The sdr was created by the International Monetary Fund as an international reserve asset that is allocated to its members as a supplement to existing reserve assets. Moreover, it is the unit of account for all transactions and operations of the Fund. The SDR is currently defined as the sum of $0.54, DM 0.46, F 0.74, £0.071, and ￥ 34.0.
Parallel to the development of the Fund’s, or official, SDR, international organizations, borrowers, and investors looking for a hedge against the considerable volatility and uncertainty in interest rates and exchange rate developments have started to use the same unit of account, thereby creating the commercial, or private, SDR. The value of private SDRs is determined on the basis of the same basket of currencies as the official SDR. But private SDRs are subject to the conventions of the marketplace and are not constrained by the rules governing the uses of official SDRs.1 The simplification of the SDR basket in 1981 enhanced the attractiveness of the SDR in international financial markets, and the SDR is now used to denominate a wide range of private financial instruments and obligations, such as commercial bank current accounts and deposits, syndicated loans, fixed- and floating-rate certificates of deposit, floating-rate notes, and Eurobonds.
The use of private SDRs has expanded to meet organizations’ needs for a more stable unit of account to enable them to cope with the high exchange and interest rate volatility seen in recent years. In fully arbitraged foreign exchange and capital markets, the ex ante total returns—interest income plus currency appreciation or depreciation—expected from investments in otherwise comparable instruments are equal for all currencies, putting aside legal constraints and factors of convenience and political risk. If expectations were always realized, any one such investment (properly adjusted by its forward rate against the SDR) would do as well as any other—that is, there would be no benefit in using a basket. In reality, however, and especially since the system of floating exchange rates has become generalized, currencies tend to appreciate or depreciate in unexpected ways, and divergent and frequently revised expectations of inflation rates and real factors lead to sudden and often unpredictable gyrations in exchange and money markets, resulting in large discrepancies in ex post returns.
A large and sophisticated organization may wish to try to monitor these fluctuations or to hedge itself by constructing a tailor-made basket of currencies. For the smaller or more conservative organization, however, the SDR—which is a standardized basket, or portfolio, of currencies—is often a lower-cost means of diversifying the risk of being exposed to unexpected returns. When exchange exposure is unavoidable, an investment in SDRs is thus intrinsically less risky than an investment in financial instruments denominated in any individual national currency. Moreover, for the smaller organization, there may be economies of scale and lower transactions costs in doing business in SDRs.2
This superior stability encompasses both components of total return: exchange rate changes and interest income. The stability of the exchange rate results from changes in the exchange value of each currency in the basket being offset, fully or partially, by smaller changes in the same direction, or by opposite changes, in exchange values of the other currencies. Because the exchange rate movements of the different currencies in the SDR basket are not perfectly correlated, the standard deviation of the SDR’s exchange rate in terms of a particular currency will be less than the weighted average of the five individual standard deviations in terms of the same currency.
By the same token, the interest rate on the SDR represents a blending of interest rates. But the intrinsic diversification characteristic is somewhat less pronounced than for exchange rate movements, because interest rates in different countries, while affected by movements in relative rates, also respond to common factors affecting the absolute level of yields, and thus tend to move in the same direction. Table 1 demonstrates that the pairwise correlations between the changes in nominal interest rates on the SDR and its component currencies are consistently positive and often high for the period studied. The stability of the SDR interest rate thus derives predominantly from the fact that it is an average of various absolute magnitudes of interest rates, rather than from offsetting interest rate movements.
This paper tries to measure the relative attractiveness, in terms of both total return and risk, of SDR-denominated investments. It simulates investments, sequentially using each of the component currencies and the SDR itself as a base currency and investing alternatively in the native base currency, in the four other component currencies, and in SDRs.
It is interesting to examine the picture for each currency in turn for two reasons. First, it permits one to conduct a sequential examination of the return obtained and risk incurred by residents in each of the five countries whose currencies compose the SDR who invest solely in instruments denominated in their native currency and, therefore, ex ante, avoid any foreign exchange risk, though the five countries experience different inflation rates.
Second, both ex post nominal and real returns differ in each country. When investing any one currency in instruments denominated in the same or other currencies, adjustment of interest returns to take account of forward exchange premiums or discounts results in parity of yields, because of the effect of covered interest arbitrage on forward premiums or discounts. Unadjusted nominal interest rate differentials, though they reflect different expectations of inflation rates, are also heavily influenced by other (i.e., real) factors, the principal ones being the monetary and fiscal policy stances in each country. Because of these latter factors—combined with imprecision in, and frequent revisions of, forecasts—the ex post changes in exchange rates do not always reflect actual inflation differentials, thereby invalidating strict purchasing power parity and interest rate parity across countries. Consequently, the covered return obtained in any currency by a resident of one country is different from the covered return on the same currency obtained by a resident of another country and from the uncovered ex post return obtained in another currency.
