The exact relationship is multiplicative, not additive. Purchasing-power growth is the nominal growth divided by the price growth, so a real yield is (1 + nominal) ÷ (1 + inflation) − 1. Subtracting inflation from the nominal yield is the everyday shortcut and is close enough at ordinary rates, but the two answers separate as rates rise. At a 4.3 percent nominal yield and 2.5 percent inflation, subtraction gives 1.8 percent and the exact calculation gives about 1.76 percent. At 12 percent and 9 percent the same shortcut is off by nearly a quarter of a percentage point. That arithmetic is the same one the real rate of return uses; what is different here is that on an inflation-indexed bond the market quotes the real figure and leaves the nominal one to be discovered.
Treasury publishes the market's answer every trading day. The Daily Treasury Par Real Yield Curve Rates, which Treasury also calls Real Constant Maturity Treasury rates or R-CMTs, are read from a curve estimated with a monotone convex spline method whose inputs are "bid-side prices for the most recently auctioned TIPS securities." The published points are 5, 7, 10, 20 and 30 years. That series is the closest thing to an observable price for future purchasing power that a US investor can look up.
The gap between the nominal and real curves is inflation compensation, and it is not a forecast. Subtract the real yield at a maturity from the nominal Treasury yield at the same maturity and you get what the market calls the breakeven inflation rate: the average annual inflation over that horizon at which the two bonds would produce the same result. Federal Reserve Board staff who built and maintain the TIPS yield curve describe the measure carefully. Their working paper on the subject reports evidence that these measures "are affected by an inflation risk premium that varies considerably at high frequency", and that in the early years of the sample inflation compensation was "held down ... by a premium associated with the illiquidity of TIPS at the time". The paper's own summary of the components is expectations plus an inflation risk premium minus the TIPS liquidity premium. Treating a breakeven as a clean forecast of inflation ignores two of the three terms.
A negative real yield is a real thing, not an error. When the published real yield on a TIPS is below zero, a buyer holding to maturity is contracting to receive less purchasing power than they paid, and doing so knowingly. What they are buying is the certainty: a known real outcome, backed by the Treasury, instead of an unknown one. Cash and short-term nominal bonds can deliver a negative real result too, but only after the fact and without the buyer having agreed to it in advance.
Real yields matter to plans, not just to bond buyers. A retirement projection stated in today's dollars has to be discounted at a real rate, and the market's real yield curve is the least arbitrary place to start. It is also why an inflation-linked bond ladder is used to fund a spending stream measured in purchasing power: the instrument's promise is denominated in the same units as the liability.