Real return: what is left after inflation
The real return shows how much more you can actually buy with your money. It is the return after deducting inflation and, over long periods, the difference between the “number in your account” and genuine prosperity. If you are planning goals such as retirement, you should always think in real terms.
How to calculate the real return
real return = (1 + nominal return) / (1 + inflation) − 1- nominal return
- return in dollars, as it appears in your account
- Inflation
- rise in consumer prices over the same period
The relationship was formulated by Irving Fisher (Fisher 1930): (1 + nominal) = (1 + real) × (1 + inflation). The simple difference is a usable approximation when inflation is low. When inflation is high, the error becomes noticeable: 10% nominal at 8% inflation is not 2% in real terms, but 1.10 / 1.08 − 1 = 1.85%.
What this means over 30 years
| $100,000 over 30 years | Result |
|---|---|
| nominal at 7% a year | $761,226 |
| in today's purchasing power (4.39% real) | $362,909 |
| $100,000 without any return, after 2.5% inflation | purchasing power of $47,674 |
Even moderate inflation halves the purchasing power of uninvested money in just under 30 years: at 2.5% a year, it takes ln 2 / ln 1.025 = 28.1 years. For planning such as withdrawal plans, amounts should therefore be calculated in real terms. Otherwise future sums look larger than they are. If you need $2,000 a month to live on today, you will need around $4,200 in 30 years at 2.5% inflation to afford the same.
Formulas: $100,000 × 1.07^t, × (1.07 / 1.025)^t and / 1.025^t, final values as in the table above. The gap between account balance and purchasing power grows every year; without any return, half of the purchasing power is gone after 28.1 years.
Taxes hit the nominal return
It is the nominal income that is taxed, not the real income. This makes inflation more expensive for investors than the pure purchasing power calculation shows. A simplified example with a flat tax rate of 26.375% on the full annual income, as with interest (the German rate on investment income, used here only as an illustration):
With equity ETFs, the effect is smaller, because price gains are typically only taxed on sale. The principle remains: the higher the inflation, the larger the tax's share of the real return.
Real return in financial planning
For goals that lie in the future, the real return is the right quantity to calculate with. If you want to achieve 3% a year in real terms and expect 2.5% inflation, you need 1.03 × 1.025 − 1 = 5.575% nominal, not 5.5%. Conversely, any nominal return assumption can be translated into a real one before you compare it with today's prices.
In practice, this means: state contributions, withdrawals and target amounts in today's purchasing power and calculate with real returns. A savings plan that rises with inflation every year is a constant savings plan in real terms; a withdrawal that stays constant in nominal terms shrinks in real terms. Tools such as Financial goals or the Monte Carlo simulation can handle both. What matters is not to mix nominal returns with real spending.
Common fallacies
- Money illusion: a salary or portfolio that rises in nominal terms feels like prosperity, even if prices have risen faster.
- Comparing returns from different decades: 8% interest in the 1980s with 5% inflation was worth hardly more in real terms than 3% today at 0% inflation.
- Setting goals in nominal terms: “a million by retirement” sounds like a lot, but in 30 years at 2.5% inflation it is only around $477,000 in today's purchasing power.
- Underestimating costs: ongoing charges of 0.5% a year are an eighth of the income at a real return of 4%, not a two-hundredth of the wealth.
- Ignoring your own inflation: if you rent or drive a lot, you may experience significantly higher price increases than the average index.
Which inflation?
- The official consumer price index of your country, for example the US consumer price index (CPI) or, in the euro area, the Harmonized Index of Consumer Prices (HICP).
- Inflation for your own cost of living may differ, for example due to rent, mobility or health.
- Inflation-protected government bonds (linkers) pay a real return plus inflation. Their yield shows the real return the market expects for safe investments.
From conventional and inflation-protected government bonds with the same maturity, you can read off the breakeven inflation: the inflation rate at which both deliver the same return. If the conventional bond yields 2.6% and the inflation-protected one 0.5% in real terms, it is 1.026 / 1.005 − 1 = 2.09% a year. However, it also contains a premium for inflation risk, which Bekaert and Wang (2010) estimate for several countries. So it is not a pure forecast.