While this study emphasizes a comparison of total returns (interest income plus exchange rate changes) and variability of these returns, a separate examination of both interest income and exchange gains or losses is warranted for analytical purposes and because differing tax treatment of the two components of total return can have different implications for the after-tax yield.
I. Working Assumptions
The main assumption in the paper is that the SDR basket has existed in its present five-currency form since January 1, 1977. The exchange rates used for the five constituent currencies are the monthly averages of the daily noon midrates in London, with the exception of January 1977 through April 1977, for which the monthly averages of the daily representative rates, as published in International Financial Statistics (IFS), are used because the London noon rates are only available from May 1977 onward.3 The interest rates used are the one-month Eurodeposit rates for each of the constituent currencies. The SDR interest rate is the weighted sum of the interest rates on the component currencies, with each weight equal to the percentage share of a currency’s spot value in the basket.4
The paper simulates an investment made in January 1977 that is rolled over each month through December 1982. Interest income is not reinvested in order to compensate for the fact that the spot exchange rates are used to derive the weights attributed to the currencies. If interest income were reinvested at the prevailing rate, currencies which, on average, have proportionally higher nominal interest rates would obtain greater weights in the basket at the end of each investment period, and currencies with proportionally lower nominal interest rates would obtain lesser weights in the basket at the end of each investment period. Consequently, the composition of currencies at the end of the investment period would no longer reflect their original weights in the SDR. The use of forward exchange rates decreases the effect of high interest rates on currencies expected to depreciate and increases the proportionate importance of low-interest-rate currencies expected to appreciate in the future, thereby resulting in a more exact calculation. Since interest incomes are not reinvested at the end of each month and the value of the SDR is recalculated each month, the bias created by using the spot exchange rates to calculate the weights is offset.
The interest rate and exchange rate returns for each of the currencies and the SDR are calculated monthly at an annual rate, and the month-to-month standard deviations in interest and ex-change rate returns are computed. The total yield, which is the sum of the interest rate and exchange rate returns, and its standard deviation are then computed. Also, the real total yield is assessed by deflating the nominal total yield for each base currency by the annualized monthly change in the retail price index in the native country of that base currency. It was demonstrated earlier that because the forward premium or discount does not equal the expected exchange rate change, ex post real total returns differ from one country to the next. Consequently, past behavior of, and expectations about, real total returns play a role in influencing decisions concerning foreign exchange exposure.
For calculation of the SDR’s real total yield, the weighted average of changes in retail price indices in the five countries is deducted from the nominal total yield obtained when the SDR is used as a base currency. It has been argued that the consumer price index (CPI) does not reflect true price changes because of the different methods used to derive it in the various countries, but it is used here because it is the index on which financial markets tend to focus most often. The whole exercise is repeated sequentially, considering each of the constituent currencies and the SDR itself as base currency.
Once all of the above calculations have been made, the risk-return relationship of the SDR and each of the base currencies is assessed and compared. For this purpose, total return is measured, as it was earlier, as the sum of the interest income and the exchange rate gain or loss; and risk is defined as the total variability, as measured by the standard deviation of the total return. Moreover, a study of the volatility of the total return on individual currencies, defined as that part of total variability of the returns that is the result of changes in the return on the SDR, is undertaken. The causes of changes in the total return on a currency are broken down into two categories: first, an evolution common to all currencies, defined in the model as the movement of the SDR; second, factors specific to that currency. Consideration of volatility, measured by a simple statistic called the beta coefficient, indicates how much of the change in the total return on an individual currency is the result of movements in the value of the basket rather than the result of isolated changes in the value of that currency. A beta coefficient of one is given to the SDR, and the beta coefficient for each currency is calculated. If a currency’s beta coefficient is also equal to one, the yield on that currency varies proportionally with the return on the SDR. A beta coefficient greater than one means that the currency’s return varies more than proportionally with the return on the SDR, and the reverse is true for a beta coefficient lower than one. Given a linear risk-return relationship, the greater the beta of a currency, the greater the risk and the greater the expected return required to compensate risk-averse investors. By the same token, the lesser the beta, the lesser the risk and the lesser the expected return required. Finally, the paper discusses some features that could make use of the SDR in international financial markets more attractive.
As was indicated earlier, the period covered extends from January 1977 to December 1982. Two subperiods are also considered: in the first subperiod, the investment is rolled over from January 1977 to December 1979, and in the second from January 1980 to December 1982. The rationale for choosing the subperiods is the evolution of the exchange rate of the dollar, given the pre-eminent weight of the dollar in the SDR basket, as shown in Table 2.
