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____________ Rev i e w ____ ____ Vol. 66, No. 8 October 1984 5 The Recent Decline in Agricultural Exports: Is the Exchange Rate the Culprit? 15 Hedging Interest Rate Risk with Financial Futures: Some Rasic Principles 26 An Early Look at the Volatility o f Money and Interest Rates under CRR The Review is published 10 times p e r year by the Research and Public Inform ation Department o f the Federal Reserve Bank o f St. Louis. Single-copy subscriptions are available to the public fre e o f charge. Mail requests f o r subscriptions, back issues, o r address changes to: Research and Public Inform ation Department, Federal Reserve Bank o f St. Louis, P.O. Box 442, St. Louis, M issouri 63166. The views expressed are those o f the individual authors and do not necessarily reflect official positions o f the Federal Reserve Bank o f St. Louis o r the Federal Reserve System. A rticles herein may be reprinted provided the source is credited. Please provide the Bank’s Research and Public Inform ation Department with a copy o f reprinted material. Federal Reserve Bank of St. Louis Review October 1984 In This Issue . . . After expanding rapidly throughout the 1970s, the volume o f U.S. exports of agricultural products has declined in recent years. Many economists have argued that the high value o f the dollar — caused, at least in part, bv what they view to be restrictive m onetaiy policy — is responsible for these declines. In the first article o f this Review, Dallas S. Batten and Michael T. Belongia attempt to separate fact from fiction in the debate over monetary policy’s role in determining the value of the dollar and the effect o f exchange rate movements on the volume o f U.S. agricultural exports. Batten and Belongia first draw distinctions between nominal and real changes in the exchange rate and conclude that monetary policy causes nominal changes in the value o f the dollar whereas real changes — associated primarily with nonmonetary factors — are the exchange rate movements that affect trade flows. The authors examine data on real exchange rate changes and agricultural exports from several perspectives and conclude that the exchange rate has been only one factor in the recent export decline. Their analysis finds that foreign real income, depressed by the recent w orld recession, has also been a primary reason for the low er volume o f U.S. agricultural exports. In the second article, “ Hedging Interest Rate Risk with Financial Futures: Some Basic Principles,” Michael T. Belongia and G. J. Santoni discuss the problem of interest rate risk facing depositoiy institutions in an era o f financial deregulation and volatile interest rates. The authors use simple examples to show how changes in interest rates affect a depository institution’s equity value. Because share owners are interested in protecting their wealth, some institutions have initiated efforts to hedge the value o f their equity. Belongia and Santoni then discuss the econom ic principles o f hedging the interest rate risk of a financial portfolio with futures contracts. They show how interest rate risk can be measured and, based on that measurement, how futures contracts can preserve a given equity value w hether interest rates rise or fall. The examples also illustrate that a variety o f cash flows are consistent with a true hedge based on insulating a firm's equity. This result is important because many hedging strategies are designed to maintain a fixed cash flow. While this may be important for some management purposes, such a strategy w ill often result in a hedge that does not protect the wealth o f share owners. Therefore, focusing attention solely on cash flows, as many hedging strategies seem to do, will often result in a hedge that does not protect equity. In the third article, “An Early Look at the Volatility of Money and Interest Rates Under CRR," Daniel L. Thornton examines w hether the Federal Reserve’s adop tion o f a system o f contemporaneous reserve requirements (CRR) in February 1983 has had any noticeable effects on the variability o f m oney growth and interest rates. Although CRR was adopted with the expectation that it would reduce the variability o f money growth, Thornton points out that there are two reasons w hy this w ould not necessarily occur. First, depositoiy institutions may react in ways that reduce the contemporaneous link between reserves and de posits (and, hence, money) under CRR. Second, the October 1982 change in the Federal Reserve's operating procedures may have weakened the contemporane- In This Issue ous relationship between reserves and money; the argument that CRR w ould reduce the variability in money growth was predicated on the use o f a strong reserve aggregate targeting procedure. Thornton then examines the week-to-week variability o f m oney growth and. interest rates before and after February 1984 and to see if the adoption o f CRR had any impacts. He finds that there have been no significant changes in the variability of m oney growth on interest rates associated with CRR. The Recent Decline in Agricultural Exports: Is the Exchange Rate the Culprit? Dallas S. Batten and Michael T. Belongia 4 J- M.FTER increasing at an annual rate o f 5.9 percent between 1973 and 1980, the volume o f U.S. exports of agricultural products exhibited no growth in 1981 and declined at a 5.0 percent annual rate in 1982 and 1983. Many analysts blame these export declines on the appreciation of the U.S. dollar. Chattin and Lee, for example, attribute at least half of the export decline in 1982 and 1983 to this cause: “Over the last two years, the real value of the dollar has appreciated just over 25 percent (on a trade-weighted basis) for importers of U.S. com and 16 percent for importers o f U.S. wheat. Our analysts estimate that . . . the United States has lost up to $6 billion in farm export sales due to the strong dollar.” ' Similarly, Schuh, using the nominal agricultural ex port and exchange rate data plotted in chart 1, con cludes that “the export boom o f the 1970s is seen to be closely tied to the fall in the value o f the dollar. The decline in our export performance is closely associ ated with the rise in the value o f the dollar in the 1980s.”- Dallas S. Batten is a senior economist and Michael T. Belongia is an economist at the Federal Reserve Bank of St. Louis. Sarah R. Driver provided research assistance. 'Chattin and Lee (1983), p. 19. 2Schuh (1984), p. 244. Other papers drawing a similar causal relationship between exchange rates and agricultural exports in clude Chambers and Just (1982), Tweeten (1983) and Hathaway (1983). The problem with these statements is that such simple analyses generally are inadequate in establish ing a cause-and-effect relationship between exchange rates and agricultural exports. First, the comparison in chart 1 fails to distinguish nominal changes in ex change rates, which reflect changes in relative rates of inflation across countries, from real changes in ex change rates, which reflect structural changes. An analysis o f the impact o f exchange rates on trade must first separate these two types o f exchange rate changes, because only changes in real magnitudes influence trade flows. Second, a simple two-variable comparison will not correctly identify the relationship between exchange rate movements and exports because factors other than exchange rate fluctuations influence export flows. This being the case, the relevant procedure is to isolate the marginal impact o f exchange rates on trade, holding constant the impact o f the other forces that affect export flows. The purpose o f this article is to explain the funda mental differences between nominal and real changes in exchange rates and to show w hy only real changes in exchange rates influence trade flows. In addition, the effects o f real changes in exchange rates on export volume during the 1982-83 decline are estimated by using a simple econom etric m odel o f the determi nants o f w orld trade. 5 FEDERAL RESERVE BANK OF ST. LOUIS THE SOURCES OF EXCHANGE RATE FLUCTUATIONS Analysts generally agree that observed changes in exchange rates are either nominal or real in nature.' Nominal changes occur when the rates o f inflation differ among countries. For example, if the U.S. rate of inflation is consistently below those o f its trading partners, then the U.S. dollar should appreciate at rates roughly equal to the spread between inflation rates.4 Real changes, on the other hand, reflect chang ing relative prices (due to diverging structural devel opments among countries) that have different effects on the exchange rate than on the relative rates of domestic inflation. For example, some w ould argue that the discoveiy o f North Sea oil in the United Kingdom induced a substitution o f domestically pro duced for im ported oil, thereby causing the British pound to rise in value independent o f any differences in inflation rates.’ Money Growth and Nominal Exchange Rate Changes OCTOBER 1984 value o f the dollar, all other things equal. Thus, a monetary disequilibrium, through its impact on the rate o f aggregate spending, simultaneously induces a change in the rate o f domestic inflation and the foreign exchange rate. In the long run, the change in the foreign exchange rate will offset exactly the change in the rate of domestic inflation, all other things equal. Therefore, while domestic inflation changes the domestic prices of exportable goods, it also changes the number o f domestic currency units that a unit o f foreign cur rency can purchase in proportion to the difference between the foreign and domestic inflation rates. Consequently, changes in the rate o f m oney growth should have no long-run effects on either the foreign currency price o f U.S. exports or the competitive positions o f U.S. exporters in foreign markets. Purchasing Power Parity This link between nominal changes in the exchange rate and relative rates o f domestic inflation is summa rized bv the concept o f purchasing pow er parity (PPP), which can be expressed as: (1) % A e = TTF — TTlIS , The rate o f domestic inflation and, hence, nominal changes in the exchange rate are determined jointly by the rate o f domestic m oney growth relative to the growth o f the amount o f m oney that individuals, domestic and foreign, desire to hold. A country’s m oney supply is determined primarily bv its m one tary authority; the demand for m oney (i.e., the sum total o f individual desires to hold a portion o f their wealth in the form o f money) is determined primarily by income, real interest rates, prices and price expec tations in that country and abroad. The equilibrium rate o f inflation is the one that maintains continuous equality between the aggregate supply of and demand for money. Any other inflation rate generates a “m one tary disequilibrium,” which motivates individuals to alter their spending rate in order to bring their money holdings nearer to the amount they desire to hold. Changes in the rate o f consumer spending affect the demand for both domestically produced goods and services and those produced abroad. Altered de mands for foreign goods and services, in turn, produce changes in the U.S. demand for foreign currencies and, as a consequence, changes in the foreign exchange 3See, for example, Korteweg (1980) and Pigott (1981). “For a more detailed discussion, see Batten and Ott (1983). 