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Finance & Development, December 1974
Article

SDRs: valuation and interest rate: An explanation of the steps used in the new technique of valuation based on the “basket” of currencies

Author(s):
International Monetary Fund. External Relations Dept.
Published Date:
December 1974
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David S. Cutler and Dhruba Gupta

In June of this year, following the final meeting of the Committee of Twenty on the Reform of the International Monetary System, the Fund’s Executive Directors took a number of important decisions, including the adoption of interim methods of valuing the SDR in terms of currencies and of determining its rate of interest. Both these decisions came into effect on July 1, 1974. Under the new valuation technique, which will be reviewed after two years, the market value of a “basket” of currencies will be used to set exchange rates against SDRs for currencies transferred in SDR transactions and in operations in the Fund’s General Account. The interest rate was increased to 5 per cent on July 1, and will be subject to adjustment every six months on the basis of a formula related to short-term interest rates in international money markets unless the Fund’s Executive Directors reach agreement on an alternative rate.

The Fund’s Articles of Agreement provide that the unit of value of SDRs shall be equivalent to 0.888671 gram of fine gold; thus, there are SDR 35 per ounce of gold, and this relationship remains fixed unless this provision of the Articles were to be amended. Since, however, all transfers of SDRs between those Fund members that participate in the Special Drawing Account are made against payment of currency by the recipient of SDRs, it is necessary for the Fund to have a method of translating the gold value of the SDR into a value in terms of currencies. The Articles provide that a country using SDRs shall receive the same value regardless of which currencies are used in the transaction, and the Fund’s Executive Directors are required to adopt regulations to give effect to this principle. Thus, while the value of the SDR in terms of gold cannot be changed without the lengthy procedures of amending the Articles, the Executive Directors are able to decide the method of valuation of the SDR in terms of currencies. Their decision on the new method of valuation exercised this authority.

The interest rate on SDRs is also subject to decisions of the Executive Directors. The rate of interest must equal the highest rate of remuneration paid to Fund member countries on their net creditor positions in the General Account; this rate may be increased or reduced from the 1½ per cent initially set, but any increase above 2 per cent or reduction below 1 per cent requires a three-fourths majority of total voting power. The decision taken in June raised the interest rate to 5 per cent and thus required this high measure of agreement.

The initial method of SDR valuation

The initial method of valuing the SDR in terms of currencies, which remained in effect until June 30, 1974, was decided prior to the start of 1970, when the first allocation of SDRs was made and when operations and transactions in SDRs began. Under this method, the exchange rate for the U.S. dollar in terms of the SDR was determined by the par value of the U.S. dollar. This method of valuation meant that when the Fund’s Special Drawing Account began operations at the start of 1970, SDR 1 was equal to US$1 since both were equal to 0.888671 gram of gold. After the second devaluation of the U.S. dollar in February 1973, the relationship became SDR 1 = US$1.20635, or its reciprocal, US$1 = SDR 0.828948, which is the way in which SDR/currency exchange rates are expressed for Fund operational and accounting purposes. Exchange rates for other currencies in terms of the SDR were derived from their market exchange rates against the dollar. For example, with an exchange rate for the deutsche mark of DM 2.50 equal to US$1, the DM/SDR rate would be calculated by dividing 0.828948 by 2.50 to yield DM 1 = SDR 0.331579.

At the time when the SDR scheme was being put into effect, the fixed relationship between the par value of the U.S. dollar and the SDR seemed the most suitable basis for valuation in the light of the way in which the international monetary system was operating. The U.S. dollar was at the center of this system, being the currency against which, for practical purposes, all other countries set the values of their currencies and in which a high proportion of countries’ reserves were held. The United States legally maintained the value of the U.S. dollar by standing ready to convert dollar balances into gold. The majority of other Fund members were generally observing their obligations under the par value system and maintaining market rates within 1 per cent either side of the dollar. It followed, therefore, that the value of the SDR in terms of a member’s currency could move only within narrow margins unless the member itself, or the United States, decided on a change in par value. Thus, the so-called gold guarantee on SDRs was, in effect, a guarantee that the dollar value of the SDR would be maintained in the event of a devaluation of the dollar. If, however, a weakness of the dollar did not give rise to a dollar devaluation but to revaluations of other major currencies, the value of SDRs would decline in terms of those other currencies. This was not regarded as an important disadvantage, since revaluations had been relatively few and far between in the preceding years.

