Currency
Depreciation:
Estimation and
Applications
By
A.L.M. Abdul Gafoor
Appropriate Technology
Foundation
Groningen, The Netherlands
Introduction
In
another work (Gafoor, 1999) we looked at inflation and its measurement in some
detail. In it we also developed a new
method appropriate for the measurement of inflation on capital, and we used it
to compensate capital erosion due to inflation in lending and borrowing
transactions as well as in investment and finance. It was necessary to develop a new measure
because it was found that the existing measures of inflation (such as the
consumer price index) were not appropriate for the measurement of inflation on
capital.
In
another work on money (Gafoor, 2001), the history of money was traced from
antiquity to the present and its transformation from gold coins and gold-backed
paper currency to the present fiduciary currency, whose value is dependent on
market forces. Currency depreciation is
defined as the value depreciation of currency relative to gold; that is, how
much less gold a given amount of the currency would buy from one point in time
to another point in time. For example,
if 1000 units of currency bought one gram of fine gold last year and 1100 units
of currency were needed this year to buy the same amount of the same quality of
gold, then the currency has depreciated by 100 units during the year. This is also the magnitude of the value
erosion of capital due to inflation during the year, and it may also be called
the inflation on capital. Consequently,
the new measure (or index) developed to measure inflation on capital is also
the same as currency depreciation.
This
measure is based on the market price of gold.
Very briefly defined, the price of gold for the current week is the
average open market price of gold in the local (meaning national) market, for
the past 13 consecutive weeks. Thus it
is the 13-week moving (or rolling) average price.
In this
essay we propose to demonstrate how this measure (or index) is computed using real-life
data. The procedure explained below
could then be used to compute the magnitude of the value erosion of capital due
to inflation in any given country in any given time period.
Data
The data
necessary for the exercise is the daily price of gold (of a specified quality
and quantity) in terms of the national
currency at the local (meaning national) open market, collected and collated
consistently and continuously by an independent body (or authority) using predetermined
and documented transparent procedures and a single national price determined
and reported daily, and published in the official and public media. Each of the adjectives and adverbs used in
the last sentence are of high importance for the success of the procedure and
the systems that use the results – daily price, specified quality, local open
market, consistently and continuously, predetermined and documented transparent
procedures, single national price, daily reporting, public media, etc. This is to ensure that no room is left for
any manipulation of the data or the results before, during or after their
collection, collation, computing and reporting.
Once published in the media the raw data is in the public domain, and
any manipulation afterwards can be checked and challenged.
In practice
the price can be defined as “the price of one ounce (or gram) of fine gold in
the national currency in the local open market”. The competent body could be the central
bank of the country, the national statistics bureau or any other competent public
or private organisation. It is important that the methods of
collection, collation and computation are well documented and published and
that the procedures are transparent. It
is also important that the price data are collected and collated each working
day and the single realised market price computed, recorded and published the very following day.
Data collection and price
determination
The
competent body mentioned earlier is entrusted with the data collection,
collation and estimation process. These
are statistical procedures and we have to leave it to the competent authority
to decide on the parameters and to the statisticians of the authority to devise
a sample survey plan. The parameters
include the required accuracy, coverage, time frame and cost
considerations. This exercise will
result in the publication of a single national price of gold that was realised in the market during the previous
day.
For the
purpose of this essay we will describe the raw data we have obtained and,
in the next section, describe the
procedures for computing the 13-week rolling average price that will be used as
the gold price for the next (14th) week. This may be called the operative price for
the week since it will be the price used in all relevant lending and borrowing
operations during the current week.
The data
used in this essay to illustrate the methodology is the daily gold price in
Amsterdam, the Netherlands, as reported in Edelmetalen
Amsterdam (Precious Metals, Amsterdam), a publication of the Hollandsche Bank-Unie
(Dutch Bank Union). The data relates to
January 1999 to July 2000, and is given in Dutch Guilders per gram. See Table 1.
The first column gives the week number and columns 2 to 6 the prices as
obtained in the workdays (Monday to Friday) of the week. N/A stands for “not
available”, most probably the day having been a holiday and the market closed.