5For example, see Chrystal (1984) and Korteweg. http://fraser.stlouisfed.org/ 6 Federal Reserve Bank of St. Louis where %Ae is the rate o f change o f the foreign cur rency price o f a U.S. dollar, and ttiis and ttf denote the rates of inflation in the United States and a foreign country, respectively.6 If, for example, the rate o f in flation in the United States falls relative to inflation rates abroad, the number o f units o f foreign currency per dollar will rise; that is, the dollar w ill appreciate. Under PPP, nominal changes in exchange rates will offset differences in domestic inflation rates across countries. Therefore, if PPP is maintained, the offset ting effects o f foreign and domestic inflation rates do not permit a change in the value o f the dollar — over the long run — to affect trade o f any type, including agricultural trade. Consequently, if the appreciation of the dollar has produced the recent decline in U.S. agricultural exports, PPP must not have been main tained during this era o f flexible exchange rates. Money Growth and Real Exchange Rate Changes: Deviations fro m PPP Real changes in exchange rates im ply deviations from PPP. Even though real changes in the exchange Equation 1 actually represents the concept of relative PPP, which states that changes in the exchange rate will exactly offset the inflation differential. See Frenkel (1981). FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Chart 1 N om in al U.S. Agricultural Exports a n d N o m in a l Exchange Rate March 1973=100 150 Billions of d o lla rs 50 T r a d e - w e ig h t e d e x c h a n g e rate SCALE 1967 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 1984 S o u r c e s : U.S. D e p a r t m e n t o f C o m m e r c e S u r v e y o f C u r r e n t Business a n d B o a r d o f G o v e r n o r s o f t h e F e d e r a l Reserve System. Q_ S e a s o n a l l y a d j u s t e d a n n u a l r a te . rate typically are associated with structural differ ences in real econom ic performance across countries, the short-run adjustment to a monetary disequilib rium may generate temporary deviations from PPP. If, for example, there is an unexpected decline in money growth, producers cannot discern im m edi ately whether the associated decline in aggregate demand (spending) is permanent or merely tem po rary. Thus, they respond initially to a monetaryinduced reduction in demand by lowering their rate of production, which reduces the rate o f real econom ic activity below its normal rate. Only when producers recognize that the decline in spending is a permanent adjustment to slower m oney growth w ill they respond by reducing prices and returning production to its normal rate. Hence, the impact o f the monetary dis equilibrium on output eventually vanishes, leaving only the rate o f inflation permanently lowered. These long-run adjustments do not occur immediately, how ever, because there are lags in the transmission of information on the origin and magnitude o f the shock to aggregate demand. Unlike domestic com m odity prices, exchange rates respond quickly to a monetary disequilibrium/ The exchange rate is determ ined in highly organized, internationally integrated markets that quickly and efficiently assimilate new information. Consequently, it will change before com m odity prices change suf ficiently to regain the domestic monetary equilibrium. 7 See Mussa (1979, 1982) and Dornbusch (1976). 7 FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 C hart 2 Inflation D ifferen tial and N o m in a l Exchange Rate M arc h 1 9 7 3 =1 0 0 P ercen t 6 -2 S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F u n d I n t e r n a t i o n a l F i n a n c i a l S ta ti s ti c s a n d B o a r d o f G o v e r n o r s o f t h e F e d e r a l R eserve S ystem L I U.S. i n f l a t i o n m i n u s t r a d e - w e i g h t e d f o r e i g n i n f l a t i o n [2 F o u r - q u a r t e r m o v i n g a v e r a g e o f n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e . Between these two events, exporters w ill face a temporarily deteriorating competitive position in for eign markets. The exchange value o f the dollar— and, therefore, the prices paid by foreign importers o f U.S. goods — will rise before the rate o f domestic inflation and domestic com m odity prices have declined by the full amount consistent with the reduction in the rate of m oney growth. This monetary-induced deviation from P P P , however, cannot persist for long. MONEY SHOCKS AND DEVIATIONS FROM PPP: THE EVIDENCE The general relationship between exchange rates and inflation differentials since 1976 is exhibited in chart 2. This chart shows the trade-weighted foreign currency value o f the U.S. dollar and the difference http://fraser.stlouisfed.org/ 8 Federal Reserve Bank of St. Louis between the U.S. rate o f inflation (as measured by the CPI) and the trade-weighted rate o f inflation o f the U.S.’s 10 major trading partners.8 It is apparent from the chart that the foreign cur rency value o f the dollar rises w hen the rate o f dom es tic inflation falls relative to that o f its major trading partners, and vice versa.8 This chart should not be “For a description of the calculation of the trade-weighted exchange rate and the weights employed, see “ Index of the WeightedAverage Exchange Value of the U.S. Dollar" (1978). The tradeweighted inflation differential is the difference between the rate of growth of the U.S. CPI and the rate of growth of the trade-weighted foreign CPI for the same countries and weights as used for the exchange rate. 9The simple correlation coefficient between the two series for the period 1/1976-1/1984 is - 0.766; the correlation between changes in the two series for the same period is -0.465. Each is statistically significant at the 5 percent level. This analysis simply extends Batten and Luttrell (1982). FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Chart 3 Deviations from Purchasing P o w er Parity 1976 77 78 79 80 11 81 82 83 1984 S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F und I n t e r n a t i o n a l F i n a n c i a l S ta ti s ti c s a n d B o a r d o f G o v e r n o r s o f th e F e d e r a l Rese rv e System L i F o u r - q u a r t e r p e r c e n t c h a n g e in t h e n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e p l u s t h e c o r r e s p o n d i n g i n f l a t i o n d i f f e r e n t i a l interpreted as proof o f the existence o f PPP; it does, however, demonstrate that these series are inversely related, which is consistent with the notion that the rate o f inflation and nominal changes in the exchange rate are jointly determ ined by excess m oney growth. The issue o f PPP is examined more closely in chart 3. Using the data in chart 2 to calculate values for equation 1 reveals that there have been significant and consistent positive deviations from PPP during the past four years. In other words, the rise in the value of the dollar has more than compensated for the decline in U.S. inflation relative to inflation in the rest o f the world.'" Although this indicates the existence of devia ,0The use of a trade-weighted index of the foreign exchange value of the U.S. dollar may bias the calculation of PPP. Its use here is mainly for illustrative purposes. tions from PPP, there is no w ay to tell directly whether short-run adjustments to changes in m oney growth or changes in real phenom ena are responsible. Attribut ing a cause-and-effect relationship between some event and exchange rates is difficult because it in volves a complete understanding o f the dynamic pro cess that characterizes the adjustment to a monetary shock. There are, however, several indirect routes to take. Previous Empirical Studies One source o f evidence is the existing literature on changes in money growth and exchange rates. Frankel (1979), for example, has analyzed the deutsche mark/ dollar relationship over the period from July 1974 to February 1978. He found that with a once-and-for-all 1 percent expansion o f the U.S. money supply, the DM/$ 9 FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Chart 4 Deviations from Purchasing P o w e r Parity and M o n e ta ry Shocks 1976 77 78 79 80 81 82 83 1984 S o u r c e s : I n t e r n a t i o n a l M o n e t a r y F und I n t e r n a t i o n a l F i n a n c i a l S t a t i s t i c s a n d B o a r d o f G o v e r n o r s o f th e F e d e r a l R e s e r v e System l_L F o u r - q u a r t e r p e r c e n t c h a n g e in t h e n o m i n a l t r a d e - w e i g h t e d e x c h a n g e r a t e p l u s t h e c o r r e s p o n d i n g i n f l a t i o n d i f f e r e n t i a l 1 2 C u r r e n t o n e - q u a r t e r m o n e y g r o w t h m i n u s p r e v i o u s 1 2 - q u a r t e r m o n e y g r o w th _ exchange rate overshot its PPP rate by 0.23 percent, all other things constant. After one year, approximately 44 percent o f this PPP deviation was eliminated. Pigott also investigated the relative importance of real and nominal sources o f monthly exchange rate changes. Using data from May 1973 to August 1980 for six currencies, he found that “real factors have repre sented a major source . . . o f exchange-rate fluctua tions. . . .'M Moreover, monetary influences did not l appear to have been substantially responsible for real changes in the exchange rate. Finally, using Granger causality tests, Throop (1984) could find no statistically significant relationship be tween changes in the real exchange rate and current "Pigott (1981), p. 49. http://fraser.stlouisfed.org/ 10 Federal Reserve Bank of St. Louis and past rates o f m oney growth during the period from 1973 to 1980. Therefore, unless the w orld has changed dramatically since 1980, it appears unlikely that monetary shocks could have been the primary cause o f the substantial and persistent deviations from PPP that w e have seen in the past four years.1 2 A Comparison o f the Data Another approach to assessing the link between money and PPP is sim ply to compare deviations from PPP with a measure o f m onetaiy shocks. Chart 4 does this using deviations from PPP (from chart 3) and m onetaiy shocks measured as deviations o f the quar ,2M1 growth does not Granger-cause changes in the real tradeweighted exchange rate even when the sample is extended to March 1984. OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS Table 1 Changes in Bilateral Real Exchange Rates and Real Imports of U.S. Agricultural Products: Selected Countries 1982 1981 Country France United Kingdom Germany Venezuela Brazil Japan Morocco Saudi Arabia Mexico Spain Canada Netherlands Exchange Rate 21.3% 3.8 27.5 -7 .2 -18.8 -1.9 26.3 8.5 -12.5 22.9 1.5 26.5 Imports Exchange Rate -35.6% -19.8 -16.8 35.3 10.3 6.1 15.0 31.3 25.4 -25.0 5.1 -18.3 15.5% 16.4 10.1 -3.2 0.0 15.0 13.4 8.0 44.1 11.6 -1.9 9.4 1983 Imports 20.8% 12.7 2.8 -5.3 -20.0 -3.2 15.7 5.2 -33.6 63.8 2.9 15.6 Exchange Rate Imports 12.3% 14.4 5.7 -3 .0 57.6 3.0 14.6 2.8 40.2 20.9 -2.9 7.4 -19.4% -8.9 -5 .5 -15.3 -28.7 5.1 37.1 -1.1 21.0 -27.1 3.3 -12.3 NOTE: Figures are percent changes from previous fiscal year. A positive change in the real exchange rate indicates an appreciation of the dollar against that country's currency. SOURCES: IMF’s International Financial Statistics, Agricultural Statistics, Annual Supplement to Foreign Agricultural Trade of the U.S. terly rate o f U.S. M l growth from the previous 12quarter moving average. If quarterly deviations o f M l growth from its trend growth accurately measure monetary shocks, and if monetary shocks were re sponsible for generating deviations from PPP, a nega tive relationship should be revealed between the se ries in chart 4. That is, faster than expected money growth should induce negative deviations from PPP, and vice versa. A comparison, however, reveals no statistically significant relationship