The need for change in the valuation method

Beginning in August 1971, when the United States declared that it would no longer convert dollars into gold, the international monetary system underwent a series of important changes, each of which raised doubts about the validity of continuing with the method of SDR valuation described above. First, there was the fact that the United States would no longer convert dollar balances into gold; that raised the question as to whether the gold value of the dollar was sufficiently meaningful for the SDR to be based on a fixed relationship with the dollar. Second, as the system of wider margins agreed at the Smithsonian negotiations in late 1971 was largely replaced by February 1973 by generalized floating, it became possible for the value of the SDR, while remaining fixed in terms of the U.S. dollar, to fluctuate widely in terms of other currencies. This problem was particularly acute in 1973, when the dollar weakened appreciably against most of the major European currencies, which were no longer maintaining margins against the dollar, and the issuers of these currencies saw the value of their SDRs declining markedly in terms of their own currencies. Moreover, throughout the period from August 1971 there was growing opposition to linking the value of an internationally created reserve asset to an individual currency, and the policies of its issuer, and a growing desire to provide the SDR with stability of value in terms of currencies in general rather than in terms of one currency. It was felt that such stability of SDR value would assist in establishing the SDR as the main reserve asset of a reformed system.

Attention was therefore mainly concentrated on forms of SDR valuation that employed a “basket” of currencies, although it was also suggested that SDR transactions might take place at the par values of whatever currencies were involved in those transactions. This latter solution would, of course, require a par value system to be in operation. Several variations on the “basket” approach were extensively discussed in the Fund and in the Committee of Twenty. Each “basket” approach relied basically on linking the value of the SDR to changes in the value of a group of currencies, and the variations in the techniques that were proposed were aimed at achieving greater “strength” for the SDR or at least avoiding a “weak” SDR. It was eventually agreed that the so-called “standard” basket would be adopted for the interim period prior to the reform of the international monetary system.

The standard basket

Under the standard basket method of valuation, the SDR is regarded as equal to the sum of a fixed set of currency amounts; for example, 40 U.S. cents, plus 40 German pfennige, plus 4 new pence, plus 40 centimes, and so on, depending on the number of currencies in the basket and the weights to be assigned to each. The value of one SDR in terms of any individual currency is the value of each of the currency amounts in the basket expressed in terms of this one currency at the prevailing spot exchange rates. This is essentially a less complex system than the other “basket” proposals and its major practical advantage, and possibly the deciding factor in its adoption from July 1, 1974, was that the ability to calculate the rate for the SDR in terms of currencies relies solely on the existence of market exchange rates. Thus, the “standard” basket can be employed whether the exchange rate regime is one of generalized floating or one in which margins are maintained around par values or central rates.

The final discussions of the Executive Directors in the first half of 1974 were concerned mainly with the number of currencies to be included in the standard basket and the weights to be assigned to each. It was decided that the standard basket was to contain the 16 currencies that had a share in world exports of goods and services in excess of 1 per cent, on average, over the five-year period 1968-72. The percentage weight assigned to each currency in the basket was based on the share in world exports of the issuer of that currency, although these weights were subject to adjustment and rounding to reflect the fact that the U.S. share of world exports does not provide an adequate measure of the importance of the U.S. dollar in international transactions. The percentage shares decided for the 16 currencies were as follows:

U.S. dollar33.0
Deutsche mark12.5
Pound sterling9.0
French franc7.5
Japanese yen7.5
Canadian dollar6.0
Italian lira6.0
Netherlands guilder4.5
Belgian franc3.5
Swedish krona2.5
Australian dollar1.5
Spanish peseta1.5
Norwegian krone1.5
Danish krone1.5
Austrian schilling1.0
South African rand1.0

On June 28, 1974 the Fund made the calculations necessary to convert these weights into amounts of each of the 16 currencies. These amounts, which remain fixed, are shown in column (1) of Table 1. As can be seen from that table, the value of one SDR is equal to the sum of 40 cents, 38 pfennige, 4½ new pence, 44 centimes, and so on.