Column 7 gives the weekly average price.
The next column gives the 13-week rolling average, and the last column
the weekly operative price. Figure 1
gives a plot of the weekly averages prices and the 13-week average prices. Note the volatility of the weekly averages
and the smooth movement of the 13-week averages.
Computations
The daily
price data is arranged in weekly blocks, Table 1. Generally a week consists of five working
days but in some weeks one or more holidays may occur making it a 4- or
3-workday week. Therefore the average
daily price for the week is obtained by dividing the total in each block by the
number of working days in that week (data points in that block). We may call this the weekly average price or
the average price for the week.
Next, the
13-weeks average price is obtained by computing the average of the weekly
average prices of 13 consecutive weeks.
This will be the operative price for the next consecutive week – the 14th
week. This price will be used for all
transactions during the 14th week.
The
operative price for the 15th week is obtained as follows. During the 14th week, enter the
daily price for each day as it is published.
At the end of the week, the weekly average for the 14th week
is computed and recorded. Now, add the
14th week average price to the total of the 13 consecutive preceding
weekly averages computed earlier, and drop (subtract) the 1st week’s
average price from the new total. This
gives the total of the 13 consecutive weeks immediately preceding the 15th
week (i.e. 2nd to 14th weeks). Divide the total by 13 to obtain the 13-weeks
average price, and this will be the operative price for the 15th
week. Similarly, the operative price for
the 16th week is obtained by computing the average of the 13 weeks
immediately preceding the 16th week (i.e. 3rd to 15th
weeks).
Operative price and its
operation
At this
point we need to explain what is meant by operative price (for the week). Keeping it short (refer to Gafoor, 1999 for
details), though deposits and loans of a duration longer than 13 weeks (3
months) will be accepted and granted, respectively, in terms of the local
currency the accounts will be kept in terms of gold units – say, so many grams
of fine gold. When the depositor wishes
to withdraw it the same amount as was recorded in terms of gold units will be
returned to him, even though he may receive more (than he deposited) in terms
of currency units. In theory, this is
exactly as if he deposited a certain amount of gold at the bank and later
retrieved the same without any loss or gain – absolutely riba-free. In the case of loans, the borrower is obliged
to return the same amount of gold units as was recorded in the books when he
borrowed, but this amount of gold may now cost more in terms of currency and
consequently he may have to pay more than he received in terms of currency.[1] The conversion factor used – to convert
currency units to gold units and vice versa – is the operative price of
gold. If the week’s operative price is
denoted as “wop” (i.e. say, 1 gram of gold is wop units of the local currency),
then when 1000 units of local currency is deposited it will be recorded as
1000/wop units of gold.
In order
to fix the idea firmly, let us take an example.
Suppose a deposit of 1000 units of currency was made in a certain week,
and the wop in that week was 50. Then
this is equivalent to (1000/50 =) 20 units of gold. Say, the depositor returned after 40 weeks
asked for his deposit, and the wop in that week was 55. His deposit in the bank’s records is still 20
units of gold, but since the wop this week is 55 he will be given (20x55 =)
1100 units of currency. The extra 100 he
receives is compensation for the value loss his capital suffered during the 40
weeks it was with the bank.
This
means that he could go out to the open market and buy the same amount of gold
today that he was able to buy 40 weeks ago – that his depositing the money with
the bank (or lending it) has not eroded the purchasing power of his money in
terms of gold, a basic metal with an intrinsic value, which used to be the
universal currency from antiquity till very recent times. The fiat money (paper currency) can still
perform the functions of unit of account and medium of exchange, but the
function of store of wealth, which it had lost in recent times, has now been
restored to it through this devise. Thus
this method builds a bridge between the two extremes of going back to the gold
coins as currency and the inevitable collapse of the monetary system if the
present state of the un-anchored fiat currency (at the mercy of currency
traders, government printing and bank credit creation) is allowed to continue. It will retain the convenience of the paper
currency, which is more convenient to carry than bags of gold, on account of
which the paper currency was originally invented, without losing the currency’s
function as a store of wealth.