between monetary shocks and deviations from PPP over the entire period.,;l FACTORS AFFECTING AGRICULTURAL EXPORT DEMAND this period has been blamed as the primary cause o f the recent decline in agricultural exports. The extent to which the real appreciation o f the exchange rate has actually affected exports, however, remains to be investigated. To do so requires identifying the marginal impact of real changes in the exchange rate on exports. A variety of factors other than exchange rates could be im por tant determinants o f the w orld ’s demand for U.S. agricultural exports. In fact, these factors could dom i nate the effect that exchange rates have had on the competitive trade position o f U.S. agriculture. Agricultural Exports and Exchange Rates The evidence presented above suggests that m one tary policy has not been responsible for deviations from PPP during the 1980s. Thus, the real rise in the exchange rate came from other sources. Whatever the source, the real appreciation of the exchange rate over As an introduction to investigating the relationship between exchange rate changes and U.S. trade, con sider how the volum e o f agricultural exports to spe cific countries has behaved since the dollar began to appreciate in real terms in 1981. The countries listed in table 1 represent a broad cross-section o f developed 13The simple correlation coefficient between the two series in chart 4 is -0.137, which is not statistically different from zero at the 5 percent level. There is a subperiod, however, during which the hypothesized relationship is supported. In particular, the correlation between these series for the period 1/1976—IV/1979 is -0.84. The correlation over the subsequent period (1/1980-1/1984) is only -0.085. Thus, monetary shocks are highly correlated with devia- tions from PPP during the former period, but not at all during the latter one. Furthermore, when Granger causality tests were performed be tween monthly changes in the real trade-weighted exchange rate and monthly monetary shocks for the period March 1973-March 1984, Granger-causality was statistically significant at the 5 percent level in only one of 144 different lag specifications investigated. 11 FEDERAL RESERVE BANK OF ST. LOUIS and developing nations with a variety o f capacities for domestic agricultural production. Moreover, because each nation’s currency has changed in value relative to the dollar by a different amount, these data show individual cases for which a given movement in the real exchange rate has been associated with a particu lar change in a nation's imports o f U.S. agricultural products. The nations listed represent about half of U.S. agricultural exports in the three years shown. The data in the table reveal no consistent relation ship across countries between changes in the real value o f their currencies relative to the dollar and changes in their real imports o f U.S. agricultural prod ucts. No country’s trade pattern was com pletely con sistent with an exchange rate explanation o f trade flows: imports decreasing in years when the value o f the dollar rose and increasing when the value o f the dollar fell. Indeed, M orocco and Saudi Arabia gener ally increased their imports even though their curren cies depreciated against the dollar in all three years. The import patterns o f the other countries followed no consistent pattern over this interval. For example, the pound/dollar exchange rate increased between about 4 percent and 16 percent over the period, but changes in British imports ranged between 12.7 per cent and —19.8 percent. Similarly, the Spanish peseta declined in both 1981 and 1982; imports in those iwo years, however, first fell by 25 percent, then rose by 64 percent. OCTOBER 1984 higher the level o f foreign real econom ic activity, other things equal, the larger w ould be foreign dem and for U.S. agricultural exports. The higher the price o f U.S. exports relative to those abroad, other things equal, the smaller w ould be the demand for U.S. agricultural exports. On the other side o f the market, the supply o f U.S. agricultural exports was expressed as a function o f the prices o f U.S. agricultural exports relative to the prices o f other goods and services produced in the United States and exogenous factors such as weather, embar goes, etc. Other things equal, the higher the price o f U.S. agricultural exports relative to prices o f other goods, the larger the production o f U.S. agricultural products for export. To generate an estimating equation for this model, a market equilibrium was assumed and a reduced form obtained. Furthermore, since adjustment to price changes w ill not occur immediately, each relative price variable was specified as a distributed lag to capture the dynamics o f this adjustment process.1 5 The real exchange rate was included to measure U.S. prices relative to those in the rest o f the w orld (ex pressed in dollars), net o f changes in inflation differen tials. Finally, a log-linear specification was employed, yielding the following equation estimated for the p e riod 1/1971— 1/1984: (2) In (AGX), = 0.73 + 1.32 In (FGNP), (0.54) (10.93) 2 A Simple Model o f U.S. Agricultural Exports Since the data in table 1 reveal no consistent rela tionship between real changes in the exchange rate and the volume o f U.S. agricultural exports, other factors must also be important determinants o f for eign demand for U.S. agricultural products. To isolate the relative importance o f these other influences, as w ell as to assess the marginal impact o f exchange rate changes, a simple m odel o f agricultural exports was constructed.1 4 This m odel focuses on the forces that affect the world demand for and the supply o f U.S. agricultural exports. The w orld dem and for U.S. agricultural ex ports was assumed to depend on just two factors: the level o f foreign real econom ic activity and the price of U.S. exports relative to those o f other countries. The 14This model is fashioned after those in Clark (1974), Goldstein and Khan (1978), Spitaller (1980) and Stevens, et al. (1984). 12 - - RJ = 0.94 0.30 I b, In (USAGP/USCPI)W (5.43) i = 1 5 0.71 2 Cj In (RTVVER)h (4.49) j = 1 SE = 0.058 DW = 1.51 where AGX = the volume of U.S. agricultural exports (in 1972 dollars), FGNP = the trade-weighted index of foreign real GNP, USAGP = the price index o f U.S. agricultural exports, USCPI = the U.S. consumer price index, RTWER = the real trade-weighted index o f the foreign exchange value of the U.S. dollar, and ,5The lag lengths were chosen using procedures described in the appendix to Batten and Thornton (1984). A search for a distributed lag for foreign real income was also conducted, but none was found. FEDERAL RESERVE BANK OF ST. LOUIS In = the natural logarithm.'6 The absolute value o f the t-statistic for testing the hypothesis that the estimated coefficient equals zero is reported in parentheses below each estimate. The equation fits the data well, explaining 94 percent of the variance o f the natural logarithm o f the volume o f U.S. agricultural exports. Since our objective is to assess the relative impacts o f foreign econom ic activity and real exchange rates on export volume, the coefficients o f FGNP and RTWER are o f particular interest. The log-linear speci fication generates estimated coefficients that are par tial elasticities. A partial elasticity measures the per centage change o f the dependent variable (AGX here) resulting from a 1 percent change in one o f the independent (right-hand-side) variables, holding all other variables constant. For example, the estimated coefficient o f RTWER measures the percentage change in the volume o f U.S. agricultural exports resulting from a 1 percent change in the real exchange rate. In this case, a 1 percent increase in the real exchange rate leads to a 0.71 percent decline in the volume o f U.S. agricultural exports. The significantly negative coef ficient o f RTWER suggests that increases in the value of the dollar indeed have contributed to the recent decline in U.S. agricultural exports. At the same time, however, the estimated equation contradicts the no tion that exchange rate changes are the most im por tant determinant o f U.S. agricultural exports. This contradiction can be seen by calculating the standardized regression coefficients for the explana tory variables in the equation. The reported coef ficients give no indication o f the relative explanatory pow er o f the independent variables, because these ,6Since weather Is an important exogenous determinant of agricul tural production, a dummy variable (0, 1) was included initially to reflect periods of below-normal rainfall in the United States. The estimated coefficient of this variable is not statistically significant and, consequently, is not reported. The real trade-weighted exchange rate, included to capture relative price changes, was calculated as: RTWER = TWER x (USCPI/TWFCPI), where TWER = nominal trade-weighted exchange rate, and TWFCPI = trade-weighted foreign CPI (see footnote 9 for further details). 17The sum of the estimated coefficients of (USAGP/USCPI) should be positive. The significantly negative coefficient may represent an example of the classical identification problem. For example, this may denote that the supply of agricultural exports may be shifting relatively more than the demand for agricultural exports during the period over which the equation is estimated. OCTOBER 1984 variables are expressed in different units. In contrast, the standardized regression coefficient is calculated from an equation in which the variables have been standardized (i.e., expressed in the same units). Con sequently, a comparison o f these coefficients indi cates the relative importance o f the independent vari ables in explaining the dependent variable. In this case, the estimated standardized regression coefficient o f foreign real incom e is 0.69, w hile that of the real trade-weighted exchange rate is —0.39. In other words, foreign dem and for U.S. agricultural exports has been about 75 percent more sensitive to changes in foreign real econom ic activity (FGNP) than to changes in the real exchange value o f the dollar. Based on these reduced-form coefficients, changes in foreign incom e have been primarily responsible for the changes in foreign demand for U.S. agricultural exports from 1/1971 to 1/1984. The 1982— Decline 83 Though the data demonstrate that the level of foreign real econom ic activity has been a more im por tant determinant o f real U.S. agricultural exports than the real exchange rate since the early seventies, they shed no light on the question o f w hy the volume o f agricultural exports has declined recently. Since the income effect and the exchange rate effect have op p o site signs, identifying whether the recent impact of changes in foreign real incom e is larger or smaller than that o f changes in the real exchange rate w ould be straightforward if both w orld real incom e and the real exchange rate had risen during 1982 and 1983. During this period, however, the w orld experienced an econom ic recession as w ell as a real appreciation of the dollar. Consequently, both effects resulted in low er exports o f U.S. agricultural products. To isolate these two effects, the following experi ment was performed. First, the level o f foreign real income was held at its IV/1981 level. (This date was chosen because it marks the beginning o f the w orld recession.) Next, the m odel’s predicted values for exports, holding foreign incom e constant, w ere com pared with predicted export values, allowing foreign income to vary for the period 1/1982-1/1984. The differ ence represents the marginal impact o f changes in foreign real incom e on the predicted level o f real agricultural exports. The simulation was repeated under conditions that held the real exchange rate constant, then allowed it to vary as it did between 1 / 1982 and 1/1984. 