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.

 

 

Return to Main Page



[1] How the bank is compensated for the services it provided the depositor and the borrower (safekeeping, recording, accounting, handling, etc) is an entirely different issue.  See Gafoor, 1995 (2002), 1999 for details.

[2] A general theory of interest, which considers bank interest as consisting of several components is presented in Gafoor, 1995 (rev. ed.2002).  The rationale, derivations and applications are also given.  See also Gafoor 1999 and 2004 for more details.

[3] When money is held in hand as cash too it loses its value daily due to inflation.