In one chart a property price series is at 130, another at 115. Which properties are more expensive? Without the definition of the series this question cannot be answered. An index describes a development relative to a fixed base. The displayed figure is not automatically a purchase price and not a price per square metre either.
The following calculations are our own entirely fictional learning examples for Austria and Germany. They do not depict any real statistics and do not claim any official index method. In an actual report the source, scope of collection, calculation and data status of the specific series used must be read.
First ask about the meaning of the series
For a real index check what is being observed at all: listings or completed transactions, which property types, which area and which period. A properly converted series cannot automatically make a series with different content comparable.
Also note whether the source describes a particular adjustment or weighting. Do not adopt such characteristics simply because the headline reads “Immobilienindex”. The calculation aid here merely shows how an already defined numerical series can be considered relatively.
For a specific property, even with a suitable general index, the individual classification is still missing. An index increase is not a certification of its current value or of a realisable sales price.
A higher index level can arise from a different base
Our first fictional example uses the same values: in the base year the price under consideration is 200 units, in the next year 220, then 240. With the base year equal to 100 the normalised values are 100, 110 and 120.
If instead the middle year is chosen as base 100, the last year is around 109,1. The underlying price in the last year remains 240 units. Only the presentation relative to the other base is changed.
A level of 120 in the first presentation and around 109,1 in the second therefore do not describe a different last price. Two real series with different base years cannot be ordered by the height of their end points alone.
Always relate a change to its starting value
In another fictional series the level rises from 120 to 126. The difference is six index points. The relative change, however, is six divided by 120, i.e. five per cent. Six points here are not six per cent.
A return to the earlier value also needs the correct direction: from 100 to 120 is a twenty per cent increase. From 120 back to 100 the decline is twenty divided by 120, i.e. around 16,7 per cent. Simply changing the sign would not correctly reverse the calculation.
State the starting and end dates in the report. A rate of change without a period leaves open whether a monthly movement, a year-on-year comparison or a longer development is meant.
Use the same base for a joint presentation
If two content-wise suitable series are scaled differently to a common starting point, you can for a pure presentation calculation set both to 100 at the common start. Each later value is divided by its respective starting value and multiplied by 100.
Fictitious example: series A rises from the common start 80 to 88. Series B rises in the same period from 150 to 162. Rebased to 100 A ends at 110 and B at 108. In the described period the relative change of A is greater, although B had the larger original figures before and after.
This conversion does not create a common collection basis. If area, object scope or method do not agree sufficiently, this remains a reservation. A neatly overlaid curve must not conceal it.
Separate nominal change and comparison benchmark
For a simple own purchasing power consideration we set two fictional series to 100 at the start. The property price level grows to 110. The chosen general price comparison benchmark grows in the same period to 108. The relative size is now 110 divided by 108, i.e. around 1,0185 relative to the start ratio of one.
In this expressly simplified calculation model that corresponds to around 1,85 per cent relative change compared with the chosen benchmark. The mere subtraction ten minus eight yields two percentage points and is not the same calculation. Such a comparison must in the real case suit the question and the data basis.
The result is neither a personal return nor the individual affordability of an apartment. Acquisition and financing costs, ongoing expenses and one’s own income circumstances are not captured by this model calculation. It must not be used as investment advice.
Keep the scope of the claim in the graphic
Label the base, period, unit and source of each actual series. If the presentation has been renormalised, this is explained. A missing observation is not supplemented as zero; a methodological break is not quietly connected into a continuous development.
When writing an accompanying text of your own, check every sentence against the displayed calculation. “Has risen more since the chosen starting point” is different from “more expensive today”. “Changed relative to this benchmark” is different from “has become more affordable for all people”.
Maintain a concise reading order
First ask what was measured. Then determine the base and period. Only then calculate the required relative change and check whether the comparison is meaningful in content. Finally, formulate the limited claim and its open question.
A good comparison does not need to contain as many curves as possible. It should make clear which development is actually depicted and which conclusion the figures do not support.