13 FEDERAL RESERVE BANK OF ST. LOUIS The results are striking. From 1/1982 to IV/1982, the marginal impact o f the w orld recession was to reduce predicted U.S. agricultural exports by almost 2 per cent, while the marginal impact o f the appreciation of the U.S. dollar was negligible. As the w orld econom y began to recover in 1/1983, the marginal impact o f foreign income became positive, stimulating pre dicted U.S. agricultural exports by nearly 5 percent from 1/1983 to 1/1984. During the latter period, how ever, the continued appreciation o f the dollar de pressed predicted U.S. agricultural exports by almost 7 percent, outweighing the positive impact o f the w orld recoveiy. In sum, only during the past five quarters can the fall in U.S. agricultural exports be “blam ed” on the appreciating dollar. Before that, the w orld reces sion was the culprit. SUMMARY AND CONCLUSIONS A number o f economists have argued that increases in the foreign exchange value o f the dollar have been responsible for recent declines in exports o f U.S. agricultural commodities. These arguments, however, generally have been based on simple comparisons o f exchange rates and exports. Moreover, they have not recognized essential distinctions between real and nominal exchange rate changes. The analysis presented in this article explained the fundamental differences between nominal and real movements in exchange rates and investigated the effects o f variables other than the exchange rate on exports. Tabular data for 1981-83 indicated no con sistent pattern between changes in the real value of the dollar and imports o f U.S. agricultural com m odi ties by foreign countries. More detailed empirical evidence on factors affecting the volume o f U.S. agri cultural exports showed that real exchange rates were related negatively to exports, but their impact was dominated by the level o f real GNP in importing nations. Overall, the analysis suggests a weak link between U.S. m oney growth and real exchange rates and indicates that foreign incom e — not exchange rates — has been the primary determinant o f agricul tural exports. REFERENCES Batten, Dallas S., and Clifton B. Luttrell. “ Does Tight Monetary Policy Hurt U.S. Exports?" this Review (August/September 1982), pp. 24-27. Batten, Dallas S., and Mack Ott. "Five Common Myths About Floating Exchange Rates," this Review (November 1983), pp. 515. Batten, Dallas S., and Daniel L. Thornton. “How Robust Are the 14 OCTOBER 1984 Policy Conclusions of the St. Louis Equation?: Some Further Evidence,” this Review (June/July 1984), pp. 26-32. Chambers, Robert G., and Richard E. Just. “An Investigation of the Effect of Monetary Factors on Agriculture,” Journal of Monetary Economics (March 1982), pp. 235-47. Chattin, Barbara, and John E. Lee, Jr. “United States Agricultural Policy in a 'Managed Trade’ World,” in United States Farm Policy in a World Dimension, Special Report 305, Agricultural Experiment Station, University of Missouri-Columbia (November 1983), pp. 18-27. Chrystal, K. Alec. “Dutch Disease or Monetarist Medicine?: The British Economy under Mrs. Thatcher," this Review (May 1984), pp. 27-37. Clark, Peter B. “The Effects of Recent Exchange Rate Changes on the U.S. Trade Balance,” in Peter B. Clark, Dennis E. Logue and Richard James Sweeney, eds., The Effects of Exchange Rate Adjustments, the Proceedings of a Conference sponsored by OASIS Research (Department of the Treasury, 1974), pp. 201-36. Dornbusch, Rudiger. “ Expectations and Exchange Rate Dy namics," Journalof Political Economy (December 1976), pp. 1161— 76. Frankel, Jeffrey A. “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials,” American Economic Review (September 1979), pp. 610-22. Frenkel, Jacob A. “The Collapse of Purchasing Power Parities During the 1970s,” European Economic Review (May 1981), pp. 145-65. Goldstein, Morris, and Mehsin S. Khan. “The Supply and Demand for Exports: A Simultaneous Approach,” Review of Economics and Statistics (May 1978), pp. 275-86. Hathaway, Dale E. “Agricultural Trade: 1984 and Beyond,” in Outlook '84, Proceedings of the Agricultural Outlook Conference, U.S. Department of Agriculture, Washington, D.C. (November 1983). “Index of the Weighted-Average Exchange Value of the U.S. Dollar: Revision,” Federal Reserve Bulletin (August 1978), p. 700. Korteweg, Pieter. Exchange-Rate Policy, Monetary Policy, and Real Exchange-Rate Variability (Princeton University Press, 1980). Mussa, Michael. "Empirical Regularities in the Behavior of Ex change Rates and Theories of the Foreign Exchange Market,” in Karl Brunner and Allan H. Meltzer, eds., Policies for Employment, Prices, and Exchange Rates, Carnegie-Rochester Conference Series on Public Policy (1979), pp. 9-57. ________. “A Model of Exchange Rate Dynamics,” Journal of Political Economy (February 1982), pp. 74-104. Pigott, Charles. “The Influence of Real Factors on Exchange Rates,” Federal Reserve Bank of San Francisco Economic Review (Fall 1981), pp. 37-54. Schuh, G. Edward. “Future Directions for Food and Agricultural Trade Policy,” American Journal of Agricultural Economics (May 1984), pp. 242-47. Spitaller, Erich. “Short-Run Effects of Exchange Rate Changes on Terms of Trade and Trade Balance,” IMF Staff Papers (June 1980), pp. 320-48. Stevens, Guy V. G., et al. The U.S. Economy in an Interdependent World: A Multicountry Model (Board of Governors of the Federal Reserve System, 1984). Throop, Adrian W. "Anatomy of the 1981-83 Disinflation," Federal Reserve Bank of San Francisco Weekly Letter (March 23, 1984). Tweeten, Luther. “Economic and Policy Outlook for U.S. Agricul ture,” in United States Farm Policy in a World Dimension, Special Report 305, Agricultural Experiment Station, University of Mis souri-Columbia (November 1983), pp. 13-17. Hedging Interest Rate Risk with Financial Futures: Some Basic Principles Michael T. Belongia and G. J. Santoni F M . OR much o f the postwar period, stable rates o f inflation — accompanied by stable levels o f interest rates — created a comforting economic environment for managers o f depositoiy institutions. Beginning in the mid-1970s, however, more variable interest rates, brought about in part by more variable inflation, caused a substantial change in the economic conditions facing depositoiy institutions. Offering long-term credit at fixed rates became riskier as larger and more frequent unexpected changes in interest rates introduced more variation into the market value o f these assets.1 This article describes h ow variation in interest rates affects the market value o f depositoiy institutions. The discussion then demonstrates how financial futures contracts might be used to hedge some o f the interest rate risk o f a portfolio com posed o f interest-sensitive deposit accounts and loans o f unmatched maturities. Although some regulatoiy authorities have denied or strictly regujated the use o f futures contracts by de- Michael T. Belongia is an economist and G. J. Santoni is a senior economist at the Federal Resen/e Bank of St. Louis. John G. Schulte provided research assistance. 'For a general description of events that have introduced or in creased interest rate risk, see Carrington and Hertzberg (1984) and Koch, etal. (1982). positoiy institutions in the belief that futures trading is risky and unduly speculative, w e argue that the judicious use o f futures can reduce the firm ’s expo sure to interest rate fluctuations.’ DURATION GAP AND INTEREST RATE RISK In the mid-1970s, w hen large fluctuations in interest rates began to occur, it became increasingly evident that depository institutions needed some measure of the relative risks associated with various portfolio holdings. One approach to the measurement o f inter est rate risk is called Duration Gap analysis. "Dura tion” refers to the "average” life of some group of assets or liabilities. “ Gap” refers to the difference between the durations o f an institution 's assets and its liabilities.3 2Legal restrictions and guidelines on the use of financial futures by different types of financial institutions are summarized in Lower (1982). A comparison of statutes on the use of futures by insurance companies is made in Gottlieb (1984). 3For more detailed discussions of duration analysis and its applica tion to financial institution portfolios, see Kaufman (1984); Bierwag, Kaufman andToevs (1983); Toevs (1983); Santoni (1984); Samuelson (1944); and Hicks (1939), pp. 184-88. 15 FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Table 1 Expected Streams of Receipts and Payments 0 Panel A: No Change in Interest Rates Asset (loan) Receipts Payments Liabilities (borrowings) Receipts Payments Net Receipts 90 Day 180 270 $1,000.00 $909.09 909.09 -0- 360 $926.75 926.75 -0- $944.76 944.76 -0- $963.11 963.11 -0- 981.82 $ 18.18 Present Value $18.18/1.10 = $16.53 Panel B: Interest Rates Rise by 200 Basis Points Asset (loan) Receipts Payments $909.09 Liabilities (borrowings) Receipts 909.09 Payments Net Receipts -0- $1,000.00 $926.75 926.75 -0- $949.10 949.10 -0- $971.98 971.98 -0- 995.42 $ 4.58 Present Value = $4.58/1.12 = $4.09 Panel C: Interest Rates Fall by 200 Basis Points Asset (loan) Receipts Payments $909.09 Liabilities (borrowings) Receipts 909.09 Payments Net Receipts -0- $1,000.00 $926.75 926.75 -0- $940.35 940.35 -0- $954.15 954.15 -0- 968.15 $ 31.85 Present Value = $31.85/1.08 = $29.49 An Example The risk introduced into a portfolio o f assets and liabilities o f different duration is illustrated in tables 1 and 2. In this example, for expositional simplicity, the firm’s planned life is assumed to be only one year. It has extended a loan with a face value o f $1,000 to be repaid in a single payment at the end o f the year at an interest rate o f 10 percent. The present value o f the loan, and, thus, the amount paid out by the firm to the borrower, is $909.09. To finance this loan, the firm borrows $909.09 for 90 days at 8 percent interest. The two percentage-point spread is the return earned by 16 the firm for em ploying its specialized capital in inter mediating between borrowers and lenders. The amount that the firm w ill ow e in three months' time is $926.75 ( = $909.09(1.08)“ ), which it plans to pay by borrowing this amount for another 90 days. Because the firm ’s proceeds from the new loan and its payment o f the old loan cancel, its net receipts at this time are zero. The firm anticipates being able to roll the loan over every 90 days at the same interest rate. Consequently, at the end o f 180 days, the firm expects to owe $944.76 ( = $926.75(1.08)■“ ), which it plans to pay with new borrowings. At the end o f the year, the firm OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS Table 2 Interest Rate Changes and the Present Value of a Portfolio of Assets and Liabilities of Different Durations Panel A: Initial Conditions Present Values Asset: Liability: $1,000.00 „ $981.82 ------------- = $909.09 ----------- = $892.56 1.10 1.10 Equity: $909.09 - $892.56 = $16.53 Panel B: All Interest Rates Rise by 200 Basis Points Present Values Asset: Liability: $1,000.00 = $892.86 „ $995.42 = ----------------------$888.77 1.12 1.12 Equity: $892.86 - $888.77 = $4.09 Percentage change in equity = -75.26 anticipates having to pay $981.82 ( = $909.09 X 1.08). This amount will be paid out o f the $1,000 proceeds from its