In private
person-to-person lending / borrowing transactions too the same method could be
used. Again, the idea is that the same
amount of gold is borrowed and returned without any addition or subtraction –
an absolutely riba-free transaction as it would have been in the time of
the Prophet (pbuh) and until recently. Any additional amount the lender may receive
in terms of paper currency is the loss his capital suffered while in the hands
of the borrower due to currency depreciation.
In this method of transaction the lender does not suffer real loss of
value in his capital, nor does the borrower gain any advantage due to currency
depreciation. Hence this additional
amount is definitely not riba, but an accommodation necessary to adjust
to the peculiar circumstance of our time.
Hopefully this is a temporary step until such time as better counsel
prevails and paper currency is again pegged to solid gold. Perhaps this effort will help bring to a halt
the present slide towards chaos and initiate the journey back towards
gold-based paper currency.
(This
method is equally applicable when the currency appreciates – a phenomenon
rarely seen in recent times – and in that case too the lender will not gain any
advantage and the borrower will not lose.)
Applications
In
conventional banking too currency depreciation is taken into account, but
tacitly, and it is included in the all-inclusive interest rate as compensation
for value loss of capital due to inflation.
In the case of deposits it is always seen to that the interest rate is
set higher than the inflation rate and therefore the real interest rate is
always positive – or seen to be positive.
However, there are three difficulties in this concept; two are common to
everybody and one is specific to the Muslims.
1. The measure of
inflation used (or assumed to be used) is inappropriate for measuring inflation
on capital. See Gafoor (1999) for
details.
2. An estimation of
inflation is made by the bank right at the beginning of the transaction
(deposit or loan) and is effective (generally) for the total duration of the
deposit or loan – three months, one year, three years or more. But there are no measures of inflation that
could predict inflation of the future with any accuracy – the further the
future the wider off the mark the prediction.
Taking
the above two difficulties together, the inflation estimation is both
inappropriate and widely off the mark.
In order to be on the safe side the bank always uses the lowest estimate
(whatever the measure used) in setting the deposit rate, and the highest
estimate in setting the loan rate. Since
in most of the transactions the bank is an overwhelmingly powerful party, what
the bank says goes. Hence both the above
difficulties are used in favour of the bank and to the disadvantage of the customer.
3. Interest has always
been considered a single entity, both in theory and practice. But in reality, several factors are taken
into consideration by the bank in fixing this single entity. For example, the deposit interest consists of
both compensation for inflation and real interest (or usury, riba). (And the loan interest consists of these as well as the operational costs of the
bank, its profit, etc.)[2] This has consequences for a conscientious
Muslim. For when he rejects interest on
his deposit considering all of it as riba he also throws away the
compensation for inflation part. The
latter is his due since his capital lost part of its value through no fault of
his. But he has no option since he cannot
separate one from the other.
In the
method presented in the foregoing paragraphs, we have provided a theory and
procedure by which all the above three difficulties are overcome – a measure of
inflation appropriate to the measurement of inflation on capital; a procedure
that estimates and compensates the realised (and therefore accurate) loss of value
suffered by capital, thereby protecting both the lender and the borrower (and
this both transparently and equitably); and a method to separate riba
from interest and thereby help Muslims to keep away from riba without
suffering loss to their capital. The
last helps those Muslims who live in both Muslim and non-Muslim countries,
where fixed deposits in conventional banks is the only option to keep their
monetary wealth safe, to keep away from riba (by throwing away the riba
component) and still protect their capital from any value loss.[3]
In short
we have now come into possession of a method and procedure that helps us keep
capital counted in currency units to be coupled to gold so that the real value
of capital is not eroded by inflation (due to currency depreciation). This method can be applied to protect capital
in all kinds of situations, such as in bank deposits and bank loans, investment
and finance, and in person-to-person lending/borrowing.
References:
1. Gafoor, A.L.M.
Abdul, Interest-free Commercial Banking.
Groningen, the Netherlands: Apptec Publications, 1995. Revised edition, 2002. 98p.
(Reprinted in Malaysia by A.S. Noordeen, Kuala Lumpur.)
2. -----------, Commercial
Banking in the presence of Inflation.
