# Notes on the real value calculations

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:

*Real change rate*, used in the Multivariate model.*Real value*, used in Price.*Real value overrated*, used in the Rainbow model.

Data base sample, for following examples:

Year | Nominal value | Nominal rate (%) | CPI (%) | CPI, 100=1985 | Overrated inflation |
---|---|---|---|---|---|

1985 | 204 | - | 8,83 | 100 | 18,0 |

1986 | 244 | 19,61 | 8,80 | 108,8 | 39,5 |

1987 | 308 | 26,23 | 5.26 | 114,1 | 55,7 |

1988 | 404 | 31,09 | 4,83 | 118,9 | 75,2 |

1989 | 503 | 24,46 | 6,79 | 125,7 | 109,3 |

1990 | 573 | 13,93 | 6,72 | 132,4 | 147,8 |

## 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 following^{1}:

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*.

## Notes

For the mathematical notations, the Latex Math Api developed by @uechz has been used. A latex editor is accessible at TutorialsPoint.com.

- If the price index is in decimal form, the expression would simply be:
*Nominal value / Price index*.↩