Table 1.International Monetary Fund: SDR valuation on July 8, 1974
CurrenciesCurrency

amounts

(1)
Exchange rates

July 8, 1974

(2)
U.S. dollar

equivalent

(3)
Australian dollar0.0120.672270.017850
Austrian schilling0.2218.155000.012118
Belgian franc1.637.960000.042150
Canadian dollar0.0711.027400.072945
Danish krone0.115.927500.018558
Deutsche mark0.382.544500.149342
French franc0.444.802500.091619
Italian lira47.0644.350000.072942
Japanese yen26.0288.100000.090246
Netherlands guilder0.142.652500.052780
Norwegian krone0.0995.400000.018333
Pound sterling0.0452.389000.107505
South African rand0.00820.666690.012300
Spanish peseta1.157.095000.019266
Swedish krona0.134.387500.029630
U.S. dollar0.401.000000.400000
SDR 1 – US$1.207584
SDR Value of US$1.00 = SDR 0.828100
Col. 1: The currency components of the basket.Col. 2: Exchange rates in terms of currency units per U.S. dollar except for the pound sterling and the Canadian dollar, which are expressed as U.S. dollars per currency unit. Rate sources: London noon rates except for the yen, which is the Tokyo representative rate.Col. 3: The U.S. dollar equivalents of the currency amounts in column (1) at the exchange rates in column (2); that is, column (1) divided by column (2), except for the pound sterling and the Canadian dollar for which the amounts in the two columns are multiplied.
Col. 1: The currency components of the basket.Col. 2: Exchange rates in terms of currency units per U.S. dollar except for the pound sterling and the Canadian dollar, which are expressed as U.S. dollars per currency unit. Rate sources: London noon rates except for the yen, which is the Tokyo representative rate.Col. 3: The U.S. dollar equivalents of the currency amounts in column (1) at the exchange rates in column (2); that is, column (1) divided by column (2), except for the pound sterling and the Canadian dollar for which the amounts in the two columns are multiplied.

The conversion of the percentage weights into amounts of each currency involved two principal elements. The first was the establishment of a set of exchange rates so that the share of each currency could be expressed as a currency amount; the rates used by the Fund were average market rates over the last three months. The second involved proportionally adjusting and rounding the currency amounts so that on June 28—the last day of the old valuation system—the old and the new systems would yield the same value for the SDR in terms of currencies.

Daily calculations

To obtain an exchange rate for a currency against the SDR, it would be possible to calculate, using market exchange rates, the equivalents in terms of that currency of the individual amounts of each currency in the basket; the sum of these currency equivalents would then yield the exchange rate of that currency in terms of the SDR. However, it would be highly inconvenient for the Fund to have to collect exchange rates against all the currencies in the basket for any currency for which an SDR rate was required. For convenience, therefore, the Fund uses market rates for the dollar, which are readily available for all currencies in the basket, to calculate the dollar/SDR rate, while rates for other currencies continue to be derived from the dollar/SDR rate and market exchange rates for these other currencies. The vital difference is, of course, that under the basket the dollar/SDR rate fluctuates from day to day, while under the previous method of valuation it remained fixed. This method of calculating rates is, however, largely a question of convenience, and does not confer on the dollar any special status vis-à-vis the SDR. In fact, with consistent cross rates, the rate for the SDR in terms of, say, the Belgian franc, will be the same under this method of calculation as it would be if each currency component in the basket were valued at its market rate against the Belgian franc.

