bond markets (although they are linked to one and the same).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.