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Wednesday, 18 January 2012

Financial capital maintenance in units of constant purchasing power requires a daily rate


Financial capital maintenance in units of constant purchasing power requires a daily rate

It is noted that:

(1) When it is intended to maintain the real value of an item, for example, a government inflation-indexed bond, it is immediately realized that a daily rate is required since these bonds trade on a daily basis. Many countries use Daily CPIs to value these bonds on a daily basis.

(2) During hyperinflation a daily US Dollar parallel rate is always spontaneously used by the population and in the consumer markets.

(3) Brazil, for example, used government supplied daily index rates from 1964 to 1994 to index variable and constant real value non-monetary items on a daily basis in the entire economy.

(4) Chile has been using a monetized daily indexed unit of account, the Unidad de Fomento, since 1977. Its daily value has been calculated and published daily by the Central Bank of Chile since 1990.

(5) Prof. Robert Shiller stated:

‘Another coordination problem is that we must decide, and agree, on a way to smooth the CPI. We should not define prices just in terms of the latest CPI because the CPI is vulnerable to sudden jumps from month to month. This is particularly true when we are talking about indexing financial contracts to the CPI. A unit of account like the UF would smooth out the CPI movements, otherwise there would be important jumps in deposit balances on the dates of new announcements of the CPI. Thus, the smoothing of the CPI in producing the UF has also been a fundamental part of the functioning of the UF as an analogue of money.’


A Daily CPI is thus a fundamental requirement when implementing financial capital maintenance in units of constant purchasing power as the basic accounting model in the economy.

Many countries issue government and commercial inflation-indexed bonds. The most liquid markets are US Treasury Inflation Protected Securities (TIPS), the UK Index–linked Gilts and the French OATi/OAT€I market. Japan, Germany, Italy, Canada, Australia, Sweden, Iceland, Portugal, Greece, Finland, Netherlands, Spain, Saudi Arabia, Qatar, Kuwait, UAE, South Korea, New Zealand and Hong Kong also issue inflation–indexed government bonds, as well as a number of Emerging Markets such as Brazil, Turkey, Chile, Mexico, Colombia, Argentina and South Africa.

The British government began issuing inflation–linked Gilts in 1981.

Most of these countries use a Daily Consumer Price Index to value these bonds on a daily basis. A Daily CPI is a one or two month lagged, daily interpolation of the monthly published CPI.

A country which issues inflation–indexed government bonds and uses a one or two month lagged interpolated Daily CPI to determine the daily price of these bonds can use the Daily CPI for the implementation of financial capital maintenance in units of constant purchasing power in terms of a daily rate at all levels of inflation and deflation as proposed by the Argentinean Federation. Daily CPIs are thus already in use in many economies. A country with no inflation–indexed sovereign bond market can use a Daily CPI based on the formula used to calculate the Unidad de Fomento in Chile.

The Central Bank of Chile translates the Unidad de Fomento on their website as An Inflation–Indexed Accounting Unit and CPI–Indexed Unit of Account (UF).

The UF´s nominal value in Chilean escudos was originally (1967) updated every quarter which would be the official rate for the following quarter. The nominal index was updated monthly from October 1975, with the currency changeover to pesos, till 1977. Since July 1977 the change in the nominal value was calculated daily by interpolation between the tenth of each month and the ninth of the following month, according to the monthly variation of the Indice de Precios al Consumidor (IPC), the Chilean Consumer Price Index. The Banco Central de Chile has calculated and published the UF´s value daily since 1990. The UF is a monetized lagged daily interpolation of the monthly published Chilean CPI. The IPC is independently calculated and published monthly by the Chilean National Statistical Institute.

The UF daily rate is available on the Chilean Central Bank´s website.

A daily instead of a monthly general price–level index is required to implement financial capital maintenance in units of constant purchasing power at all levels of inflation and deflation. Using the CPI published monthly may result in sudden increases or decreases in values on the date the new monthly CPI is published. A Daily CPI solves this problem. The UF is a very successful monetized daily indexed unit of account used in Chile during the last 45 years (2012) and was copied by Colombia, Ecuador, Mexico, and Uruguay.

A 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 formula to calculate the daily price of TIPS in the US, or is based on the formula used to calculate the UF in Chile.

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

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.

Formula

‘The UF is now a lagged daily interpolation of the monthly consumer price
index. 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)

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 monthly 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 monthly inflation rate for a calendar month is calculated using the CPI for that month and for the preceding month. The Daily CPIs within a given calendar month thus depend on the CPI for each of the three preceding months. For example the July Daily CPIs depend 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 automatically 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 non–monetary general price–level index value. Monetization depends on generally accepted monetary practices in an economy (see 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.

Nicolaas Smith

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