As can be readily seen in the table, the first subperiod, extending from January 1977 to December 1979, can roughly be earmarked as one of weakening of the dollar; the second subperiod, extending from January 1980 to December 1982, can be ear-marked as one of strengthening of the dollar. For the period as a whole, as shown by the point-to-point exchange rate changes in the last column of Table 2, the dollar was, on average, fairly stable against the deutsche mark, the pound sterling, and the SDR; it appreciated markedly against the French franc and depreciated against the yen.
II. Interest Return
In this section, the first component of total return—interest income on each of the constituent currencies and on SDR deposits—is examined separately. While interest returns are available in each of the constituent currencies held by potential investors, differences in these returns clearly cannot be exploited without incurring exchange rate exposure. As was mentioned earlier, though, interest rates prevailing in a country reflect both expectations of inflation rates and real factors, such as the monetary and fiscal policy pursued in that country, so that a study of interest rates’ evolution has its own merit. Moreover, in most countries, interest income is considered current income, while exchange rate gains are considered capital gains, which are normally taxed at a much lower rate. Consequently, the allocation of investments will also be influenced by prevailing nominal interest rates. A separate study of interest incomes also permits detection of the degree of risk reduction involved in interest rates on SDR-denominated deposits. Table 3 displays the nominal and real interest rate returns, the standard deviation of these returns, and the coefficients of variation for the whole period and for the two subperiods. Chart 1 compares the nominal interest rates simulated for the SDR with the rates on its component currencies for the selected period.
|Whole Period||Subperiod 1||Subperiod 2|
|deviation||of variation||deviation||of variation||deviation||of variation|
|Interest||of interest||of interest||Interest||of interest||of interest||Interest||of interest||of interest|
|Nominal Interest Rates|
|Real Interest Rates|
|SDR||2.46||4.37||1.776||–0.31||3.00||–9.620||5.24||3.73||0.712|Chart 1.SDR and Component Currencies: Nominal One-Month Eurocurrency Deposit Interest Rates, 1977–82
The standard deviations of the interest returns reveal that the nominal interest rate on the SDR has not systematically been the most stable rate. For both subperiods and for the whole period, the deutsche mark interest rates are more stable than the SDR interest rates, which, in turn, are more stable than the remaining interest rates. When the coefficient of variation, which measures the relative spread of the distribution around its mean and thus has the advantage of being a comparable measure, is used, the interest return on the pound sterling turns out to be the most stable for 1977–82, followed closely by the SDR interest return. During the 1977–79 subperiod, only the French franc had more stable interest rates than the SDR; while during the 1980–82 subperiod, all five constituent currencies had more volatile interest rates than the SDR.
In order to also assess the real interest returns, the nominal interest rates for each component currency have been deflated by the changes in the retail prices in their respective countries and the nominal SDR interest rates have been deflated by the weighted average of the changes in retail price indexes in the five countries. The results are displayed at the bottom of Table 3.
Interestingly, the first subperiod (1977–79) is characterized by very low or negative real interest rates, and the second subperiod (1980–82) by relatively high real interest rates.
Both during the whole period (1977–82) and during the two subperiods, the SDR real interest rate remains above the average. During the 1977–79 subperiod, the dollar and SDR real interest rates are the most stable when measured by the standard deviation. During the 1980–82 subperiod, the deutsche mark real interest rate is marginally more stable than that of the SDR as measured by the standard deviation, but the SDR real interest rate displays the lowest total variability when measured by the coefficient of variation. As was true of nominal interest rates, the deutsche mark has the lowest variability in real interest rate returns for 1977–82. But the SDR real interest return is higher, though only marginally more variable than the deutsche mark return.
III. Exchange Rate Changes
In order to make the various national interest rates described above comparable, they must be adjusted by exchange rate changes experienced in moving from one currency to the other. In this section, the returns derived from particular exchange rate changes are examined separately, and the exchange-risk reduction obtained when investing in SDR-denominated assets is assessed. This is of interest in that it shows the relative gain or loss and the stability of exchange rate changes if currency (rather than interest-bearing assets) is held. In order to capture the fluctuations of all the currencies included in the SDR basket, the pairwise correlation coefficients of changes in exchange rates using the SDR as a unit of account were calculated. These appear in Table 4.