Groningen, the Netherlands: Apptec Publications, 1999. 134p.
(Reprinted in Malaysia by A.S. Noordeen, Kuala Lumpur.)
3. -----------, Money, Gold and Inflation: Some history and observations. 2002. Unpublished. Available from the author on request. E-mail: abdul@bart.nl.
4. -----------, Interest,
Usury, Riba, and the Operational Costs of a Bank. Groningen, the Netherlands: Apptec
Publications, 2004. 80p.
© A.L.M. Abdul Gafoor 2004.
30 November 2004.
Table 1
|
Amsterdam |
Local
Daily Gold Price, NL Guilders/Gram |
Jan
1999 - Jul 2000 |
||||||
|
|
|
|
|
|
|
|
|
|
|
Week |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Weekly Average |
13-week average |
Operative price |
|
|
|
|
|
|
|
|
|
|
|
1999 - 1 |
17.030 |
16.900 |
17.000 |
17.200 |
17.400 |
17.106 |
|
|
|
2 |
17.500 |
17.750 |
17.200 |
17.100 |
17.050 |
17.320 |
|
|
|
3 |
17.250 |
17.250 |
17.200 |
17.300 |
17.250 |
17.250 |
|
|
|
4 |
17.200 |
17.350 |
17.300 |
17.300 |
17.400 |
17.310 |
|
|
|
5 |
17.500 |
17.800 |
17.700 |
17.800 |
17.850 |
17.730 |
|
|
|
6 |
17.900 |
17.700 |
17.700 |
17.800 |
17.850 |
17.790 |
|
|
|
7 |
17.950 |
18.000 |
17.700 |
17.700 |
17.900 |
17.850 |
|
|
|
8 |
18.250 |
18.100 |
18.150 |
18.150 |
18.200 |
18.170 |
|
|
|
9 |
18.200 |
18.400 |
18.300 |
18.400 |
18.600 |
18.380 |
|
|
|
10 |
18.450 |
18.750 |
18.600 |
18.800 |
18.750 |
18.670 |
|
|
|
11 |
18.600 |
18.400 |
18.050 |
18.000 |
18.100 |
18.230 |
|
|
|
12 |
18.250 |
18.300 |
18.140 |
18.150 |
18.200 |
18.208 |
|
|
|
13 |
18.150 |
18.250 |
18.200 |
18.200 |
NA |
18.200 |
17.863 |
|
|
14 |
NA |
18.150 |
18.150 |
18.100 |
18.200 |
18.150 |
17.943 |
17.863 |
|
15 |
18.200 |
18.200 |
18.350 |
18.200 |
18.550 |
18.300 |
18.018 |
17.943 |
|
16 |
18.650 |
18.650 |
18.700 |
18.600 |
18.600 |
18.640 |
18.125 |
18.018 |
|
17 |
18.600 |
18.450 |
18.450 |
18.550 |
NA |
18.513 |
18.218 |
18.125 |
|
18 |
18.900 |
18.900 |
18.750 |
18.600 |
18.300 |
18.690 |
18.292 |
18.218 |
|
19 |
18.250 |
18.050 |
NA |
18.250 |
18.100 |
18.163 |
18.320 |
18.292 |
|
20 |
18.050 |
17.900 |
17.900 |
18.000 |
18.050 |
17.980 |
18.330 |
18.320 |
|
21 |
NA |
17.900 |
17.750 |
17.950 |
18.050 |
17.913 |
18.310 |
18.330 |
|
22 |
18.000 |
17.800 |
17.950 |
17.800 |
18.000 |
17.910 |
18.274 |
18.310 |
|
23 |
18.050 |
17.750 |
17.450 |
17.200 |
17.200 |
17.530 |
18.187 |
18.274 |
|
24 |
17.300 |
17.400 |
17.400 |
17.450 |
17.600 |
17.430 |
18.125 |
18.187 |
|
25 |
17.400 |
17.450 |
17.500 |
17.550 |
17.400 |
17.460 |
18.068 |
