Inflation and Real Returns

Nominal and real: what money buys

A **nominal** return is what the statement shows: dollars in, dollars out. A **real** return is what those dollars can buy — the nominal return with the effect of rising prices taken out. The difference is invisible month to month and decisive over a working life, because inflation compounds exactly as returns do. At 3% a year, prices double in about 24 years by the same rule of 72 you used in PF4, so money that merely sits loses half its purchasing power over that time without a single dollar disappearing from the account. The exact conversion divides rather than subtracts: real return = (1 + nominal) ÷ (1 + inflation) − 1. A 4% return with 3% inflation is 1.04 ÷ 1.03 − 1 = 0.97% real. The shortcut “nominal minus inflation” gives 1.00% — close enough at low rates and increasingly wrong as inflation rises: at 10% nominal and 8% inflation the shortcut says 2.0%, the truth is 1.85%. The point of the formula is not the decimals; it is the habit of asking, of every return quoted to you, what it is in goods rather than in dollars. Inflation is measured by price indexes, most often the Consumer Price Index, which prices a weighted basket of what households buy. It is an average, so your own inflation can differ — a renter in a fast-rising market, a retiree whose spending leans toward health care — and the plan should use a rate that fits the household rather than the headline. What the index does capture is the long arc: it rose roughly thirty-two-fold between 1913 and 2024, which is to say a 1913 dollar bought about what three cents buy now. • Nominal = the dollars on the statement; real = what they buy. • Real return = (1 + nominal) ÷ (1 + inflation) − 1; subtracting is only an approximation. • Rule of 72 for prices: years for purchasing power to halve ≈ 72 ÷ inflation rate. • Your inflation is not the index’s — plan with a rate that fits your spending. How long until cash buys half as much? — 2% inflation: About 36 years · 3% inflation: About 24 years ← · 5% inflation: About 14 years · 9% inflation — the mid-2022 pace: About 8 years

The tax falls on the nominal return

Inflation and tax interact in a way that is easy to miss and expensive to ignore. Tax on interest, dividends and realised gains is charged on the nominal amount — including the part that only kept up with prices. So the after-tax real return is lower than either adjustment alone suggests. The savings account in the prediction pays 4.0%; a 30% tax leaves 2.80%; and 3% inflation turns that into −0.19% a year. The account is not earning a small real return; it is losing a little purchasing power every year while reporting interest every month. The same arithmetic explains why high inflation is hard on savers even when interest rates rise with it. If rates and inflation both go up by three points, the pre-tax real return is roughly unchanged — but the tax bill rises with the nominal rate, so the after-tax real return falls. It also explains where to hold things. Assets whose returns arrive as fully taxed interest are best held in tax-advantaged accounts when there is room (PF6 and PF7 work through the rules), and assets whose returns arrive mostly as long-deferred gains suffer less from this effect in a taxable account. For planning purposes the conclusion is a single rule: compound real, after-tax returns. A projection that assumes 7% nominal growth and quotes the result in future dollars is not wrong, but it is easy to misread — a million dollars thirty years from now at 3% inflation buys what about $412,000 buys today. Either state goals in today’s money and grow them with real returns, or state them in future dollars and inflate the goal; never mix the two. • Tax is charged on the whole nominal return, including the inflation part. • After-tax real return = [1 + nominal × (1 − tax)] ÷ (1 + inflation) − 1. • Fully taxed interest suffers most — hold it in tax-advantaged accounts where possible. • Plan in real terms, or inflate the goal — never mix today’s and tomorrow’s dollars. One savings account, three lenses (4% rate, 3% inflation, 30% tax) — Nominal, before tax: +4.00% · Real, before tax: +0.97% · Nominal, after tax: +2.80% · Real, after tax: −0.19% ← A savings rate that beats inflation before tax can still lose purchasing power after it. Check the after-tax real number before calling cash “safe” for long-term money.

What a century of real returns looks like

Over long histories the order of real returns is consistent. Across the twentieth century and since, U.S. stocks have returned roughly 6–7% a year above inflation, high-quality bonds about 2%, and short-term government bills about 1% — figures assembled in long-run studies such as the Dimson, Marsh and Staunton yearbook. That ordering is the reason a long-term plan holds stocks at all: they are the asset with the highest expected real return, paid for by the willingness to sit through their falls. Averages over a century hide decades that went the other way, and the exceptions are the lesson. In the 1970s inflation ran faster than nominal stock returns, so U.S. stocks lost purchasing power across the decade even though their prices rose; long bonds did worse, as rising rates and rising prices hit them together. In 2022 a sudden rise in inflation and rates took both stocks and bonds down in real terms in the same year (MR17 tells that story). Over shorter horizons nothing reliably keeps pace with a sudden inflation shock except assets built to do so. Cash is the special case. Its real return is usually small and sometimes negative, and in exchange it holds its nominal value exactly — which is precisely what an emergency fund (PF2) and money for near-term spending need. The mistake is not holding cash; it is holding long-term money in cash and calling the result safe. Over thirty years a balance that earns 1% less than inflation loses about a quarter of its purchasing power, without ever showing a loss on the statement. • Long-run U.S. real returns: stocks ≈ 6–7%, bonds ≈ 2%, bills ≈ 1% a year. • Whole decades have run the other way — the 1970s for stocks and bonds, 2022 for both. • Cash keeps its nominal value exactly — right for buffers, wrong for decades. Real returns, long run against bad decades — U.S. stocks, a century and more: Roughly +6–7% a year after inflation · U.S. stocks, the 1970s: Below inflation across the decade ← · High-quality bonds, long run: About +2% a year after inflation · Stocks and bonds, 2022: Both down after inflation in the same year

