## Saturday, 25 January 2014

### Daily CPI formula

Daily CPI formula

"9.6 Consumer Price Index

The Consumer Price Index is the weighted average index value of a typical basket of consumer goods purchased by a typical consumer statistically stated as an initial index value of 100 at the initial date. The CPI is thus fixed in real terms – not in nominal terms. It changes monthly in nominal terms, but it stays fixed in real terms over time.

An example is the harmonized CPI of the European Monetary Union stated as the index value of 100 in 2005. This fixed internal unit of real value is then compared to the weighted average price of the typical basket of consumer goods and services a year later in order to determine the annual rate at which inflation is eroding the real value of only unstable money and other unstable monetary items in only the monetary economy or deflation is creating real value in only unstable money and other unstable monetary items in only the monetary economy. Inflation and deflation have no effect on the real value of non–monetary items. The same is true for high inflation and hyperinflation.

The stable measuring unit assumption (not low inflation, high inflation and hyperinflation) erodes the real value of constant items never maintained constant during low inflation, high inflation and hyperinflation under the HC paradigm. Similarly, it is not deflation, but the stable measuring unit assumption that creates real value in constant items never maintained constant under HCA during deflation.

The annual percentage change in the CPI indicates the annual rate at which only the real value of the national (or monetary union, e.g., the European Monetary Union) unstable monetary unit (unstable money) and other unstable monetary items is being eroded by the economic processes of low inflation, high inflation and hyperinflation or being increased by the economic process of deflation.

The Daily CPI is the daily index value used to calculate the daily price of a government inflation–indexed bond in a particular country, e.g., the Daily Reference CPI value used to calculate the daily price of TIPS in the US, or can, e.g., be based on the formula used to calculate the UF in Chile.

Every country which issues inflation–indexed government bonds already has a Daily CPI based on the respective monthly published CPI. In practice, a Daily CPI or a monetized daily index would be used to inflation–adjust monetary items, to update historical variable items and to measure constant items in units of constant purchasing power on a daily basis during low inflation, high inflation and deflation under Constant Item Purchasing Power Accounting;
i.e., under financial capital maintenance in units of constant purchasing power as authorized in IFRS in the original Framework (1989), Par. 104 (a).

The UF in Chile is the most successful monetized daily indexed unit of account to date.

A Daily CPI is calculated daily, for example the Daily Reference CPI used to price TIPS on a daily basis. The monthly published CPI for the first day of any month is only available – at the earliest – round–about the tenth of the next month; up to 41 days later. The South African CPI for the first day of a calendar month can become available up to the twenty-fourth day of the next calendar month; i.e., up to 55 days later. This is very impractical for daily financial capital maintenance in units of constant purchasing power.

9.7 UF Formula

‘The formula for computation of the UF on day t is:

UF t = UF t–1 × (1+ π) 1/d

where π is the inflation rate for the calendar month preceding the calendar month in which t falls if t is between day ten and the last day of the month (and d is the number of days in the calendar month in which t falls), and π is the inflation rate for the second calendar month before the calendar month in which t falls if t is between day one and day nine of the month (and d is the number of days in the calendar month before the calendar month in which t falls).’

Shiller 1998:3

The above formula applies to the UF in Chile where the CPI for the current calendar month used to be available on the tenth of the next calendar month.
The general case formula for a UF–based Daily CPI is stated as follows:

On day t

DI t = DI t–1 X (1 + π) 1/d

where π is the monthly inflation rate for the second calendar month before the calendar month in which t falls if t is on or between day one and the day of publication of the CPI of the previous calendar month (and d is the number of days in the calendar month before the calendar month in which t falls), and π is the inflation rate for the calendar month preceding the calendar month in which t falls if t is on or between the day the CPI for the previous calendar month is published and the last day of the month (and d is the number of days in the calendar month in which t falls).

The inflation rate for a calendar month is calculated using the CPI for that month and for the preceding month. The Daily CPI within a given calendar month thus depends on the CPI for each of the three preceding months. For example, the July Daily CPI depends before the day the June CPI is published on the CPI for April and May, and starting with the day the June CPI is published on the CPI for May and June.

A Daily CPI is very similar to, but not exactly the same as a monetized daily indexed unit of account, e.g., the UF in Chile. The UF is monetized; i.e., it is stated in terms of the Chilean peso. That is not the case with a Daily CPI. A

Daily CPI is not automatically monetized.

A Daily CPI is, like the monthly CPI on which it is based, a general price level index value. Monetization depends on generally accepted monetary practices in an economy (e.g., the UF in Chile). A Daily CPI can be monetized and used as a monetized daily indexed unit of account with payments being made in the national monetary unit – depending on users in an economy. Monetization is not a necessity.

A Daily CPI is not a unit of account just like the CPI is not a unit of account for accounting purposes. The US Dollar, Euro, Yen, Yuan, etc. are the nominally fixed monetary units of account, unstable in real value, used in their respective countries as the national unstable monetary unit of account for accounting purposes during low inflation, high inflation, hyperinflation and deflation. The US, EU, Japanese and Chinese CPI are not units of account for accounting purposes. They are general price level indices. So are their Daily CPI. Prices are not quoted in CPI or in Daily CPI – although they can be."

Smith N. J., CONSTANT ITEM PURCHASING POWER ACCOUNTING per IFRS, 2012

Nicolaas Smith