18.125 |
|
26 |
17.400 |
17.600 |
17.650 |
17.700 |
17.900 |
17.650 |
18.025 |
18.068 |
|
27 |
17.900 |
17.850 |
17.400 |
17.550 |
17.600 |
17.660 |
17.988 |
18.025 |
|
28 |
17.600 |
17.500 |
17.550 |
17.350 |
17.400 |
17.480 |
17.924 |
17.988 |
|
29 |
17.400 |
17.000 |
16.900 |
16.900 |
16.900 |
17.020 |
17.800 |
17.924 |
|
30 |
16.600 |
16.700 |
16.700 |
16.600 |
16.700 |
16.660 |
17.657 |
17.800 |
|
31 |
16.700 |
16.700 |
16.600 |
16.550 |
16.550 |
16.620 |
17.498 |
17.657 |
|
32 |
16.700 |
16.700 |
16.700 |
16.950 |
17.000 |
16.810 |
17.394 |
17.498 |
|
33 |
17.050 |
17.150 |
17.300 |
17.100 |
16.850 |
17.090 |
17.326 |
17.394 |
|
34 |
16.850 |
16.900 |
16.900 |
16.900 |
16.950 |
16.900 |
17.248 |
17.326 |
|
35 |
16.900 |
16.850 |
16.750 |
16.650 |
16.600 |
16.750 |
17.158 |
17.248 |
|
36 |
16.750 |
16.900 |
16.850 |
16.900 |
16.950 |
16.870 |
17.108 |
17.158 |
|
37 |
17.350 |
17.300 |
17.300 |
17.150 |
17.150 |
17.250 |
17.094 |
17.108 |
|
38 |
17.050 |
17.050 |
17.400 |
17.600 |
17.650 |
17.350 |
17.085 |
17.094 |
|
39 |
18.800 |
19.150 |
20.500 |
19.800 |
19.600 |
19.570 |
17.233 |
17.085 |
|
40 |
20.200 |
21.150 |
20.750 |
20.850 |
20.900 |
20.770 |
17.472 |
17.233 |
|
41 |
20.700 |
21.200 |
20.800 |
20.950 |
20.250 |
20.780 |
17.726 |
17.472 |
|
42 |
20.350 |
19.950 |
20.050 |
19.800 |
19.600 |
19.950 |
17.952 |
17.726 |
|
43 |
19.750 |
19.500 |
19.050 |
20.000 |
19.850 |
19.630 |
18.180 |
17.952 |
|
44 |
19.400 |
19.400 |
19.350 |
19.500 |
19.700 |
19.470 |
18.399 |
18.180 |
|
45 |
19.350 |
19.550 |
19.600 |
19.900 |
19.600 |
19.600 |
18.614 |
18.399 |
|
46 |
19.800 |
19.700 |
19.800 |
19.750 |
19.850 |
19.780 |
18.821 |
18.614 |
|
47 |
19.950 |
20.050 |
20.300 |
20.450 |
20.500 |
20.250 |
19.078 |
18.821 |
|
48 |
20.250 |
20.100 |
20.200 |
20.050 |
19.500 |
20.020 |
19.330 |
19.078 |
|
49 |
19.250 |
19.000 |
19.350 |
19.050 |
19.150 |
19.160 |
19.506 |
19.330 |
|
50 |
19.250 |
19.400 |
19.500 |
19.300 |
19.300 |
19.350 |
19.668 |
19.506 |
|
51 |
19.650 |
19.700 |
19.900 |
19.900 |
19.850 |
19.800 |
19.856 |
19.668 |
|
52 |
19.850 |
19.900 |
20.150 |
20.150 |
NA |
20.013 |
19.890 |
19.856 |
Table 1 (continued)
|
Amsterdam |
Local Daily
Gold Price, NL Guilders/Gram |
Jan
1999 - Jul 2000 |
||||||
|
|
|
|
|
|
|
|
|
|
|
Week |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Weekly Average |
13-week average |
Operative price |
|
|
|
|
|
|
|
|
|
|
|
2000 - 1 |
19.900 |
19.200 |
18.950 |
18.900 |
19.100 |
19.210 |
