# Notes on the real value calculations

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The real value is the measure that takes into account the time period's inflation rate, being the purpose to remove the price effect from a data series. It is important to clarify how the real value has been calculated, since 3 different methods have been used for 3 different visualizations:

1. Real change rate, used in the Multivariate model.
2. Real value, used in Price.
3. Real value overrated, used in the Rainbow model.

Data base sample, for following examples:

YearNominal valueNominal rate (%)CPI (%)CPI, 100=1985Overrated inflation
1985204-8,8310018,0
198624419,618,80108,839,5
198730826,235.26114,155,7
198840431,094,83118,975,2
198950324,466,79125,7109,3
199057313,936,72132,4147,8

## 1. Real change rate#

The real change rate is the difference between the change in nominal price year-on-year minus the inflation rate (CPI) year-on-year. The expression is the following: Where t means the reference year.

Let's see a basic example for the year(t) 1989: Therefore, the real price rate increased by 17,67% in 1989.

## 2. Real value#

The real value is a methodology to deflate any nominal data series into real values, using a concrete base year for a selected price index. The method is explained in more depth in this entry from the Federal Reserve - Bank of Dallas. The expression is the following1: Where t means the reference year.

Let's see an example for the year(t) 1987, using the year 1985 as the base year (100) for the price index (CPI): Therefore, the real house value (at 1985 euros) for the year 1987 equals to 269,93€.

## 3. Real value overrated#

The real value overrated is a formula that discounts the amount of inflation rate on a yearly basis, generating a compound that overrates inflation. It is inaccurate for analyzing the real value (the previous real value should be used instead), but convenient for maximizing trends. The expression is the following: Where t means the reference year, and the Overrated inflation is expressed as follows: Where the sum expression starts at the year 1985(t), and ends at the year (n).

Let's see a basic example for the year 1987(n).

As for the Overrated inflation, it is the sum of the years 1985, 1986 and 1987: Then: Therefore, the real overrated house value (at 1985 euros) for the year 1987 equals to 252,30€.

### Real value vs. Real value overrated#

As means of comparison, in the following charts we can see the behaviour of both the Real value and the Real value overrated.