matured asset. The firm ’s expected net receipt at year-end is $18.18, as shown in panel A o f table 1. Panel A of table 2 is a balance sheet summary o f the present value o f this investment plan. The present value o f the expected net receipt at year-end is $16.53 and is equal to the difference between the present value o f the asset, $909.09 ( = $1,000/1.10), and the present value o f the expected liability, $892.56 ( = $981.82/1.10). Both future values are discounted at 10 percent, the firm ’s opportunity cost. The Effects o f Changing Interest Rates on Equity This package o f assets and liabilities is subject to considerable interest rate risk because the 10 percent interest rate on the firm's loan is fixed for one year w hile its borrowings must be refunded every 90 days. In this example, the gap between the durations of the asset and liability is 270 days ( = 360 — 90).4 As a practical matter, the asset’s longer duration implies that a given change in interest rates w ill change the present value o f the asset more than it w ill affect the present value o f the liability. This difference, o f course, w ill change the value o f the firm ’s equity. Panel B o f table 1 shows the effect o f an unexpected 200 basis-point rise in interest rates. The increase raises the firm ’s anticipated refunding costs. As a result, the amount the firm expects to pay at year-end increases to $995.42. Net receipts fall to $4.58 and the present value o f the investment plan falls to $4.09. Panel B o f table 2 presents a balance sheet summary o f the effect o f the change on the present values o f the asset, liability and ow ner equity. The increase in interest rates reduces the present values o f both the asset and liability, but the asset value falls by relatively more because its life is fixed for one year, w hile the liability must be rolled over in 90 days at a higher interest rate. The increase in interest rates causes ow ner equity to fall by $12.44, or about 75 percent. In contrast, had the interest rate declined by 200 basis points, the net present value o f the firm ’s equity w ould have risen to $29.49 (see panel C o f table 1), an increase of about 78 percent. This extreme volatility in the firm ’s equity is due to the mismatch o f the durations o f the asset and liability that make up the firm ’s portfolio. Table 3 illustrates this point. The only difference between this and ear lier examples is that, in table 3, the duration o f the liability has been lengthened to match the duration of the asset. W hile a 200 basis-point increase in the interest rate still causes the present value o f the portfolio to fall, the change, —$0.30 or —1.8 percent, is much less than before. Clearly, matching the dura tions o f the asset and liability exposes the value o f the portfolio to much low er interest rate risk. COPING WITH THE GAP Depository institutions, particularly savings and loan associations, maintain portfolios o f assets and liabilities that are similar to the one shown in the initial example.5 That is, the duration o f their assets 4The durations of single-payment financial instruments are equal to the maturities of the instruments. In other cases, calculation of duration is not as straightforward. See footnote 3. 5Savings and loan associations are required to maintain a significant share of their portfolios in long-term home mortgages in order to obtain federal insurance of deposits. See Federal Home Loan Bank Act of 1932, sec. 4(a). 17 FED ER A L R E S E R V E BA N K OF ST. LOUIS O CT O B ER 1984 Futures Markets and Risk Table 3 Interest Rate Changes and the Present Value of a Portfolio of Assets and Liabilities of the Same Duration Panel A: Initial Conditions Present Values Asset: Liability: $1,000.00 = $909.09 „ $981.82 = -------------------- -$892.56 1.10 1.10 Equity: $909.09 - $892.56 = $16.53 Panel B: All Interest Rates Rise by 200 Basis Points Present Values Asset: Liability: $1,000.00 „ $981.82 —J--------- = $892.86 ----------- = $876.63 1.12 It may seem odd that the futures market, which is generally thought of as being very risky, can be used to reduce risk. Futures trading is risky for people w ho bet on the future price movements o f particular com m od ities or financial instruments by taking long or short positions in futures contracts. Such speculative bets on future price movements, however, are not unique to futures market trading. The nature o f most types o f businesses requires a speculative bet about the future course o f a particular price. 1.12 Equity: $892.86 - $876.63 = $16.23 Percentage change in equity = - Growing crops, for example, gives farmers long positions in physical comm odities during the growing season. These long positions expose the farmer to the risk o f price declines — declines that can reduce the profits from efficient farming (the activity that the farmer specializes in). Judicious use o f the futures market allows the farmer to offset his long position in the com m odity by selling futures contracts. Since the sale reduces his net holdings o f the commodity, the farmer's exposure to the risk o f future price declines is reduced. Similarly, futures trading presents deposi tory institutions with the opportunity to reduce their exposure to the risk o f interest rate changes. 1.8 Futures Contracts typically is longer than the duration o f their liabilities. As a result, the market values o f these institutions have been particularly sensitive to interest rate fluctua tions. This, along with the recent experience o f highly variable interest rates, has led these institutions to seek out methods to reduce their exposure to interest rate risk. Am ong other things, these firms have made greater use o f floating rate loans and interest rate swap agreements. Recent regulatory changes have allowed them to allocate more o f their loan portfolios to short term consumer loans. In addition, a number o f institu tions are using financial futures to reduce their expo sure to interest rate risk.6 6See Booth, Smith and Stolz (1984). While a number of financial firms are employing the futures market, it seems that accounting requirements have discouraged the use of futures to hedge interest rate risk. Until recently, regulators and accountants feared that losses from futures transactions could be hidden in financial reports. Therefore, they would not permit a hedge to count as one transac tion with spot gains or losses offsetting futures markets losses or gains. Instead, they required futures losses to be marked to the market while spot gains could be deferred. This asymmetric treat ment of gains and losses on the two sides of a hedge distorted earnings estimates and, therefore, discouraged the use of futures. 18 A futures contract is an agreement between a seller and a buyer to trade some w ell-defined item (wheat, com , Treasury bills) at some specified future date at a price agreed upon now but paid in the future at the time o f delivery. The futures price is a prediction about what the price o f the item w ill be at the time of delivery. In the case o f commodities, the price o f the good today (the spot price), on average, w ill be equal to the futures price minus the cost o f storage, insurance and foregone interest associated with holding the good over the interval o f the contract. A similar relationship exists between the spot and futures prices o f financial instruments. However, since the storage and insur ance cost of holding these instruments is very low, the spread between the spot and futures prices is largely determined by the interest cost. See Morris (1984) for more detail on changes in accounting stan dards. Asay, et al. (1981) provide examples of how former account ing standards discouraged the use of futures by banks and thrift institutions. FED ER A L R E S E R V E BA N K OF ST. LOUIS The Relationship Between Spot and Futures Markets f o r Treasury Bills: An Illustration In January 1976, the International Monetary Market (IMM), now part o f the Chicago Mercantile Exchange (CME), began trading futures contracts in 13-week Treasury bills.7The basic contract is for $1 million with contracts maturing once each quarter in the third week o f March, June, September and December. Since there are eight contracts outstanding, the most distant delivery date varies between 21 and 24 months into the future. Panel A o f table 4 presents quotations for Treasury bill futures for the trading day o f August 7,1984. Panel B o f table 4 lists spot quotations for Treasury bills for the same trading day* Panel A o f table 4 is interpreted as follows: Septem ber Treasury bill futures were trading at a discount of 10.49 percent on August 7, 1984. Any person trading this contract obtained the right to buy (sell) a Treasury bill the third week in September with a remaining maturity o f 13 weeks at a discount rate o f 10.49 percent. A similar statement holds for the other con tracts listed in panel A. Panel B lists spot market quotations. For example, Treasury bills due to mature August 9,1984, traded at a discount o f 9.91 percent (bid) to 9.79 percent (ask), while those maturing September 20, 1984, traded at a discount o f 9.95 (bid) to 9.91 (ask), etc. We noted earlier that the spot and futures markets must be closely related, and the data in panels A and B can be used to illustrate this point. For example, on August 7, 1984, an investor could purchase a Treasury bill due to mature December 20, 1984 (i.e., 134 days later). If he purchases the bill on the spot market, he obtains the asked discount o f 10.39 percent. At this discount rate, the price he pays for the bill is $96.41 per $100 o f face value.3 'Futures contracts in other types of financial instruments, such as GNMA passthrough certificate contracts, 90-day CDs, Treasury bonds and Treasury notes, also are available at the Chicago Board of Trade. 8The information in table 3 is taken from pages 38 and 39 of the August 8, 1984, Wall Street Journal. The actual tables in the Wall Street Journal contain more information than is presented here. For our purposes, however, the additional information is extraneous. 9$96.41 = $100/(1.1039)37. The discount factor is raised to the power of 134/360 = .37. This calculation is slightly different from the discount calculation used in determining actual trading prices, but O CTO BER 1984 Table 4 Market Quotations for U.S. Treasury Bills: August 7 , 19841 Panel A: Treasury Bill Futures (IMM) Discount Contract settle 1984 September 10.49 December 10.85 1985 March 11.13 11.35 June September 11.52 December 11.66 1986 March 11.79 11.90 June Panel B: Treasury Bill Spot Discount Maturity Date August 9, 1984 September 20, 1984 December 20, 1984 March 21, 1985 June 13, 1985 July 11, 1985 Bid 9.91 9.95 10.45 10.63 10.72 10.73 Ask 9.79 9.91 10.39 10.56 10.66 10.69 'Wall Street Journal, August 8, 1984, pp. 38-9. Alternatively, the investor could purchase a futures contract that gives him the right to buy a Treasury bill in September that w ill mature the third week in December. This alternative gives him a discount rate of 10.49 percent. Buying the Treasury bill in September at this discount w ould require a payment o f $97.54.’" This payment w ill be made 43 days into the future, roughly, September 20, and the present value o f the payment on August 7 is $96.44." Notice that this is very near the amount that the investorw ould pay ($96.41) if he were to purchase a Treasury bill on the spot market that matured during the third week o f December. Of course, other alternatives are open to the investor as well. He could, for example, buy a Treasury bill that matured the third week in March on the spot market. numerical differences between the two formulas are small. See Stigum (1981) for the market’s discount formula. ,0$97.54 = $100/(1.1049)2S. ” $96.44 = $97.54/(1.0991 ) 12. The interest rate used in the calcula tion is the rate on August 7 for a security maturing on September 20 (43 days in the future). 