19.770 |
19.890 |
|
2 |
19.200 |
19.100 |
19.100 |
19.150 |
19.350 |
19.180 |
19.647 |
19.770 |
|
3 |
19.650 |
19.850 |
19.900 |
19.950 |
19.750 |
19.820 |
19.637 |
19.647 |
|
4 |
19.950 |
20.100 |
19.850 |
20.000 |
20.300 |
20.040 |
19.669 |
19.637 |
|
5 |
20.200 |
20.450 |
20.350 |
20.500 |
20.300 |
20.360 |
19.737 |
19.669 |
|
6 |
22.550 |
21.600 |
21.600 |
21.550 |
22.400 |
21.940 |
19.917 |
19.737 |
|
7 |
21.800 |
21.900 |
21.400 |
21.550 |
21.450 |
21.620 |
20.059 |
19.917 |
|
8 |
21.650 |
21.400 |
21.800 |
21.050 |
21.000 |
21.380 |
20.146 |
20.059 |
|
9 |
21.100 |
21.050 |
21.150 |
20.750 |
20.900 |
20.990 |
20.220 |
20.146 |
|
10 |
20.900 |
21.000 |
21.400 |
20.950 |
20.100 |
20.870 |
20.352 |
20.220 |
|
11 |
20.800 |
21.050 |
20.900 |
20.800 |
20.650 |
20.840 |
20.466 |
20.352 |
|
12 |
20.500 |
20.500 |
21.050 |
20.800 |
20.500 |
20.670 |
20.533 |
20.466 |
|
13 |
20.350 |
20.300 |
20.400 |
20.200 |
20.100 |
20.270 |
20.553 |
20.533 |
|
14 |
20.450 |
20.200 |
20.500 |
20.200 |
20.350 |
20.340 |
20.640 |
20.553 |
|
15 |
20.550 |
20.450 |
20.450 |
20.500 |
20.500 |
20.490 |
20.741 |
20.640 |
|
16 |
20.650 |
20.700 |
20.750 |
20.850 |
20.850 |
20.760 |
20.813 |
20.741 |
|
17 |
NA |
20.900 |
21.100 |
20.950 |
21.200 |
21.038 |
20.890 |
20.813 |
|
18 |
20.950 |
21.050 |
21.600 |
21.750 |
NA |
21.338 |
20.965 |
20.890 |
|
19 |
21.550 |
21.550 |
21.350 |
21.350 |
21.400 |
21.440 |
20.927 |
20.965 |
|
20 |
21.050 |
21.200 |
21.450 |
21.350 |
21.400 |
21.290 |
20.901 |
20.927 |
|
21 |
21.350 |
21.050 |
21.050 |
21.150 |
20.600 |
21.040 |
20.875 |
20.901 |
|
22 |
20.500 |
20.400 |
20.400 |
20.400 |
20.350 |
20.410 |
20.830 |
20.875 |
|
23 |
20.800 |
21.050 |
20.100 |
20.800 |
20.800 |
20.710 |
20.818 |
20.830 |
|
24 |
NA |
21.400 |
20.750 |
21.350 |
21.200 |
21.175 |
20.844 |
20.818 |
|
25 |
20.900 |
20.850 |
21.050 |
21.150 |
21.250 |
21.040 |
20.872 |
20.844 |
|
26 |
21.250 |
21.100 |
21.250 |
21.450 |
21.050 |
21.220 |
20.945 |
20.872 |
|
27 |
21.150 |
21.250 |
21.050 |
20.750 |
20.850 |
21.010 |
20.997 |
20.945 |
|
28 |
20.800 |
20.750 |
20.800 |
20.950 |
20.950 |
20.850 |
21.025 |
20.997 |
|
29 |
21.000 |
21.100 |
21.400 |
21.100 |
20.950 |
21.110 |
21.052 |
21.025 |
|
30 |
20.950 |
20.700 |
20.750 |
20.800 |
NA |
20.800 |
21.033 |
21.052 |
|
|
|
|
|
|
|
|
|
21.033 |
|
|
Source:
Edelmetalen Amsterdam; Hollandsche
Bank-Unie (NBU) |
|
|
Figure 1
Based on data in Table 1 above.
Figure 2
Based on data available with the author.