6% return turns EUR 10,000 into EUR 10,600 in one year. What looks like a respectable profit, however, is only half the truth, because at an inflation rate of 2%, the same sum loses purchasing power. In the end, you can buy only goods and services worth around EUR 10,392 in the base year. If realistic investment costs of EUR 50 and, in a simplified calculation, taxes of approximately EUR 158.25 are also deducted, real purchasing power falls to just under EUR 10,188. Very little of the supposedly high return is then left.
The terms nominal and real return therefore do not describe the same thing, because costs and taxes are always added to the return, and these are not included in many sales prospectuses.
Interest is a payment; return is the balance
Anyone who entrusts their savings to others receives an interest payment as a small compensation. While this is regularly credited to a savings balance as an interest rate, return describes the overall result of an investment in relation to the capital invested. In a broadly diversified investment, price changes can also contribute to a return in addition to interest. Distributions are added, costs are deducted and the period influences the calculation. An interest rate of 5% does not automatically result in a return of 5%.
A simple example: On paper, EUR 10,000 initially produce EUR 500 of income at 5% interest. If the entire investment costs EUR 50 per year, equivalent to around 0.5%, EUR 450 remains before taxes – the actual return is then only 4.5%, not the advertised 5%.
With an investment whose value fluctuates, the difference can be even greater. Positive interest or a distribution does not prevent a price loss from pushing the overall result into negative territory. Return therefore considers not only the ongoing cash inflow, but the entire change in wealth. Above all, this includes considering time: 10% appreciation over five years is not 10% per year, and without additional contributions via an automated savings plan, this corresponds to only an average annual return of around 1.92%.
Return figures therefore always need a clear reference: the period, deposits and withdrawals, price changes, distributions, costs and taxes must be clearly shown.
Nominal and real return do not measure the same thing
Nominal return shows how much a sum of money has risen in euros. Inflation is left out of the picture. At a nominal return of 6%, EUR 10,000 becomes EUR 10,600. The account balance has grown by EUR 600, while real return also takes purchasing power into account. Assuming inflation of 2%, the calculation is:
EUR 10,600 ÷ 1.02 = EUR 10,392.16
Measured in the prices of the base year, the final amount therefore has purchasing power of around EUR 10,392. The real return is no longer 6%, but only 3.92%:
Real return = (1 + nominal return) ÷ (1 + inflation rate) − 1
The simple calculation “6% return minus 2% inflation” is also only a useful approximation, because the difference becomes larger at higher rates. At a nominal return of 3% and inflation of 5%, for example, real return is around −1.90%. The account balance rises from EUR 10,000 to EUR 10,300, but purchasing power nevertheless falls to around EUR 9,810 and even drops below the starting level. The Bundesbank points out that at low interest rates and with price changes, the real interest rate can be approximately calculated as the difference between the nominal interest rate and the inflation rate.
Official inflation cannot serve as the correct measure for every household anyway, because the consumer price index uses a weighted basket of goods. Housing, energy, food, mobility and other expenses are included at different weights. Someone who does not own a car experiences rising fuel prices differently from a commuter. Someone who spends a large share of their income on rent and food feels price increases more strongly than a household with low fixed costs. Every household therefore has its own personal inflation rate.
For a uniform model calculation, the official inflation rate nevertheless remains the most useful benchmark. Personal inflation can be considered additionally at a later stage.
A 6% gross return becomes a 1.88% real return
A return is initially always stated in nominal terms and becomes real only when it is calculated after costs or includes possible tax deductions. The term “net return” is therefore useful only when it is clearly stated which deductions have actually been included, because the differences can be substantial by the end.
Anyone who calculates only nominally in this example arrives at EUR 10,600. Anyone who deducts the assumed 2% inflation arrives at EUR 10,392.16. Anyone who deducts only EUR 50 in costs reduces the nominal amount to EUR 10,550, and EUR 158.25 in taxes can then be deducted from the assumed taxable return of EUR 600. Only EUR 10,391.75 remains. This amount is then divided by the price factor of 1.02, leaving purchasing power of just EUR 10,187.99.
The tax calculation assumes that the entire return of EUR 600 is taxable, that the saver’s allowance has already been used up and that no church tax applies. At 25% capital gains tax plus the solidarity surcharge, the tax burden is EUR 158.25. The EUR 50 in costs is deducted separately in this example. Depending on the type of investment, exemption order, partial exemption, loss offsetting and time of taxation, the actual calculation may look different.
Depending on which circumstances are taken into account, large differences quickly emerge: the nominal gross return is the stated 6%. Before costs and taxes, 3.92% remains in real terms, and after the assumed EUR 50 in costs and EUR 158.25 share of tax, real return falls to only around 1.88%. The account balance has risen by EUR 391.75, but the purchasing power of the final amount has increased by only EUR 187.99.
Half a percentage point costs EUR 7,595 over 30 years
Costs of only 0.5% per year on the entire investment volume seem manageable at around EUR 50 in the first year on EUR 10,000. Calculated over a long period of several decades until actual retirement, however, this quickly becomes a considerable sum that affects the actual return calculation. In a simplified calculation, EUR 10,000 is again invested at 6% interest per year for 30 years and compared with a second version in which the annual return is reduced by 0.5 percentage points to 5.5% by a cost charge. For simplicity, inflation and taxes are also left out here.
After 30 years, the portfolio value in the first case amounts to a strong EUR 57,434.91. In the second case, it is only EUR 49,839.51, a substantial difference of EUR 7,595.40. The reason is the compound interest effect, which also works in the opposite direction. Half a percentage point less return leads to a significantly lower final value after 30 years. Costs may be charged once, on an ongoing basis or depending on the investment volume. They include, for example, purchase and sale costs, management fees, custody fees and other product costs. Not every fee is calculated in the same way. The actual cost ratio is therefore always individual.
Taxes do not know your personal basket of goods
Inflation and tax affect people in different ways. Inflation changes the purchasing power of money, while tax on private investments is generally linked to taxable capital income. Tax can therefore be due on a positive nominal gain even when real return is significantly lower. Part of the apparent gain consists only of prices having risen. The tax calculation does not automatically deduct this loss of purchasing power.
To determine a disposal gain, the difference between the sale proceeds and acquisition costs is generally considered. A general adjustment of acquisition costs for personal inflation is not provided for in this basic calculation. This explains why inflation can be doubly burdensome for an investment. It initially reduces the purchasing power of the final amount and can simultaneously result in a higher nominal gain being reported, on which taxes are due.
The time of taxation is not always the same either. Interest and distributions may be taxed on an ongoing basis, while gains become taxable only when an investment is sold. In addition, the German tax authorities have introduced an advance lump-sum tax for certain funds.
