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.
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
Copyright (c) 2005-2012 Nicolaas J Smith. All rights reserved. No reproduction without permission.
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