# Computed Historical Data ¶

The data in Shiller's data set is not in the exact format that this calculator needs to run computations. Some of Shiller's data must be manipulated before simulations can be run.

In this guide, we will cover the values that we compute from Shiller's data set and the formulas used to compute them.

## Inflation ¶

Shiller provides the Consumer Price Index (CPI) for each month in his data set under the column "Consumer Price Index." The equation to derive inflation from the CPI is:

$inflation = \frac{\displaystyle currentYearCpi}{\displaystyle previousYearCpi} - 1$

Inflation for the first year, 1871, is set to `1`

(representing no inflation).

### Inflation Example ¶

The CPI for January 1900 is `127.40`

, and for January 1901 it is `134.60`

. Placing these numbers into our equation yields:

$\frac{currentYearCpi}{previousYearCpi} - 1 \\[0.8em] = \frac{\displaystyle 127.40}{\displaystyle 134.60} - 1 \\[0.8em] = 1.0565 - 1 \\[0.8em] = 0.0565$

Therefore, inflation for the year 1990 is `5.65%`

.

## Stocks ¶

Shiller's data set provides the price of the S&P 500 for each month. In his spreadsheet, the value for the S&P 500 is under the label "S&P Comp. (P)".

Deriving the growth of stocks, therefore, is:

$growth = \frac{\displaystyle currentYearValue}{\displaystyle previousYearValue}$

The growth for the first year, 1871, is set to `1`

(representing no growth).

## Dividend Yields ¶

Coming soon.

## Bonds ¶

Shiller's data set includes the 10 year yields on US Treasury bonds. To determine year-over-year returns, we assume that you purchase the bonds, hold them for one year, and then sell them.

The formula for this is complicated. Documentation will be added soon.

This is the same formula used by cFIREsim. In fact, Bo, the creator of cFIREsim, deserves credit for this for creating this conversation on Bogleheads.