Protecting purchasing power: by design, over time, or not at all

Some assets are built to keep pace with prices. **Treasury Inflation-Protected Securities** (TIPS) have a principal that rises with the CPI, and their coupon is paid on the adjusted amount, so held to maturity they deliver a known real return; at maturity the holder receives the larger of the adjusted principal and the original. **Series I savings bonds** pay a fixed rate plus an inflation rate reset every six months; they are limited to $10,000 a person a year electronically, cannot be cashed in the first year, and give up three months of interest if cashed within five. Social Security benefits are adjusted each year by a cost-of-living increase. Other assets keep up only over time. Stocks represent businesses that can raise prices, so across decades they have outpaced inflation by a wide margin — but in a sudden inflation shock, when rates rise and valuations fall, they can lose ground for years. Real estate and commodities have their own versions of the same pattern. Cash in a money-market fund adjusts too, because its yield follows policy rates, but with a lag and before tax. Some assets lose when inflation rises unexpectedly: long fixed-rate bonds, fixed annuities and any contract that pays a set number of dollars far in the future. And one protection has a catch worth knowing before buying it. TIPS protect the real return if held to maturity, but their market price moves with real interest rates, so a TIPS fund sold early can lose money — as TIPS funds did in 2022, when real yields rose sharply. Inflation protection is a promise about purchasing power at the end, not about the price along the way. • By design: TIPS (principal indexed to CPI), I bonds ($10,000 a person a year), Social Security’s annual adjustment. • Over time: stocks, real estate, money-market yields — with lags and bad stretches. • Exposed: long fixed-rate bonds, fixed annuities, fixed future payments. • TIPS protect the real return at maturity, not the price before it. Inflation protection, sorted — TIPS held to maturity: Known real return; principal rises with the CPI · I bonds: Fixed rate + inflation rate reset every six months ← · Diversified stocks: Ahead over decades, can lag for years in a shock · A 30-year fixed-rate bond: Loses value when inflation surprises upward

Choosing the inflation number for a plan

Every long plan needs one inflation assumption, and the choice matters more than it looks, because the assumption compounds for decades. Over thirty years, prices rise 1.81 times at 2% a year, 2.10 times at 2.5%, 2.43 times at 3% and 3.24 times at 4%. A household that plans at the Federal Reserve’s 2% target and lives through 3% needs about a third more money at the end to buy the same life — 2.43 against 1.81 — and finds out late. There are reasonable ways to pick. The Fed’s 2% target is what policy aims for; the long U.S. record, including the 1970s and 2022, has averaged closer to 3%; and a household’s own spending may run hotter — retirees, whose budgets lean toward health care and services, have often faced faster price rises than the headline index. A sensible plan uses a central assumption a little above the target, then runs the same plan at a higher rate to see how much margin it has. If the plan only works at 2%, it does not really work. The assumption also belongs in the right place. A plan written in today’s dollars uses real returns and needs no inflation input until the end, when goals are converted back to future dollars; a plan written in future dollars has to inflate every goal and every expense line, every year. Mixing the two — growing the portfolio at a nominal return while keeping the spending in today’s dollars — quietly assumes inflation is zero, which is the most common error in household projections. • Thirty-year price multiple: 1.81× at 2%, 2.10× at 2.5%, 2.43× at 3%, 3.24× at 4%. • Planning at 2% and living through 3% needs about a third more money at the end. • Use a central assumption a little above the target, then stress the plan at a higher rate. • Real-return plans need inflation only at the end; nominal plans must inflate every line. What thirty years of inflation does to prices — 2% a year — the Fed’s target: Prices × 1.81 · 2.5% a year: Prices × 2.10 · 3% a year — closer to the long U.S. record: Prices × 2.43 ← · 4% a year: Prices × 3.24

Sources

• How the Consumer Price Index is builtU.S. Bureau of Labor Statistics, CPI Handbook of Methods
• Treasury Inflation-Protected Securities and I bondsU.S. Treasury, TreasuryDirect
• A century of real returns on stocks, bonds and billsDimson, Marsh & Staunton, UBS Global Investment Returns Yearbook
• The Fisher relation between nominal rates, real rates and inflationFisher, “The Theory of Interest” (1930)