What history shows
Over long periods, the real return determines how wealth builds up. Dimson et al. (2002) document real returns on equities, bonds and money market instruments in 16 countries over 101 years: equities came out ahead in real terms almost everywhere, but with large differences between countries and decades; bonds and the money market delivered little in real terms, and in countries with high inflation even substantial losses. Siegel (2014) shows the same picture for the US since 1802.
Our own analysis of Robert Shiller's monthly US data gives a real return for equities (with dividends) of 6.53% a year from 1881 to mid-2023. The worst twenty-year period ended in June 1921 at −0.22% a year in real terms. Even for equities, inflation was therefore an equal opponent for two decades.
In the short term, neither equities nor bonds protect reliably against inflation. Fama and Schwert (1977) found for the US that both offered hardly any protection against unexpected inflation; in 2022, equities and bonds lost value at the same time as inflation shot up. Gold, too, is often regarded as an inflation hedge. Erb and Harvey (2013) examine this claim critically and find that the real gold price fluctuates strongly (see gold in the portfolio).
For advanced readers: calculating in real terms in a backtest
- Period by period: real monthly returns are obtained from (1 + r) / (1 + monthly inflation) − 1. Chained together, they give the same real final return as dividing the final value by the price level.
- Price index instead of annual rate: for time series, you use the price index itself (deflator) and divide each value of the portfolio by the price level at the same point in time.
- Missing months: price indices are published monthly and with a delay. Between monthly values, the price level is interpolated; at the most recent end, inflation is not yet available. Real values for the last few weeks are provisional.
- Chain-linked indices: long inflation series are chain-linked from several indices (e.g. national CPI and HICP); the level is aligned at the transition.
How Portfolio Lab calculates it
In the Backtest, you can choose the inflation rate for the US, Germany, the euro area, Switzerland or the UK; by default, the region of the base currency applies, so the US with the default base currency, the US dollar. For Germany, the consumer price index is chain-linked with the HICP from 1996; for the euro area, the German index serves as a proxy before 1997. The monthly values are turned into a price level for each day (log-linear between months); outside the data series, Portfolio Lab assumes no inflation and points this out. The results show the real final value, real CAGR, the real value path and inflation per calendar year. The calculations are described in the backtest methodology. The inflation priced in by the market is shown in the Market expectations tab on Macro (see market expectations).
Frequently asked questions
What is the Fisher equation?
The relationship (1 + nominal) = (1 + real) × (1 + inflation) according to Irving Fisher. It is exactly the formula above, solved for the real return.
Is a savings account a loss in real terms?
If the interest rate is below inflation, yes: purchasing power falls, even if the account balance rises.
What real return have equities delivered?
In the US, around 6.5% a year with dividends from 1881 to 2023; in many other countries less, with large fluctuations between decades. For planning, more cautious assumptions make sense.
Should I plan with real or nominal values?
With real values: amounts then remain comparable in today's purchasing power, and you do not have to inflate your spending. All that matters is that you calculate returns and spending on the same basis.
What is breakeven inflation?
The inflation rate at which a conventional and an inflation-protected government bond with the same maturity deliver the same return. It roughly shows what inflation the market expects.
Literature
- Bekaert, Geert; Wang, Xiaozheng (2010): Inflation risk and the inflation risk premium. Economic Policy 25 (64), pp. 755–806. doi:10.1111/j.1468-0327.2010.00253.x
- Dimson, Elroy; Marsh, Paul; Staunton, Mike (2002): Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton University Press.
- Erb, Claude B.; Harvey, Campbell R. (2013): The Golden Dilemma. Financial Analysts Journal 69 (4), pp. 10–42. doi:10.2469/faj.v69.n4.1
- Fama, Eugene F.; Schwert, G.William (1977): Asset returns and inflation. Journal of Financial Economics 5 (2), pp. 115–146. doi:10.1016/0304-405x(77)90014-9
- Fisher, Irving (1930): The Theory of Interest. Macmillan. Source
- Siegel, Jeremy J. (2014): Stocks for the Long Run. McGraw-Hill Education, 5th edition.
This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.