19 FEDERAL RESERVE BANK OF ST. LOUIS The present cost o f doing this should be near the present cost o f buying a futures contract that allows him to purchase a Treasury bill in Decem ber maturing the third week in March. Table 5 uses the data in table 4 to compare the present costs o f this and other alternatives. In each case, the present costs of em ploy ing the spot vs. the futures market are very close.1 2 Because a close relationship between these markets exists, the Treasury bill futures market can be used effectively to hedge interest rate risk.1 3 HEDGING THE GAP The Streams o f Receipts and Payments The example in table 1 can be used to illustrate how futures contracts can be applied to hedge the interest rate risk caused by the mismatch in the lives (dura tions) o f the firm’s assets and liabilities. Considerable confusion appears to exist as to what the firm's hedg ing objective should be and how hedges should be constructed. One possible hedging strategy is to pro tect the equity o f the firm (in the present value sense) from interest rate fluctuations. Another often-cited strategy is to m inim ize discrepancies between cash flows over time. It seems clear, however, that firm owners w ill choose a hedge that protects their net wealth (present value o f the firm ’s equity). This focus on net wealth is crucial because, as the examples show, reducing cash flow mismatches to zero does not m inim ize the exposure o f the firm ’s equity to interest rate changes. Hedging Met Wealth: An Example Suppose it is September 15, 1984, and the firm initiates the transactions summarized earlier in panel A o f table 1. In addition, to hedge each o f its three refunding requirements, the firm sells December, March and June futures contracts at 10 percent dis counts.1 The price o f each contract is $1,000/(1.10)2 = 4 5 12Small differences are due to the existence of transaction costs. If the differences were large, profitable arbitrage opportunities would exist. These, of course, would vanish quickly as traders took advantage of the situation. ,3There is, of course, the problem that the spot instrument being hedged may not be identical to the futures market instrument. If so, the price of one may diverge from the other because of a change in a factor that affects the price of one but not the other. This is called “basis risk” and is ignored in the following examples. ,4A flat yield curve is assumed for ease of exposition. The examples become more complicated if the yield curve slopes up or down and/ or the spread between borrowing and lending rates changes. http://fraser.stlouisfed.org/ 20 Federal Reserve Bank of St. Louis OCTOBER 1984 Table 5 The Relationship Between Treasury Bill Spot and Futures Prices: August 7, 1984, Per $100 of Face Value Case 1: Purchase of a Treasury bill that matures the third week in December 1984 Present Cost Spot Market Purchase $96.41 September Futures Purchase 96.44 Difference .03 Case 2: Purchase of a Treasury bill that matures the third week in March 1985 Present Cost Spot Market Purchase $93.92 December Futures Purchase 93.94 Difference .02 Case 3: Purchase of a Treasury bill that matures the third week in June 1985 Present Cost Spot Market Purchase $91.45 March Futures Purchase 91.47 Difference .02 $976.45. These contracts obligate the firm to deliver a 13-week Treasury bill with a face value o f $1,000 during the third w eek o f December, March and June in exchange for $976.45. Panel A o f table 6 presents the firm ’s expected streams o f receipts and payments given the structure o f interest rates on September 15. It is identical to panel A o f table 1 except that the streams o f receipts and payments generated by the futures contract are included. The futures contract generates a certain stream o f receipts equal to $976.45 in December, March and June in exchange for delivery o f the 90-day Treasury bills. The firm must acquire these bills in order to make delivery and, on September 15, the expected cost o f acquiring each o f the Treasury bills is $976.45. If interest rates remain unchanged, expected and actual costs w ill be the same so that the actual receipts and payments generated by the futures con tract net out in each period. The net flow o f receipts is zero untilyear-end w hen the firm receives $18.18. The present value o f this amount is $16.53. In panel B, interest rates are assumed to rise unex pectedly by 200 basis points immediately following OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS Table 6 Expected Streams of Receipts and Payments 0 Panel A: No Change in Interest Rates Asset (loan) Receipts Payments Asset (futures) Receipts Liabilities (borrowings) Receipts Payments Liabilities (futures) Payments Net Receipts 90 Day 180 270 360 $1,000.00 $909.09 $976.45 909.09 -0- $976.45 $976.45 926.75 926.75 944.76 944.76 963.11 963.11 981.82 976.45 -0- 976.45 -0- 976.45 -0- $ 18.18 Present Value = $18.18/1.10 = $16.53 Panel B: Interest Rates Rise by 200 Basis Points Asset (loan) Receipts Payments Asset (futures) Receipts Liabilities (borrowings) Receipts Payments Liabilities (futures) Payments Net Receipts $1,000.00 $909.09 $976.45 909.09 -0- $976.45 $976.45 926.75 926.75 949.10 949.10 971.98 971.98 972.07 $ 4.38 972.07 $ 4.38 972.07 $ 4.38 995.42 $ 4.58 Present Value = $4.38/(1.12)25 + $4.38/(1.12) “ + $4.38/(1.12)75 + $4.58/(1.12) = $16.50 Panel C: Interest Rates Fall by 200 Basis Points Asset (loan) Receipts Payments $909.09 Asset (futures) Receipts $976.45 $976.45 Liabilities (borrowings) Receipts 909.09 926.75 940.35 Payments 926.75 940.35 Liabilities (futures) Payments 980.94 980.94 Net Receipts $ -4.49 -0$ -4.49 Present Value = - $4.49/(1.08)25 - $4.49/(1.08)50 - $4.49/(1.08)76 + $31.85/(1.08) = $16.52 $1,000.00 $976.45 954.15 954.15 968.15 980.94 $ -4.49 $ 31.85 21 OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS the firm’s September 15 transactions. As in panel B of table 1, the increase in interest rates raises the firm ’s refunding cost and reduces the net year-end receipt to $4.58. In addition, however, the increase in interest rates reduces the expected cost o f acquiring the Trea sury bill to $972.07. Since the firm will receive $976.45 upon delivery o f the Treasury bills, the futures con tract w ill generate a net flow o f receipts equal to $4.38 in December, March and June. The present value of this flow added to the present value o f the net receipt at year-end ($4.58) is $16.50, which is nearly identical to the present value for the case in which interest rates remained unchanged (the small difference is due to rounding errors). Panel C illustrates the outcom e for a 200 basis-point decline in interest rates. In this case, the futures contract generates negative net receipts for the firm in December, March and June. The present value o f this negative flow added to the present value o f the higher positive net receipt at year-end sum to $16.52. As the examples show, this hedge protects the net wealth of the firm regardless o f the direction o f the change in interest rates. While this hedge protects net wealth from changes in interest rates, it does so by allowing net cash receipts to vary. Net cash receipts, both in amount and timing, are considerably different in panels A, B and C. In panel A, net receipts are $18.18 at year-end while in panel B net receipts are spread out over the year and total only $17.72. In panel C, the firm has negative net receipts during the year and a large positive net receipt at year-end for a total o f $18.38. However, the present value o f the firm is the same in all three cases. The Balance Sheet Panel A o f table 7 presents the firm ’s balance sheet position in terms o f present values. The futures con tracts are entered as both assets and liabilities, leaving equity the same as that shown in panel A of table 2.1 5 The futures asset is the present value o f the future receipt o f a fixed amount. The futures liability, on the other hand, is the present value of the expected cost of covering the futures contract given the structure o f interest rates on September 15. Panels B and C illus 15Strictly speaking, futures contracts entered into by member banks of the Federal Reserve System are treated as balance sheet memo randa items. These are reported on Schedule L, Commitments and Contingencies, of the Call Report. Hence, for accounting purposes, futures contracts do not affect the assets and liabilities of the firm until the contracts are exercised. http://fraser.stlouisfed.org/ 22 Federal Reserve Bank of St. Louis trate the effect on the present values o f the firm ’s assets, liabilities and equity if, immediately following the above transactions, interest rates rise unexpect edly (panel B) or fall unexpectedly (panel C) by 200 basis points. An unexpected increase in interest rates causes the present value o f the loan to fall relative to the present' value o f the liability. By itself, this w ould cause a reduction in the firm ’s equity. At the same time, however, the increase in interest rates generates a positive expected net cash flow from the futures contracts, which, o f course, has a positive net present value. Other things the same, this causes equity to rise. The net effect o f both changes is that equity remains unchanged. The reverse occurs if interest rates de cline by 200 basis points. This hedge has eliminated the firm ’s exposure to interest rate risk. In contrast, recall that a 200 basispoint change in the interest rate causes the equity of the unhedged firm in table 2 to change by about 75 percent. Hedging as a “Profit Center” The purpose o f hedging is to reduce the variance o f a firm ow ner’s wealth. In a textbook example o f a perfect hedge, the gain or loss from a short position in the futures market w ill offset exactly the compensat ing loss or gain on the spot assets and liabilities held by the firm. A hedge is constructed because — in the presence o f an uncertain future — wealth is greater if the institution foregoes a profit stream that is higher on average (if it goes unhedged) in exchange for a profit stream that is low er on average (by the cost of the hedging operations) but more certain. Some portfolio managers, however, lose sight o f this fact and assume speculative positions in the futures market with the objective o f earning profits from the position if interest rates change in their favor. While speculative positions in futures (or spot instruments) can increase earnings, they can have the opposite effect as well. One potentially significant danger in the use of futures contracts to hedge interest rate risk is that the firm may misunderstand the nature o f the hedging function. Trading futures for hedging is not intended to generate profits from the trading itself. Rather, its purpose is to establish futures positions so that the ow ner’s wealth is held constant; this w ill occur if the increase (decrease) in the value o f the firm's spot holdings o f assets and liabilities is offset exactly by the loss (gain) in the futures market. FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Table 7 Interest Rate Changes and the Present Value of a Hedged Firm Panel A: Initial Conditions (9/15/84) Present Values Assets: Liabilities: Loan: $1,000.00/1.10 = $ 909.09 90-day CD: $981.82/1.10 = Contracted Future Receipts Expected