Table 4 shows that the exchange rate movements of the dollar have a negative correlation with the exchange rate changes of the four other currencies included in the SDR basket. This is not surprising, because, given the importance of the U.S. economy and the dollar in the world financial system, the evolution of the dollar rate is principally influenced by domestic events in the United States, resulting in quite independent movements of the currency. By definition, other currencies move in the opposite direction from the dollar, but the degree of negative correlation is markedly different from one currency to the other. It is very pronounced for the deutsche mark and the French franc, less for the yen, and even less for the pound sterling. The small correlation coefficient between the dollar and the pound sterling is due to a marked independent appreciation of the pound sterling in 1979 and 1980 because of the emergence of the United Kingdom as a major oil producer and its implementation of stringent monetary and fiscal policies.
Tables 1 and 4 reveal a strong positive correlation between the deutsche mark and the French franc, evidently because both currencies are members of the European Monetary System (EMS), which contains exchange rate changes within narrow limits. As the correlation coefficient measures the relationship between the exchange rate fluctuations in each of the months under study, it is not influenced significantly by periodic revaluations or devaluations. Moreover, normal depreciations before a formal devaluation and normal appreciations before a formal revaluation are artificially constrained by the EMS mechanism; consequently, the true movements of the French franc vis-à-vis the deutsche mark are masked.
The relatively high correlation between the French franc and the yen cannot be explained by any institutional setup and must therefore be considered accidental. The relatively high correlation between the pound sterling and both the French franc and the deutsche mark when the dollar is used as a base currency disappears completely when the SDR is used as the numeraire. Consequently, the correlation is due mainly to the simultaneous fluctuations of these three currencies against the dollar rather than to synchronous movements among themselves.
Chart 2.SDR and Component Currencies: Foreign Exchange Rate Indices, 1977–82 Chart 3.SDR and Component Currencies: Foreign Exchange Rate Indices, 1977–82
IV. Total Return
In this section, the total return opportunities, defined as the sum of interest income and exchange rate gain or loss, available to an investor in each base country investing either in his native currency or in each of the other component currencies and the SDR itself are examined in sequence. Different results are obtained depending on the base currency used, because, as was mentioned earlier, actual total returns do not coincide with expected returns; consequently, a stepwise analysis is undertaken. The results are shown in Tables 5–10 and illustrated in Charts 4 and 5.
|Pairwise Correlations of Total Returns, 1977–82|
|Pairwise Correlations of Total Returns, 1977–82|
|Pairwise Correlations of Total Returns, 1977–82|
|Pairwise Correlations of Total Returns, 1977–82|
|Pairwise Correlations of Total Returns, 1977–82|
|Pairwise Correlations of Total Returns, 1977–82|
|¥||–0.11||–0.46||–0.03||–0.10||0.13||1.00|Chart 4.Risk-Return Relationships, 1977–82 Chart 5.Risk-Return Relationships, 1977–82
Because other currencies tend to move in the opposite direction from the dollar, a dollar-based investor could use any non-dollar currency in the SDR basket or the SDR itself as a hedge against the fluctuations of his own currency. As the dollar constituted, on average, 45 percent of the SDR in the period under study, the movements of the SDR exchange rate encompassed a high degree of autocorrelation of the U.S. dollar, with the result that investments in SDRs were prima facie less risky for a dollar-based investor than investments in the other, non-dollar currencies. Moreover, movements of one of the non-dollar currencies tend to be partially offset by smaller or divergent movements in the other non-dollar currencies. As a matter of fact, the exchange rate variation incurred by investing in one of the four non-dollar currencies would have been, on average, more than twice the exchange rate variation of the SDR, as shown by the standard deviations of the exchange rate movements for the whole study period and for both subperiods.
During 1977–82, a dollar holder investing in foreign currencies would have obtained the highest total return by investing in pound sterling and the second highest total return by investing in SDRs. However, the coefficients of variation reveal that the total SDR return would have been nearly twice as stable as the total return on pound sterling and three times more stable than the total return on the other currencies. This is clearly illustrated at the top of Chart 4.
During 1977–79, the highest return that a deutsche mark-based investor could have obtained would have been earned by investing in pounds sterling, but at a relatively high risk. The lowest risk, as measured by the standard deviation of the total returns, would have been realized by investing in SDRs, closely followed by the low risk of investing in French francs, given the efficacy of the EMS. But when the coefficient of variation is used to measure the variability of returns, the French franc investment is more stable than the SDR investment, because of the low total yield obtained on SDRs during that period. This low yield on the SDR, incidentally, somewhat distorts the relevance of the coefficient of variation.
During the second subperiod (1980–82), an investment in dollars would have yielded the highest return but also the highest standard deviation. In the low-risk category, the two lowest- ranking investments are the same, but the situation regarding measures of variability is reversed: when measured by the standard deviations of the total returns, the French franc investment is slightly less volatile than the SDR investment; while when the coefficient of variation is used, the reverse is true.
