Nominal vs real return: the difference

Nominal means as stated. Real means after inflation.

A nominal return counts currency units. The balance went from one number to a larger number, and the percentage between them is the nominal return. It is an accurate count of something whose own value is moving underneath it.

A real return counts goods. It asks how much more the money commands at the end than it did at the start, which is the question a saver actually has. If prices rose by as much as the balance did, the real return is zero however healthy the nominal figure looked.

Almost every published return is nominal. Bank rates, fund factsheets, bond coupons and the growth line on a pension statement all count currency, because currency is what the institution is holding for you. Nothing in that machinery measures inflation, so nothing in it separates out the part of the return that only kept pace with prices. That part is genuine in currency terms and worth nothing in the shops.

The same distinction applies to an interest rate rather than a return, where the two names are nominal rate and real rate.

The two returns are linked by multiplication rather than addition:

$$1 + r_{\text{nominal}} = (1 + r_{\text{real}})(1 + i)$$

Rearranged for the figure you want:

$$r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + i} - 1$$

Here $i$ is inflation over the same period as the return, and both rates go in as decimals.

Division is the right operation because inflation applies to the gain as well as to the money you started with. Earn 7 percent while prices rise 3 percent and the extra currency you gained is itself worth about 3 percent less by the time you are holding it, so the whole ending balance has to be marked down, not just the opening balance. Done properly, 7 percent against 3 percent inflation is a real 3.88 percent a year rather than 4.

The shortcut error has a formula of its own. Subtraction minus the true answer is $(r_{\text{nominal}} - i) \times \frac{i}{1 + i}$, so it grows with inflation and with the gap between the two rates, and it takes the sign of that gap. Above inflation it reads high: 0.12 percentage points at 7 percent against 3 percent, small enough to survive a glance and compounding along with everything else in a long projection, and 2.31 points at 40 percent against 30 percent, where the shortcut says 10 percent and the answer is 7.69 percent. Below inflation it reads low, so at 2 percent against 3 percent the truth is -0.97 percent and subtraction says -1, making the loss look slightly worse than it is.

It depends on the question, and the split is clean.

Use the nominal figure to rank options over the same period. Two funds, two savings accounts, two bonds priced in the same currency and held over the same stretch of calendar all faced the same inflation, so converting both changes the numbers and never changes the order. What converting does add is the separate answer to whether either one beat inflation at all, which no ranking can tell you.

Use the real figure to answer whether the money gained ground at all, and in any plan that runs for years. That is where the comparison is against a quantity of goods rather than against another product, and only the real figure is denominated in goods. A goal stated in today's money and reached at a real rate keeps its meaning the whole way; the same goal stated as a nominal sum quietly shrinks while you save for it.

Tax sits between the two, and it comes first. In the United States and most systems like it, tax on a taxable account is charged on nominal interest and nominal gains rather than on the real part, so some of the bill lands on the portion of the return that merely covered rising prices. A few countries index the taxable gain to inflation instead, so check the rule where you file. Either way, work out the after-tax nominal rate first, then take inflation out of that. The real return calculator runs the adjustments in that order and puts the result on a balance.

Three mistakes account for most of the trouble.

The first is a period mismatch. The return and the inflation figure have to cover the same stretch of time, so an annual return needs an annual inflation rate, not the latest monthly print annualised in your head. The same applies to compounding: convert a quoted rate to what it actually pays over a year before dividing, which is what the APR against APY calculator is for.

The second is counting inflation twice. Inflating a target to a future date and then discounting the projection at a real rate applies the same adjustment at both ends. Pick one. Grow at the nominal rate against an inflated target, or grow at the real rate against a target in today's money.

The third is letting the horizon hide the gap. A single year of low inflation is a rounding error and thirty years of it is not, because inflation compounds in the same way interest does. At 3 percent a year, an ending balance thirty years out buys 41.2 percent of what its face value suggests, and at that same 3 percent money left alone halves in buying power in roughly 23 years. Where inflation runs in double digits, no year is a rounding error and the conversion matters from the first one. The guide to inflation and purchasing power works through what that does to a balance.