Real vs Nominal Return Calculator

The same, for the nominal return. This is usually the larger of the two by a long way: a diversified equity portfolio has a one-year standard deviation around fifteen percent against inflation's one or two, which is most of the reason the band on the real return is wide. Zero means certain.

Optional. The share of the return that goes in tax, as a percentage of the RETURN rather than of the balance. Leave it blank for a sheltered account or where the return is untaxed. Tax is taken before inflation here, which is how it actually works and is why tax and inflation together can turn a positive return negative.

The return before inflation: the number on the statement, the rate on the account, the yield quoted on the bond. Enter it as an annual percentage. Everything this workbook does is the difference between this figure and what it is actually worth.

How fast prices rise over the same year, as a percentage. A published index is an average over a basket nobody buys, so if your own spending is weighted towards housing or energy your real inflation rate is not the headline one, and this field is where you say so.

How unsure you are about the inflation rate, as one standard deviation. Quote it as an annual figure: unlike the projection calculators in this cluster there is no scaling by time here, because the answer is an annual rate rather than a balance at a horizon. One and a half percent is a reasonable starting point for a developed economy over one year. Set it to zero to say you are certain, and the grid collapses along that axis.

What that same balance will actually buy, expressed in today's money. It is the statement figure divided by the compounded inflation over the same years, which is the honest way to read a long projection.

The values across the top of the grid: the nominal return. Read a column to hold the return fixed and vary inflation. The middle entry is your own figure.

The real after-tax return in a lucky tenth. The distance between this and the unlucky tenth is the honest width of the answer, and on an equity-like return uncertainty it is wide enough to be the finding.

The real after-tax return in an unlucky tenth of the grid: high inflation, a weak return, or both. If this is well below zero, a return that looks comfortable on paper is not comfortable once the two rates are allowed to move.

The middle of the weighted grid. It sits near the single-point answer rather than on top of it, because the real return is not symmetric in inflation: one plus inflation sits in the denominator, so the same step down helps more than the step up hurts.

Machinery, and NOT an input. The same for the column axis: Excel substitutes into it while filling the grid, and the rest of the time it mirrors Nominal_Return.

The body of the grid: the real after-tax return recomputed for every combination of the two axes. One hundred and twenty-one cells, each one the whole calculation run again. It is a component of the table rather than a result on its own.

The nominal return less what is left of it in real terms, in percentage points. It is what the two of them took between them, and on a taxed deposit in a normal year it is usually larger than the return that survives.

Machinery, and NOT an input. Excel substitutes each value from the row axis into this cell while it fills the grid; the rest of the time it mirrors Inflation_Rate. Change Inflation_Rate above, never this: the axis is derived from it, so editing the mirror moves the axis while the table walks and the grid comes out meaningless.

Machinery. Excel requires the formula being tabulated to sit in the grid's top-left corner, where it means nothing to a reader, so it is formatted away. It holds Real_After_Tax_Return.

The values down the left of the grid: the inflation rate. Read a row to hold inflation fixed and vary the return. The middle entry is your own figure, and every other entry is floored so the grid never claims prices fell by more than everything.

The nominal return that merely keeps pace: enough to cover inflation and the tax charged on the return itself. It is inflation divided by one less the tax rate, which is higher than the inflation rate whenever there is any tax at all, and the gap surprises people.

Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.

How far the nominal return sits above the rate that merely keeps pace. Positive means the money gains ground in real terms; negative means it loses it. It carries exactly the same sign as the real after-tax return and is the same statement in nominal language.

The nominal return with tax taken out of it, before inflation is considered at all. Blank tax means this equals the nominal return.

How much the subtraction overstates the real return, in percentage points. It is the nominal-less-inflation gap multiplied by inflation over one plus inflation, so it grows with both the gap and the inflation rate. Twenty basis points at ten against three; more than a point once inflation reaches double figures.

What the starting amount on the Data sheet grows to over the years set there, at the after-tax nominal return. This is the number a statement would show, and it is the one that looks reassuring.

The same quantity as almost every calculator and most conversations compute it: the return with inflation subtracted. It is shown so you can see how far off it is, not because it is an alternative answer.

What the return is worth after inflation, by the Fisher relation. This is the figure to rely on, and it is always smaller than the return less inflation when inflation is positive.

What the return is worth after both tax and inflation. This is the headline figure and the one the grid below tabulates. A negative value means the money buys less at the end of the year than at the start, however healthy the statement looks.

The share of the grid below, weighted by how likely each pair of rates is, in which the real after-tax return is above zero. Read it as a shape rather than a forecast: it is the chance under YOUR assumptions about how uncertain the two rates are, and it says nothing about whether those assumptions are right.

The gap between the two: what inflation takes out of the projected balance over the period. It is not a loss you would ever see on a statement, which is precisely why it goes unnoticed.