For the whole period under study, the investment in French francs turns out to be slightly less volatile than the investment in SDRs, but the total yield obtained is lower on the former. This unexpected behavior is accounted for by the participation of both the deutsche mark and the French franc in the EMS.
For the three periods under consideration, a sterling-based investor would have obtained the greatest stability in foreign investments, when this is measured by the standard deviations of the total returns, by investing in SDRs. Moreover, he would have obtained an above-average total yield. When the coefficient of variation is used to measure risk, an investment in either deutsche mark or French francs would have been more stable than an SDR investment in 1977–79, but an investment in either currency would have been more risky than an investment in SDRs or in any of the other component currencies in 1980–82. For the whole period, the SDR investment is the most stable one, whichever measure is used.
The conclusions obtained for the deutsche mark-based investor are equally valid for the French franc holder. Because of both currencies’ inclusion in the EMS and the narrow margins of exchange rate fluctuations permitted under the system (except for occasional realignments of the EMS currencies), a French resident’s total risk in investing in deutsche mark was somewhat lower than his risk in investing in SDRs during the period under review. But, for both deutsche mark-based and French franc-based investors, the total yield obtained by holding SDRs was superior to the yield obtained by holding the other currency.
The interest and exchange rate movements of the Japanese yen over the study period were more influenced by domestic monetary and fiscal policies than were other non-dollar currencies. The correlations of the total return of the yen versus the other currencies are, therefore, extremely low. But the yen-based investor would nonetheless have enjoyed the most stable return by investing in SDRs, according to the standard deviations of the returns. But, unlike the results for the other currencies, the differences between the standard deviations are small. When the coefficient of variation is used as a measure of risk, an investment in pounds sterling turns out to be fractionally more stable than an investment in SDRs for 1977–82 because of the high yields available on sterling then.
This last case is somewhat unusual. The starting point is a “world resident” in a low-risk situation who is acquiring more risky assets in an effort to improve his return. The first column of the pairwise correlation table at the bottom of Table 10 shows that only the dollar returns have a positive correlation with the SDR returns. (Given the pre-eminent weight of the dollar in the basket, a large part of this positive correlation is autocorrelation of the dollar.) The returns on the non-dollar currencies move slightly in the opposite direction and are thus potentially more risky. For the period studied, the standard deviations of the total returns are nearly identical, except for that of the yen, thus indicating that yen investments are more volatile than investments in the other currencies in SDR terms. But only two currencies produce a total yield superior to the SDR return—the dollar and the pound sterling.
At this stage, it can be concluded that during the period under review, the SDR has produced above-average total returns and, except for the pairwise low-risk relationship between the deutsche mark and the French franc, has been more stable than any of its components. Though certain investors are prepared to face exchange rate risks and to adopt a strategy of frequently switching among currencies in an effort to earn a higher return than is yielded by a prepackaged portfolio such as the SDR, most investors faced with a world of widespread floating are concerned about the variability of rates of return and prefer a conservative portfolio management strategy. For the latter category of investors, one useful way to rank investments is the reward-to-variability ratio, which is defined as the ratio of the total return to the standard deviation. Using a ranking of previous investments by the rate of return obtained per unit of risk, an investment manager may be able to take better decisions concerning future investments. The results for investments in SDRs or its component currencies for 1977–82 are as follows:
It is evident from the table that if an investor invests in currencies other than his own—with the exception of investors based in the deutsche mark or the French franc who invest in the other currency—the SDR is a superior investment for a conservative investor because it provides a higher return for the same variability.
V. Real Total Return
The real total returns from investing in each currency comprising the SDR basket are calculated by deflating the nominal total returns obtained for each base currency by the annualized monthly changes in the retail price index in the country issuing that base currency. To calculate the SDR real total yield, the weighted average of the changes in retail price indices is deducted from the total returns obtained when the SDR is used as a base currency. The results are displayed in Table 12 and illustrated in Charts 6 and 7. The conclusions on total variability reached in the previous sections remain the same, except when the SDR is used as a base currency.
|Dollar||Deutsche mark||Pound sterling|
|SDR||13.00||23.49||1.81||3.14||30.65||9.76||5.24||3.73||0.71|Chart 6.Risk-Return Relationships, 1977–82 Chart 7.Risk-Return Relationships, 1977–82
During 1977–79, the pound sterling and the French franc have the highest nominal, as well as real, yields, whichever currency is used as a base. The SDR does not display a very high real yield because of the high negative returns on the U.S. dollar in that period, but it nevertheless earned systematically higher returns than the yen and the dollar. When the SDR is used as the base currency, the yen replaces the dollar as the currency bearing the lowest yield.