Since July 1, 1974, when the new method of valuation went into effect, the Fund has made daily calculations to establish exchange rates for currencies in terms of SDRs. The method of making the daily calculation of the dollar against the SDR is shown in Table 1, which takes as an example the calculation made by the Fund on July 8, 1974. Once the dollar/SDR rate has been established in the manner illustrated, rates for other currencies in terms of the SDR are readily calculated, using the U.S. dollar/SDR rate and market rates for those currencies against the U.S. dollar (see box). For example, with a representative rate for the Netherlands guilder of f. 2.65 per $1, the guilder/SDR rate for July 8 would be calculated by dividing 0.828100 (that is, the SDR value of $1 shown in Table 1) by 2.65 to yield f. 1 = SDR 0.312491. Each day the Fund first establishes the dollar/SDR rate and then calculates rates for the SDR in terms of a range of currencies that are used in SDR transactions and in operations in the Fund’s General Account. All Fund operations and transactions are denominated in SDRs, and the rates for currencies against the SDR, calculated in the manner described, determine the currency equivalents involved. A table with all the available rates is made public each day and is carried by several wire services; it is also published every two weeks in the IMF Survey. Some daily newspapers and financial periodicals publish the rates for major currencies.

The market rates used in the calculation of rates for currencies against the SDR, other than the U.S. dollar, are so-called representative rates. For each currency for which a calculation is made, the Fund has agreed a definition of the market rate to be employed. For example, for sterling it is the noon rate in the London market. These rates are supplied to the Fund each day by central banks.

How rates move

It will be apparent from the method of establishing rates described above, and from the example of the calculation of the SDR/dollar rate shown in Table 1, that a movement in the exchange rate of any currency in the basket will affect the exchange rates of all other currencies in terms of the SDR. The extent to which it does so will depend on its weight in the basket. If, for example, the only change in a market exchange rate was a strengthening of the deutsche mark by 10 per cent, the dollar equivalent of the 38 pfennige in the basket would increase by 10 per cent. The dollar, however, would depreciate against the SDR by about 1.25 per cent, which is 10 per cent of the 12.5 per cent weight of the deutsche mark in the basket. The deutsche mark itself will appreciate against the SDR by 8.75 per cent; that is, by 10 per cent of the percentage share of all other currencies in the basket, which is 87.5 per cent. (For simplicity, this example does not take account of the fact that as exchange values change, the percentage shares of each currency in the basket shift away from the shares initially decided.) If, as was assumed, the rates of all other currencies remained unchanged against the dollar, these currencies would also depreciate by 1.25 per cent against the SDR. This would broadly reflect economic reality in the sense that these currencies would have all weakened by 10 per cent against the deutsche mark and the weight of the deutsche mark in the basket is a rough measure of its importance in international transactions. In practice, of course, the rates for most currencies in the basket change from day to day, with some strengthening and some weakening, and thus the change in the rate of a currency against the SDR is the resultant of these individual changes and the weights of the currencies that have changed.

As an example of the type of fluctuation that is likely to be experienced, the graph shows the movement in the dollar/SDR rate during the period July 1-September 30, 1974. From the starting point of July 1 up to July 24, the dollar was generally weaker in the foreign exchange markets and its rate against the SDR declined by about 0.5 per cent, after briefly being fractionally above its rate at the start of the month. From July 24 through the end of September, the general trend was upward, as the dollar strengthened appreciably in the market, and at the end of September the dollar/SDR rate was 1.6 per cent above the rate on July 1 and 2.1 per cent above the low point of July 24. Table 2 shows the percentage changes in market exchange rates for nine currencies in the basket; the movement in the dollar/SDR rate is largely accounted for by the average of these changes weighted by the shares assigned to each of these currencies in the basket. Similarly, the movement of any other currency against the SDR can be viewed as the weighted average of its movement against the currencies in the basket.

Table 2.Percentage change in market exchange rates and rates against the SDRJuly-September 1974
Change from July 1-

September 30
Market

exchange

rates
Rates

against

the SDR
U.S. dollar+1.6
Deutsche mark−4.3−2.6
Pound sterling−2.2−0.7
French franc+1.8+3.4
Japanese yen−4.7−3.0
Canadian dollar−2.3−0.7
Italian lira−2.1−0.5
Netherlands guilder—1.8−0.2
Belgian franc−3.0−1.4
Swedish krona−1.2+0.4
Note: The weights of the currencies listed account for 92 per cent of the basket.
Note: The weights of the currencies listed account for 92 per cent of the basket.