Cost of Covering the Futures Contract: December Future: $976.45/(1.10)25 = 953.46 December Future: $976.45/(1.10)25 = March Future: $976.45/(1.10)50 = 931.01 March Future: $976.45/(1.10)50 = June Future: $976.45/(1.10)75 = 909.09 June Future: $976.45/(1.10)75 = 3,702.65 Equity: $ 892.56 953.46 931.01 909.09 3,686.12 16.53 3,702.65 Panel B: All Interest Rates Rise by 200 Basis Points Note: The expected cost of covering each contract falls to $1,000/(1.12)2S = $972.07 while the contracted future receipt remains unchanged. Present Values Assets: Liabilities: $ 888.77 Loan: $1,000.00/1.12 = $ 892.86 90-day CD: $995.42/1.12 = Contracted Future Receipts: Expected Cost of Covering Futures Contract: December Future: $976.45/(1.12)26 = 949.17 December Future: $972.07/(1.12)25 = 944.92 March Future: $976.45/(1.12) 50 = 918.52 922.66 March Future: $972.07/(1.12)50 = June Future: $976.45/(1.12)75 = 896.88 June Future: $972.07/(1.12)75 = 892.86 3,661.57 3,645.07 Equity: 16.50 3,661.57 Panel C: All Interest Rates Fall by 200 Basis Points Note: The expected cost of covering each contract rises to $1,000/(1.08)25 = $980.94 Present Values Assets: Liabilities: Loan: $1,000.00/1.08 = $ 925.93 90-day CD: $968.15/1.08 = Contracted Future Receipts: Expected Cost of Covering Futures Contract: December Future: $976.45/(1.08)25 = 957.84 December Future: $980.94/(1.08)25 = March Future: $976.45/(1.08) 50 = 939.59 March Future: $980.94/(1.08)50 = June Future: $976.45/(1.08)75 = 921.68 June Future: $980.94/(1.08)75 = 3,745.04 Equity: $ 896.44 962.25 943.91 925.92 3,728.52 16.52 3,745.04 23 FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Real World Complications in Hedging The examples in tables 6 and 7 simplify real w orld problems to illustrate the basic concepts of interest rate risk and hedging. In practice, a number o f complicating factors will make the construction o f a hedge considerably more difficult. The first difficulty to note is that the calculation o f present values for a large portfolio com posed of many different assets and liabilities will require a great deal o f information. Moreover, resources will be needed to estimate interest elasticities lor dura tions). And, unlike our examples, which are based on single-payment loans and deposits o f known durations, firms face the additional problem of loans that are subject to early payment and de posits that are subject to early withdrawal. Even with a good estimate o f its exposure to interest rate risk, firms will face practical problems in implementing a hedge. Typically, liquidity is very thin in futures contracts dated for delivery more than nine months in the future. Firms also are not likely to find futures contracts for the exact dollar amount they wish to hedge or for the specific spot SUMMARY Higher and m ore variable interest rates have in creased the risk faced by financial institutions associ ated with attracting deposit funds and extending credit. This article presented some simple examples of techniques that can isolate and quantify sources o f a financial institution’s exposure to interest rate risk. The discussion also described h ow financial futures can be used to reduce this risk. A simple hedging example indicated that relatively conservative use of futures markets can have a potentially large impact on reducing risk exposure. The use o f futures trading is a threat to the long-run performance o f a financial firm only if applied in a manner inconsistent with hedging. REFERENCES Asay, Michael R., Gisela A. Gonzalez, and Benjamin Wolkowitz. “ Financial Futures, Bank Portfolio Risk, and Account ing," Journal of Futures Markets (Winter 1981), pp. 607-18. Bierwag, G. 0., George G. Kaufman and Alden Toevs. "Bond Portfolio Immunization and Stochastic Process Risk,” Journal of Bank Research (Winter 1983), pp. 282-91. 24 asset or liability being hedged. For example, m oney market certificates (MMCs) might be hedged with Treasury bill futures. It is possible, however, that interest rates on MMCs and Treasury bill futures will not move by identical amounts or in the same direction, an event that w ill reduce the effectiveness o f a hedge. When the futures contract does not correspond exactly to the spot commodity, as in this case, the firm is exposed to “basis" risk. Firms also face the possibility o f changes in the slope o f the yield curve; that is, unlike our exam ples, short- and long-term rates could change by differing amounts. If, for example, long rates in creased 200 basis points but short rates increased only 100 basis points, the change in the difference between the present values o f spot assets and spot liabilities w ould not be com pletely offset by a change in the difference between the present val ues o f the futures asset and liability. True hedges, however, are im plem ented under the expectation of no change in the yield curve’s slope. It is easy to see, therefore, that hedging does not eliminate this source o f risk. Booth, James R., Richard L. Smith, and Richard W. Stolz. “ Use of Interest Rate Futures by Financial Institutions,” Journal of Bank Research (Spring 1984), pp. 15-20. Carrington, Tim, and Daniel Hertzberg. “ Financial Institutions Are Showing the Strain of a Decade of Turmoil," Wall Street Journal (September 5,1984). Federal Home Loan Bank Act of 1932. Public No. 304, 72 Cong., HR 12280. Gay, G. D., and R. W. Kolb. “The Management of Interest Rate Risk,” Journal of Portfolio Management (Winter 1983), pp. 6570. Gottlieb, Paul M. “New York and Connecticut Permit Insurers to Use Futures and Options: A Comparison,” Chicago Mercantile Exchange Market Perspectives (May/June 1984), pp. 1-6. Hicks, J. R. Value and Capital (Oxford: Clarendon Press, 1939). Kaufman, George G. “Measuring and Managing Interest Rate Risk: A Primer,” Federal Reserve Bank of Chicago Economic Perspectives (January-February 1984), pp. 16-29. Koch, Donald L., Delores W. Steinhauser and Pamela Whigham. “Financial Futures as a Risk Management Tool for Banks and S&Ls,” Federal Reserve Bank of Atlanta Eco nomic Review (September 1982), pp. 4-14. Kolb, R. W. Interest Rate Futures: A Comprehensive Introduction (Robert F. Dame, Inc., 1982). Kolb, Robert W., Stephen G. Timme and Gerald D. Gay. “Macro Versus Micro Futures Hedges at Commercial Banks,” Journal of Futures Markets (Spring 1984), pp. 47-54. FEDERAL RESERVE BANK OF ST. LOUIS Lower, Robert C. Futures Trading and Financial Institutions: The Regulatory Environment (Chicago Mercantile Exchange, 1982). Morris, John. “ FASB Issues Rules for Futures Accounting,” American Banker (August 24, 1984). Olson, Ronald L. and Donald G. Simonson. 'Gap Management and Market Rate Sensitivity in Banks," Journal of Bank Re search (Spring 1982), pp. 53-58. Samuelson, P. A. "The Effect of Interest Rate Increases on the Banking System,” American Economic Review (March 1944), pp. 16-27. Santoni, G. J. “Interest Rate Risk and the Stock Prices of Financial Institutions,” this Review (August/September 1984). GLOSSARY Basis The price or yield difference be tween a futures contract and the cash instrument being hedged Basis point OCTOBER 1984 Simonson, Donald G., and George H. Hempel. ' Improving Gap Management for Controlling Interest Rate Risk,” Journal of Bank Research (Summer 1982), pp. 109-15. Stigum, Marcia. Money Market Calculations: Yields, Break-Evens and Arbitrage (Dow Jones-lrwin, 1981). Toevs, Alden. "Gap Management: Managing Interest Rate Risk in Banks and Thrifts,” Federal Reserve Bank of San Francisco Economic Review (Spring 1983), pp. 20-35. Wardrep, Bruce N. and James F. Buch. The Efficacy of Hedg ing with Financial Futures: A Historical Perspective,” Journal of Futures Markets (Fall 1982), pp. 243-54. Hedge An attempt to reduce risk by tak ing a futures position opposite to an existing cash position Interest rate swap The exchange o f two financial assets (liabilities) which have the same present value but which generate different streams o f re ceipts (payments) Long hedge A hedge in which the futures contract is bought (long position) M acro-hedge A hedge designed to reduce the net portfolio risk o f an organiza tion M icro-hedge A hedge designed to reduce the risk o f holding a particular asset or liability Open interest The number o f open futures con tracts, that is, unliquidated pur chases o r sales o f futures con tracts Short hedge A hedge that involves selling a futures contract (short position) Spot price The current market price o f the actual physical com m odity 1/100 o f 1 percent Delivery month A specified month within which delivery may be made under the terms o f the futures contract Discount yield The ratio o f the annualized dis count to the par value Evening up Buying or selling to offset or liq uidate an existing market posi tion Futures contract A standardized contract, traded on an organized exchange, to buy or sell a fixed quantity o f a defined com m odity at a price agreed to now but delivered in the future Gap analysis A technique to measure interest rate sensitivity 25 An Early Look at the Volatility of Money and Interest Rates under CRR Daniel L. Thornton February 2,1984, the Federal Reserve enacted a system o f contemporaneous reserve requirements (CRR) to replace the system o f lagged reserve require ments (LRR) that had been in effect since September 1968. The Fed made this change in response to w id e spread criticism that, under a reserve target operating procedure, LRR made it more difficult to control the monetary aggregates and contributed to the volatility of m oney and, perhaps, interest rates. Thus, critics believed a return to CRR w ould reduce the volatility o f m oney and might reduce the volatility o f interest rates as well.' The purpose o f this article is to determine whether the return to CRR has had, so far, any significant im pact on the variability o f m oney and interest rates. The article begins with a concise review o f the arguments bearing on the presumed effects o f the change from Daniel L. Thornton is a senior economist at the Federal Reserve Bank of St. Louis. John G. Schulte provided research assistance. ’See Thornton (1983b) and the references cited there. 