During 1980–82, the dollar enjoys the highest returns, both in nominal and in real terms, whichever currency is used as a base. The second best return in real terms was earned by the yen, followed by the SDR in third place; one reason for the yen’s better showing was that the inflation rate prevailing in Japan was lower than the rate then prevailing in the “world.”
For 1977–82 as a whole, the pound sterling shows the highest total nominal yield, whichever currency is used as a unit of account. The same is true of total real yield, except when the SDR is used as a base currency, in which case the dollar has the highest real yield. Otherwise, the dollar has the second-highest return, followed by the SDR, which stands in third place whichever currency is used as a base.
In summary, an above-average total yield is attached to SDR investments when total returns are deflated by consumer prices in each base currency. Moreover, the SDR’s intrinsic stability is untouched by this process.
So far, the total risk, defined as exposure to interest rate and exchange rate changes and measured by the standard deviation, has been assessed for each of the component currencies of the SDR basket and for the SDR itself. In this section, this total risk is broken down into two parts—a systematic component and an unsystematic component—in order to shed some light on the risk reduction made possible by use of the SDR. More precisely, it studies whether the balance of currencies in the SDR is appropriate, especially given the pre-eminent weight of the dollar.
Variations in interest rates and exchange rates of a particular currency are caused by a blend of two factors—(1) an evolution common to all the currencies in a basket and (2) conditions that are different for each currency. It has been demonstrated that the riskiness conferred by the second factor can be reduced by diversification, and one means of doing this is investing in SDRs. If the diversification is efficient, this unique risk attached to each of the currencies can be eliminated, and the investor then faces only the much lower risk attached to the efficiently diversified currency basket.
If an efficiently diversified currency basket existed, it would be preferred by risk-averse investors above any other means of diversification, such as adding one or more other currencies to the basket. The intrinsic riskiness of such a basket is the unavoidable risk to which anyone investing in foreign currencies is exposed. This nondiversifiable risk is called systematic risk or volatility. The difference between systematic risk and the total risk incurred by holding individual currencies is called unsystematic risk. In other words, the part of the riskiness attached to the expected return on a currency that could not be eliminated by combining that currency with others, so as to hold the efficiently diversified basket, is the systematic risk of the currency. The rest of that currency’s total risk is the unsystematic risk attached to it.
The riskiness of the efficiently diversified currency basket (systematic risk), as measured by its standard deviation, is calculated as the weighted average of the standard deviations of the component currencies (with the weights reflecting the importance of each of the currencies in the basket) multiplied by the correlation coefficients between these currencies and the basket. If the correlation coefficients between the total return of the constituent currencies and the total return of the basket are lower than one, the standard deviation of the basket will be less than the weighted average of the standard deviations of the individual currencies of which it consists.
If all currencies were perfectly correlated with the basket, the basket would be as risky as any individual currency in it—that is, diversification would be superfluous, and only systematic risk would exist.6 Most of the currencies in the SDR basket are not perfectly correlated with the basket, so that a degree of unsystematic risk is present for each of the five currencies in the basket. This unsystematic risk can be reduced through diversification; and if the diversification is efficient, the unsystematic risk can be completely eliminated, so that only systematic risk remains. If this is done, the important risk of a currency becomes the unavoidable, or systematic, risk because any unsystematic risk will be eliminated by the risk-averse investor. Thus, if efficient diversification is possible, the relevant risk for the individual currency is not the standard deviation of the currency’s yield (total risk) but the marginal effect the currency has on the standard deviation of the efficiently diversified currency basket (systematic risk).7 In short, the risk premium on a currency’s expected return should be related to its degree of systematic risk, not to its degree of total risk.
An investor will either hold the efficiently diversified basket or incur a higher degree of systematic risk, depending on his risk preference. If the investor chooses to hold a more risky combination of instruments than the efficiently diversified basket, his expected return should exceed the return on the basket only to the extent of the extra systematic risk incurred. The total increase in risk—systematic and unsystematic—need not be reflected in the risk premium because the part of the risk that might have been diversified away (the unsystematic risk) was willingly, though unnecessarily, accepted by such an investor.
This implies that if a particular currency’s return is uncorrelated with the return on the currency basket—that is, if it entails zero systematic risk—the expected return on that currency will contain no risk premium, even though investment in the currency might entail a significant amount of total risk. The question here is whether the SDR, given its currency composition, has the efficient-diversification characteristics described earlier. If the returns on the currencies included in the SDR are fairly uncorrelated with the return on the basket, a large part of the variability in returns on the component currencies can be diversified away by combining them into the basket.
