Nominal and real returns: what did the money gain?

An investment can finish with more dollars and less purchasing power. A nominal return describes the change in money. An inflation-adjusted, or real, return compares that change with a stated price index over the same period.

The index matters. A result adjusted by one price measure is not automatically a result adjusted for everything a particular household buys. Start with the amounts and dates, then name the price comparison.

Twenty percent more money

Consider an invented investment worth $1,000 at the start of a year and $1,200 at its end. There are no deposits, withdrawals or distributions during the year. This before-tax model has no fees. Its nominal return is 20 percent: the $200 increase divided by the starting $1,000.

Over those same dates, a supplied hypothetical price index rises from 100 to 110. Prices represented by that index have risen 10 percent. This is an invented index movement, not a reported CPI figure.

To compare purchasing power, express the ending $1,200 in starting-period dollars. Multiply it by the starting index divided by the ending index:

$1,200 × 100 ÷ 110 = about $1,090.91 in starting-period dollars.

The ending amount has about $90.91 more purchasing power than the original $1,000 on this price-index basis. Relative to that original amount, the real return is about 9.09 percent.

The Bureau of Labor Statistics' constant-dollar explanation uses a ratio of price indexes to express money from different periods on a common price basis.

Why subtraction is not the exact answer

Subtracting the 10 percent price increase from the 20 percent nominal return gives 10 percent. It is a quick approximation, not the exact result for these assumptions.

The original $1,000 would have to become $1,100 just to keep pace with this index. The actual $1,200 is $100 above that amount. Divide the $100 excess by the $1,100 now needed to preserve the original purchasing power: about 9.09 percent.

Equivalently, divide the investment's growth factor by the price index's growth factor, then subtract one: 1.20 divided by 1.10, less one. Using the unrounded result gives the same 9.09 percent after rounding. Subtracting the rates uses the old dollar base even though the prices being compared have changed.

More dollars, with less buying power

Change only the ending investment value to $1,050. The starting $1,000, the one-year period and the index movement from 100 to 110 stay the same. Before calculating, decide whether the nominal and real results should each be positive or negative.

The nominal return is positive 5 percent. But $1,050 multiplied by 100 and divided by 110 is about $954.55 in starting-period dollars. Its purchasing power is about $45.45 below the original $1,000, a real return of approximately negative 4.55 percent.

No cash payment of $45.45 has left the investment. The amount describes the shortfall in purchasing power after expressing the ending balance at starting-period prices. The account has risen; the amount it can buy on this index basis has fallen.

Keep the index and the period attached

Both examples cover one year and use the same stated price index. Changing the time window on one side would no longer compare the investment and prices over matching dates. Additional deposits or withdrawals would also need separate treatment before calling the change in the account an investment return.

Identify the currency before adjusting for prices

A gain in a foreign currency can be a loss in US dollars. The SEC’s international-investing guidance notes that exchange-rate changes can increase or reduce an investment return.

For a separate invented example, hold one asset unit throughout a single year. Its value rises from 100 foreign currency units to 110. Across the same start and end dates, the exchange rate changes from $1 to $0.90 per foreign currency unit. There are no distributions, deposits, withdrawals, fees, taxes or other holdings in this illustration.

Both exchange-rate quotes mean US dollars for one foreign currency unit. Convert the asset’s value at each matching date:

• Start: 100 foreign currency units × $1 per unit = $100.
• End: 110 foreign currency units × $0.90 per unit = $99.

The asset gained 10 percent in its foreign currency price. Measured in US dollars, its value fell from $100 to $99: a nominal return of negative 1 percent. The larger foreign currency amount translates into fewer dollars.

Adding the 10 percent asset gain and the 10 percent decline in the dollar value of a currency unit would give zero. That is not the result. The growth factors multiply: 1.10 × 0.90 = 0.99. Both factors cover the same year.

Read the quote before choosing multiplication or division. Here the rate is dollars per foreign currency unit, so multiplying cancels the foreign currency units and leaves dollars. If the quote instead gives foreign currency units per dollar, divide the foreign currency value by that rate.

The $99 is a dollar valuation, not evidence of a completed sale or currency conversion. The negative 1 percent is still a nominal return. Measuring purchasing power would require a stated price index for the same year.

The household-spending and CPI reference addresses a different question: why a household's purchases can change faster or slower than a published index. The return-averages example follows compounding across periods. Neither adjustment can be inferred merely from a larger ending balance.

When reading a return claim, keep its money calculation, period, price index and cost boundary together. Then ask what the adjusted amount would buy on that stated basis. For the book's decisions about money and the life around it, read the opening of Infinite Upside: Building Wealth With Room to Live.