Fisher Effect

The relationship is built as a compounding identity: one plus the nominal rate equals the product of one plus the real rate and one plus expected inflation. Expanding that product gives the real rate, plus expected inflation, plus the cross-product of the two. The familiar additive shortcut, nominal equals real plus expected inflation, simply drops that cross-product term.

The omission is trivial in low-inflation environments and material in high-inflation ones. With a 2 percent real rate and 3 percent expected inflation, the cross-product adds six basis points. With a 3 percent real rate and 40 percent expected inflation, it adds 120 basis points, and the approximation understates the required nominal rate badly. Candidates should default to the exact form whenever rates are large, and should be able to invert it: the real rate equals one plus nominal, divided by one plus expected inflation, minus one.

The clean two-part decomposition assumes lenders need compensation only for the expected loss of purchasing power. In practice they also face uncertainty about that expectation being wrong, so a fuller reading of a nominal government yield is the real risk-free rate, plus expected inflation, plus an inflation risk premium. The premium compensates for the variance of future price levels, not their expected level, and it widens when inflation becomes volatile or when the policy regime loses credibility.

This matters directly for interpreting index-linked bond markets. A breakeven rate derived from nominal and inflation-protected yields embeds that risk premium, and is further distorted by differences in liquidity and by any indexation lag. Breakevens therefore tend to sit above true expected inflation in normal conditions, which is why survey measures and market measures rarely coincide.

The proposition becomes an economic hypothesis, rather than an accounting identity, when it is asserted that the real rate is determined by real forces such as productivity, demographics and time preference, so that changes in expected inflation pass one-for-one into nominal rates. Full pass-through is the long-run implication of money neutrality: monetary expansion raises the price level and nominal rates but leaves real output and the real rate unchanged.

Short-run behaviour deviates. Central banks move the policy rate faster than inflation expectations adjust, so real rates fall when policy is loosened and rise when it is tightened. Policy rules of the Taylor type are explicitly written to force a more-than-one-for-one nominal response to inflation, precisely because only then does the real rate rise and restrain demand. Empirical estimates of pass-through are typically incomplete over short horizons and closer to complete over long ones.

Three tasks recur. First, converting between real and nominal returns, most often when a portfolio's required return must preserve purchasing power for a taxable investor, where inflation compensation is grossed up before tax rather than added after. Second, maintaining consistency in discounting: nominal cash flows must be discounted at nominal rates and real cash flows at real rates, and mixing the two is the most common source of valuation error.

Third, reading policy stance. A nominal policy rate says little on its own; subtracting expected inflation reveals whether the real policy rate is above or below a neutral estimate. The same logic explains why high-inflation economies carry high nominal yields without necessarily offering high real returns, and why cross-country nominal yield comparisons are meaningless until inflation expectations are stripped out.