The contribution of each currency to the riskiness of the SDR—its systematic risk or volatility, which, as mentioned earlier, is equal to the product of the standard deviation of the total return on the currency and the correlation coefficient between that currency and the basket—is measured by a simple statistic, the beta coefficient,8 which also indicates the sensitivity of the currency’s total return to movements of the basket. In this study, the beta coefficient of the SDR is set equal to one. If the beta coefficient of a currency is also equal to one, it means that the return on that currency varies proportionally with the return on the SDR. In other words, that currency has the same unavoidable risk as the SDR. A beta coefficient greater than one means that the currency’s return varies more than proportionally with the return on the SDR. A beta coefficient lower than one means that the currency has less unavoidable, or systematic, risk than the SDR. Entities operating in the base currency in question will incur less systematic risk by holding a currency whose beta coefficient is less than one than by diversifying into the SDR. If both that currency and the SDR were held, the yield on the SDR would need to be higher (i.e., carry a risk premium). It should be noted that the total risk on such an individual currency might still be greater than that of the SDR; therefore, holding the SDR might still be an attractive means of diversification. But as this example shows, that would not necessarily justify a lower interest rate on the SDR.
The greater the beta of a currency, the greater the systematic risk and the greater the expected return required. By the same token, the lesser the beta, the lesser the systematic risk and the lesser the expected return required. The relationship between the beta coefficient of a currency and its correlation with the SDR is as follows:
where βiSDR denotes the beta coefficient between currency i and the SDR; ρiSDR denotes the correlation coefficient between the total return on currency i and the total return on the SDR; σi, denotes the standard deviation of the total return on currency i; and σSDR2 denotes the variance of the total return on the SDR. The equation makes it clear that the beta coefficient of the SDR is equal to 1.
The beta coefficients for 1977–82 are as follows:
If changes in the total return on all currencies included in the SDR basket were perfectly correlated with the total return on the SDR, the beta coefficient of each currency would simply be the ratio of the standard deviation of the individual currency to the standard deviation of the SDR. And because it has been demonstrated that, except for the French franc/deutsche mark relationship, the standard deviations of the individual currencies are higher than the standard deviations of the SDR (see Tables 5–9), one would expect all beta coefficients to be greater than unity, with the exception of the pairwise French franc/deutsche mark beta coefficients. Consequently, the expected returns on investments in each individual currency should be greater than the returns obtained on investments in SDRs, because investments in individual currencies command a risk premium.
Because there is a high correlation between the dollar and the SDR—about half of which is autocorrelation of the dollar—the outcome meets expectations when the dollar is used as the base currency: the volatility of the non-dollar currencies is relatively high. For the same reason, the volatility of the dollar is relatively high when the non-dollar currencies are used as base currencies. But the beta coefficients of the non-dollar currencies are, on average, less than unity when the non-dollar currencies are used as units of account, principally because of the lower correlation between the non-dollar currencies and the SDR, as illustrated in the first column of the correlation matrix at the bottom of Tables 5–9.
Because of the low correlation between the returns on the non-dollar currencies and the yield on the SDR, a large part of the variability in returns on these currencies is unsystematic and thus does not command a risk premium. Examination of the beta coefficients demonstrates clearly that the risk reduction offered by the SDR is not efficient for the non-dollar currencies. The reason for this is that the SDR does not offer enough diversification for the non-dollar-currency-based investors because it either does not include enough currencies or because the dollar, the return on which is relatively volatile in terms of the base currencies examined here, is heavily weighted in the basket.9
This raises the question whether the preponderance of the dollar in the SDR basket has not been excessive. In other words, a non-dollar-based organization investing in SDRs automatically acquires a large measure of the variability of the dollar, which has been high in recent years, especially during 1980–82. Examination of the beta coefficients tends to demonstrate that if a non-dollar-based investor had not been exposed to the dollar at all, use of the SDR for investment or as a unit of account would not have been the optimal solution. The use of a basket with a proportionally much smaller dollar content would have greatly increased the correlation between the returns on the investor’s native currency and the returns on that basket, thereby more effectively diversifying his total risk. This basket would have been more effective because it coincided more closely with the needs and exposure of the investor. Investments in SDRs, on the other hand, would have increased systematic risk, indicating the need for a relatively higher return on the SDR to compensate investors.