The rate of interest

The Articles of Agreement set the rate of interest on the SDR at 1½ per cent but provided for the possibility of change.

U.S. dollar rate against the SDR

(June 28, 1974 SDR 1 = $1.20635)

In the light of current interest rate levels, this initial rate seems merely nominal, but in the late 1960s interest rates were very much lower than at present. In 1968, for example, when the Fund’s Articles were amended to establish the Special Drawing Account, the average interest rate on U.S. Treasury bills was 5½ per cent and had been much lower in previous years. One of the arguments in favor of an increased interest rate on SDRs is, of course, that interest rates have risen substantially since the rate of 1½ per cent was set.

The initial level of the interest rate has to be viewed in the light of the method of SDR valuation, which was seen as providing a guarantee against capital loss. Experience tended to show, however, that holders of SDRs appeared to attach less importance to the financial value of the exchange guarantee and more to the interest rate differential between SDRs and other reserve assets. This was perhaps not surprising, since the value guarantee would play an important role only if there were a dollar devaluation; and prior to 1970 there was little expectation that the dollar would be devalued. Thus, even before the general increase in market interest rates, there was already a strong body of opinion that the interest rate was too low.

The discussion of the future interest rate on SDRs was always closely connected with the discussion of the valuation system, since these two elements together give rise to what is usually described as the “effective yield” on the asset. It was recognized that this would be the most important single factor in determining the attractiveness of the SDR as a reserve asset, particularly if there was to be a relaxation of those provisions of the SDR facility (for example, the rules of reconstitution) that gave a measure of regulation over the holding and the use of SDRs. The Outline of Reform set out the desideratum as follows:

The effective yield on the SDR will be high enough to make it attractive to acquire and hold, but not so high as to make countries reluctant to use the SDR when in deficit. The value of the SDR in transactions against currencies will be determined in such a way as to protect the capital value of the SDR against depreciation. . . . The interest rate on the SDR will be set from time to time by the Executive Board in such a way as to maintain an appropriate effective yield, in the light of changing market interest rates.

With the value of the SDR being determined by the standard basket technique, it was logical that changes in the SDR interest rate should be linked in some way to changes in the interest rates on market instruments denominated in the currencies in the “basket.” In practice, most member countries’ reserves are held and invested in only a handful of the 16 currencies in the “basket,” and it was decided that a suitable link between the SDR interest rate and market rates could be readily established by using an average of interest rates on the 5 currencies with the largest weights in the basket—the dollar, the deutsche mark, sterling, the French franc, and the yen. The market instruments that were chosen were three-month U.S. Treasury bills, three-month interbank deposits in Germany, three-month U.K. Treasury bills, three-month interbank money against private paper in France, and unconditional call money in Japan. The weights to be used in calculating the average would reflect the relative shares of these 5 currencies in the basket; namely, 47 per cent for the U.S. dollar, 18 per cent for the deutsche mark, 13 per cent for sterling, and 11 per cent each for the French franc and the Japanese yen.

After the initial increase to 5 per cent on July 1, 1974, the procedure for setting the rate will be as follows. Before the end of each six-month period (the first will end on December 31, 1974) the Executive Directors will review the interest rate and may, by a three-fourths majority, agree on a new rate for the subsequent six months. If agreement is not achieved, the interest rate on the SDR will be determined by a formula. If the weighted average interest rate on the five currency instruments over the previous three months does not exceed 11 per cent or is not less than 9 per cent, the rate of 5 per cent will remain in force. If the combined rate is below 9 per cent, the SDR interest rate will be reduced below 5 per cent by three fifths of the difference between the combined rate and 9 per cent. In a similar manner, if the combined rate is above 11 per cent, the SDR rate will be increased by three fifths of the amount by which the combined rate exceeds 11 per cent.

The adoption in existing circumstances of the standard basket and of the method described above of setting the SDR interest rate was decided without prejudice to the arrangements for valuation and interest rate that may be adopted in a reformed system, the characteristics of which would have a strong influence on a longer-term solution. In any event, the arrangements described above will be subject to review by the Fund two years after they came into operation. Experience with these arrangements is likely to be extremely helpful in providing guidance for the longer term.

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