Lesson 9 of 9
Real against nominal
US consumer prices rose 38.6 percent in the ten years to July 2026. A return stated without an inflation basis is not yet a number.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A nominal return counts dollars. A real return counts what those dollars buy.
- Converting between them is a division, not a subtraction, and the shortcut drifts as rates rise.
- A return with no stated basis is ambiguous, and over a decade the ambiguity is large enough to reverse a conclusion.
Two figures can both be called a return. One is the change in the number of dollars. The other is the change in what those dollars purchase. Over one year the difference is small enough to ignore in conversation. Over ten it is not.
The US consumer price index, July 2016 to July 2026
- CPI-U, July of each year
Show the numbers
| CPI-U, July of each year | |
|---|---|
| 2016 | 240.101 |
| 2017 | 244.243 |
| 2018 | 251.214 |
| 2019 | 255.802 |
| 2020 | 258.352 |
| 2021 | 271.903 |
| 2022 | 294.913 |
| 2023 | 304.609 |
| 2024 | 313.569 |
| 2025 | 322.169 |
| 2026 | 332.813 |
The conversion
The real return is the nominal growth factor divided by the inflation factor, minus one. This relation between a nominal rate, a real rate and inflation is usually called the Fisher relation.
Real return equals 1 + nominal return divided by 1 + inflation.
Example1.0496 / 1.0332 = 1.0159, so 1.59 percent
The familiar shortcut is to subtract: 4.96 minus 3.32 is 1.64 percent. That is close, and it is close for a reason. The two forms differ by the product of the real rate and the inflation rate, which is small when both are small and stops being small when either is not.
The decade, measured
The index stood at 240.101 in July 2016 and 332.813 in July 2026. The ratio is 1.38614, so prices rose 38.61 percent over the ten years, which compounds to 3.3191 percent a year.
What it does to a long comparison
One dollar earning 4.96 percent a year for ten years becomes 1.6227 dollars. Divide that by the 1.38614 the price index rose and the purchasing power is 1.1707: a real gain of 17.07 percent over the whole decade, not 62.27 percent. Nearly three quarters of the nominal gain bought nothing.
That is not an argument about any investment. It is an argument about labels. A return quoted as "62 percent over ten years" and a return quoted as "17 percent over ten years" can be the same number measured on two bases, and only the version that names its basis can be checked.
Where the basis usually goes missing
Three places. A long-run market return quoted without saying whether it is real or nominal. A growth rate in a valuation model, where discounting a nominal cash flow at a real rate overstates value and the reverse understates it. And an inflation figure applied to a company whose costs do not move with a general consumer index at all.
Keep the basis consistent on both sides of every comparison. The arithmetic does not care which one you pick. It cares that you picked the same one twice.
Check yourself
Inflation runs at 3 percent and a holding returns 8 percent nominal. What is the real return?
- Exactly 5.00 percent
- About 4.85 percent
- About 5.24 percent
Show the answer
Answer: B.
1.08 divided by 1.03 is 1.04854. Subtracting gives 5 percent, which is 15 basis points too generous, and the error grows with both rates.US consumer prices rose 38.61 percent over the ten years to July 2026. A dollar of 2016 purchasing power needs to become how much by 2026 to break even?
- 1.0332
- 1.3861
- 3.3191
Show the answer
Answer: B.
The index went from 240.101 to 332.813, a ratio of 1.38614. The 3.32 percent figure is the annual rate that compounds to it over ten years.You discount a cash flow forecast that already includes price rises. Which rate should you use?
- A real rate
- A nominal rate
- Either, they give the same answer
Show the answer
Answer: B.
The basis must match on both sides. A nominal cash flow discounted at a real rate is discounted too lightly, and the error compounds with the horizon.Sources
- US Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers, all items, US city average, seasonally adjusted, series CUSR0000SA0. Values read from this product's stored copy of that series on 13 September 2026.
- US Department of the Treasury, Daily Treasury Par Yield Curve Rates, session of 11 September 2026: the 4.96 percent nominal rate used in the worked example.
- Damodaran, Investment Valuation: the requirement that cash flows and discount rates share a basis.
What this leaves out
- The consumer price index measures a general basket. It is not the inflation any single household or any single company experiences, and a company whose input costs move differently will not be described by it.
- The series used here is the seasonally adjusted one. The unadjusted series differs slightly month to month and converges over a decade.
- Index values are revised by the statistical agency. The figures here are the values held on the date stated.
- Nothing here is advice about any security.