While there is thus some merit attached to the argument that the weight of the dollar has been excessive from the point of view of many non-dollar-based organizations, two arguments nevertheless favor the present composition of the SDR basket. First, the dollar experienced an unprecedented appreciation during 1981 and 1982 that could be reversed in the coming years. The value share of the dollar in the SDR basket would thereby automatically be reduced. Second, given the preponderant role of the dollar in international trade and international financial markets, most international organizations, public or private, are either dollar-based or have a large dollar exposure, which, of course, is precisely why the dollar was given such a large weight in the first place. Consequently, the SDR remains attractive as a “world hedge”; moreover, it has a supplementary attraction because the number of currencies in the SDR basket is limited, and its constituents are widely tradable. Concededly, though, the SDR may be too global a hedge for organizations that are exposed to only a number of regional currencies. This latter phenomenon partly explains the recent success of the European currency unit (ECU) in European financial markets.10
It has also been argued that because the SDR basket is affected by developments in five domestic capital markets, the monetary policies in the five countries whose currencies make up the SDR basket have to be harmonized, if not integrated, before the SDR becomes an attractive instrument. The present study shows that this need not be so: the tendency for the exchange rates of the constituent currencies to vary in opposite directions makes the SDR relatively stable. If monetary policies in these countries were to be harmonized, the amplitude of their divergent movements would be reduced, and the natural diversification effect of the SDR would be diminished. The productivity of the SDR resides in its exchange stability relative to that of alternatives, and the possibility that exchange rate movements will remain divergent for the foreseeable future might entice a number of international market operators to use the SDR as a unit of account.
This paper reviews the performance of the SDR during the last six years. The starting point is that if the correlation coefficients between the returns on the different currencies included in the SDR basket are less than one, the standard deviation of the SDR will be less than the weighted average of the individual standard deviations. The outcome fully meets the expectation: the standard deviation of the total return on the SDR is less than all other standard deviations, whichever currency is used as a base, with the exception of the close relationship between the deutsche mark and the French franc (because of both currencies’ participation in the EMS). The study also demonstrates that an assessment of the volatility of the component currencies, as measured by beta coefficients, does not provide an adequate measure of riskiness for the non-dollar currencies because of the relatively low correlation between these currencies and the SDR during the study period. Finally, and for whichever currency is used as a unit of account, the SDR has an above-average total return during the period studied.
There are often reasons to expect future experience to differ from that in the past. But as far as the turbulence in interest rates and exchange markets is concerned, the SDR has produced above-average yields and entailed much less risk than any of the five currencies under consideration, both in periods of weakness and of strength of the dollar. If, notwithstanding prophecies to the contrary, gyrations in interest and exchange rates continue, use of the SDR as a unit of account could become more and more attractive to a wide array of international market operators.
AscheimJ. and Y.S.ParkArtificial Currency Units: The Formation of Functional Currency AreasEssays in International Finance No. 114 (Princeton, New Jersey: International Finance Section, Princeton UniversityApril1976).
CoatsWarren L. Jr.“The SDR as a Means of Payment,”Staff PapersInternational Monetary Fund (Washington) Vol. 29 (September1982) pp. 422–36.
LorieJames H. and Mary T.HamiltonThe Stock Market Theories and Evidence (Homewood, Illinois: Richard D. Irwin1973).
SharpeWilliam F.“Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,”Journal of Finance (New York) Vol. 19 (September1964) pp. 425–42.
SharpeWilliam F.“Mutual Fund Performance,”in Security Prices: A Supplement to the Journal of Business (Chicago) Vol. 39 (January1966) pp. 119–38.
SobolDorothy M.“The SDR in Private International Finance,”Federal Reserve Bank of New YorkQuarterly Review Vol. 6 (Winter1981–82) pp. 29–41.
Mr. van den Boogaerde, economist in the Operations Division for SDRs and Administered Accounts of the Treasurer’s Department, is a graduate of the University of Chicago; the Catholic University of Leuven, Belgium; and the University of Ghent, Belgium.
The author is indebted to his colleagues in the Treasurer’s Department for their useful comments.
See Coats (1982).
See Sobol (1981–82).
In the case of the deutsche mark and French franc, the differences between these two rates (which are taken at close to the same time of day) are very small. However, the differences have been significant at times for the Japanese yen because of important time differences. In 1981, for example, the average absolute deviation between the London noon rates and the representative rates were 0.05 percent for the deutsche mark, 0.12 percent for the French franc, and 0.30 percent for the yen.
A more precise way to calculate the SDR interest rate is the covered interest rate calculation (also known as the “Morgan formula”), whereby the forward exchange rates of the same maturity, rather than the spot exchange rates on each of the currencies, are used to derive the weights. The spot exchange rates are used here because of their immediate availability and because the forward rates are not readily available in the Fund’s data bank. Moreover, given the range of interest rates under consideration, the difference between the two methods of calculation should be small.
See Sharpe (1966).
See Van Horne (1977).
See Table 2.
For a study of currency areas, see Ascheim and Park (1976).