26 LRR to CRR on the volatility of m oney or interest rates. The actual behavior o f these variables is then exam ined to see w hether arguments in favor o f the return to CRR have been supported. WHAT CRR IS SUPPOSED TO ACCOMPLISH: THE STANDARD ANALYSIS The rationale for returning to CRR rests primarily on the argument that LRR weakens the contem porane ous link between reserves and deposits o f depository institutions. For example, it was argued that deposi tory institutions w ould have no incentive to curtail their lending activities under LRR because they are not required to hold reserves against the deposits that these activities create until the following week. Conse quently, an increase in loan dem and w ould be more readily transmitted into a change in the money stock in the short run under LRR. At a more formal level, the case for CRR was usually presented in terms o f the supply o f and demand for FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984 Figure l D e m a n d - S id e V a r ia b ilit y u n d e r C R A a n d LR A Figu re 2 S u p p l y - S id e V a r ia b il it y u n d e r C R A a n d LRA money. Within this framework, the proponents o f CRR argued that the m oney supply schedule is flatter un der LRR than under CRR. This is illustrated in figures 1 and 2. Consequently, random variation in the demand for m oney (represented by the shaded area in figure 1) results in more variability in the stock o f money and less variability in the interest rate under LRR, as illus trated in figure 1. Also, random variation in the supply o f money (represented by the shaded areas in figure 2) results in more variability in m oney and interest rates under LRR. Thus, compared with CRR, LRR produces greater variation in the money stock. Whether interest rates are also more variable depends on the relative magnitude o f the variance o f the supply-side and d e mand-side disturbances.2 money and interest rates, at least in the short run. Second, the suggested outcom e is predicated on the assumption that the Federal Reserve is targeting on a reserve aggregate. If the Federal Reserve is not target ing explicitly on m oney or a reserve aggregate in the short run, the variability o f money and interest rates will not necessarily be related to the reserve account ing svstem. There are two reasons w hy the result predicted above need not occur. First, depository institutions' behavior may not be as sensitive to the reserve ac counting system in effect as this analysis suggests. Consequently, the switch from LRR to CRR may not significantly alter the week-to-week variability o f The first view argues that the short-run contem po raneous link between depository institutions’ deci sions to make additional loans and investments and their holdings of reserves need not be close even under a system o f CRR. ' In the short run, depository institu tions can obtain additional reserves by borrowing from the Federal Reserve or holding temporarily fewer excess reserves than they w ould hold otherwise. These factors may be sufficient to accommodate most short-run, week-to-week supply- and demand-side disturbances. Consequently, the slopes o f the money supply schedules under LRR or CRR may be similar. Unless the adoption o f CRR fundamentally changes the way that depository institutions adjust their re serve positions, there may be no dramatic change in the volatility o f money and interest rates in the short run. 2There are other factors, not considered here, that also affect the outcome; see Thornton (1983b) and the references cited there. 3See Thornton (1983b) for a more detailed explanation of the argu ments presented in this section. An Alternative Analysis o f What to Expect under CRR 27 FEDERAL RESERVE BANK OF ST. LOUIS This conjecture is likely to be even more valid given that the new CRR system lengthened the reserve set tlement period from one to two weeks.4 Depository institutions may now make loans early in the account ing period, waiting to settle (through the discount window, the m oney market or changes in excess re serves) toward the end o f the period. By accomm odat ing loan demand at the first part o f the period and settling later in the period, week-to-week variability in m oney and interest rates could be similar under the new system o f CRR and the old system o f LRR.5 The Role o f Federal Reserve Operating Procedures Expectations o f differential effects in the variability o f m oney and interest rates under CRR and LRR are based on the assumption that the Federal Reserve is attempting to hit a monetary target by manipulating a reserve aggregate. If this is not the case, there is little reason to expect differential effects associated with a change in the reserve accounting system. For exam ple, week-to-week variability o f m oney and interest rates are unaffected by the choice o f reserve account ing system under an interest rate targeting procedure.6 This point is important because the Federal Reserve changed operating procedures in the fall o f 1982, about a year and a half before the implementation of CRR. The Federal Open Market Committee (FOMC) follow ed a reserve aggregate targeting procedure that placed greater emphasis on movements in M l as a policy guide from October 6, 1979, to early October 19827 Since then, the FOMC has placed less emphasis on the behavior o f M l in the short run, aiming instead at longer-run monetary and credit aggregate objec tives. This policy has been im plemented in the short 4For a discussion of the new system, see Gilbert and Trebing (1982). For an interesting analysis of the carryover provision of the new system of CRR, see Spindt and Tarhan (1984). 5Some have suggested that the Federal Reserve has no choice but to accommodate this credit expansion, since the additional reserves needed to support the new deposits can only come into the system via the discount window. This argument comes perilously close to saying that the Federal Reserve must accommodate credit demand completely under LRR. This position, however, ignores the dy namics of these long-run adjustments. For another view of this process, see Thornton (1982), p. 29. The short-run money supply schedule is completely flat (interestelastic). Thus, the variability of money would be completely deter mined by the random variation in the demand for money, and this would be unaffected by the reserve accounting system. 7For a discussion of the issues surrounding the decision to deemphasize M1 as an intermediate target, see Thornton (1983a). http://fraser.stlouisfed.org/ 28 Federal Reserve Bank of St. Louis OCTOBER 1984 run through a "flexible nonborrowed-reserves path.’’8 As a result o f this procedural change, the variability of m oney and interest rates immediately before and after the implementation o f CRR may reveal little change. HAS THE VARIABILITY OF MONEY AND INTEREST RATES CHANGED SINCE CRR? Before a comparison o f the weekly variability of money and interest rates for periods before and after the adoption o f CRR can be made, one must decide what measure o f variability to use. The measure used here is the average absolute percentage change (AAPC).9 This is preferable to two more comm only cited measures, the standard deviation and the coef ficient o f variation, as a measure o f the short-run, week-to-week variability that this article is concerned with (see the insert on page 30). Data are presented for various subperiods to reflect both the move from LRR to CRR and the change in Federal Reserve operating procedures. Data for the two weeks im m ediately before and after the im ple mentation o f CRR w ere excluded to guard against the possibility that they w ere contaminated by expecta tions or other problems associated with the im ple mentation o f the new procedure. Results for the m oney stock, M l, are presented in table 1. The AAPC o f seasonally adjusted M l appears to have increased significantly in the 28-week period following the implementation o f CRR, compared with that o f the 28-week period immediately before CRR. The AAPC o f seasonally adjusted M l increased from about 0.13 percent to 0.43 percent, a difference that is significant at the 5 percent level.1 When the most re 0 cent period is com pared with a similar period in 1983, the increase is much smaller; nevertheless, it is statis tically significant." These comparisons, however, are deceptive be cause revised seasonally adjusted data is “ sm oother” than preliminary seasonally adjusted data. Thus, the significant increase in the variability o f seasonally ad- 8Wallich (1984), p. 26. Also, see Solomon (1984). T 9The AAPC is defined as AAPC(X) = (1/(T -1 )) X t=1 ( | X, —X,_, |/X,_,)100. It is a measure of relative variability in that AAPC (kX) = AAPC(X), where k is an arbitrary constant. ’“The t-statistic is 5.20. "The t-statistic is 3.15. OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS Table 1 The Variability of M1 Seasonally Period adjusted 2/27/84 — 9/03/84 7/13/83— 1/18/84 3/02/83 — 9/07/83 Not seasonally adjusted 0.43% 0.13 0.24 1.61% 1.46 1.57 First-published seasonally adjusted 0.44% 0.36 0.44 Table 2 The Variability of M1 and Selected Interest Rates Revised seasonally First-published Federal Treasury1 Commercial1 Period adjusted seasonally adjusted funds bill paper 10/17/79 — 9/29/82 10/06/82 — 9/28/83 0.22% 0.24 .50% .43 4.48% 2.52 3.91% 1.90 4.11% 1.81 'For week ending two days later than date shown. justed M l with the implementation o f CRR may be a statistical artifact o f the seasonal adjustment re vision.1 2 This is investigated by a comparison o f the AAPC over the three periods using either not seasonally ad justed or first-published seasonally adjusted data. If the increased variability is primarily the result o f the seasonal adjustment revision rather than the change in the reserve accounting system, then the AAPC for the first-published or not seasonally adjusted M l should be essentially the same over these periods.'3 Likewise, a comparison of not seasonally adjusted data for the 28-week period since the implementation of CRR and the corresponding period a year earlier should reveal no change in the AAPC. The data are consistent with both o f these conditions. Thus, there appears to be no change in the variability o f M l be tween the pre- and post-CRR periods. It is indeterminant, however, w hether this result stems from depository institutions not changing their 12For example, see Hein and Ott (1983). '3A comparison of these data is perhaps more relevant because these are the figures that economic agents and policymakers use to make their decisions. behavior following the enactment o f CRR or from a change in the operating procedure in the fall o f 1982. In order to determine which explanation is more con sistent with the facts, the AAPC was calculated for M l and three interest rates — the federal funds rate, the three-month Treasury bill rate and the commercial paper rate — for the three-year period o f reserve ag gregate targeting (October 17, 1979, to September 29, 1982) and for the year immediately following the change in the Federal Reserve’s operating procedure (October 6, 1982, to September 28, 1983). These results are presented in table 2. The data indicate a decline in the AAPC for both revised and first-published M l after the fall o f 1982; however, this decline is not statistically significant at the 5 percent level.'4 Thus, it appears there was no significant change in the week-to-week variability o f M l following the change in the operating procedures. The AAPCs for all three interest rates, however, de crease significantly after the fall o f 1982. Thus, it ap pears that the change in operating procedure had some impact on the behavior o f interest rates. Hence, 14The relevant t-statistics for first-published and not seasonally ad justed data are 0.91 and 0.15, respectively. 29 The Limitations of Two Common Measures of Variability Both the standard deviation (SD) and the coef ficient o f variation (CV) measure the variability of the data relative to an average. For the SD the aver age is the mean of the raw data; for the CV the mean is unity, that is, the average o f the raw data divided by the mean. Thus, the SD is a measure o f absolute variability and the CV is a measure o f relative varia bility.1 Because both o f these statistics average squared deviations from their respective means, they may give relatively small weight to large weekly changes and relatively large weight to small weekly changes. T 'The SD = ( 2 (X, - X)2/(T -1 ))'« and the t= 1 T CV = ( 2 (X;-X*)2/(T-1))’«, t=1 where X is the mean of the raw series, *T i.e., X = 2 X/T, and X? = X/X, t=1 T so that X* = 2 ((X/TJ/X) = 1. Furthermore, while the SD t=1 depends on the scale of the data, the CV does not; i.e., the SD(kX) = kSD(X), while the CV(kX) = CV(X), where k is a constant. it is possible that the lack o f a significant change in the variability o f money after the implementation o f CRR was due to the earlier change in operating procedures. Unfortunately, these results cannot rule out the possi bility that the short-run reserve management behavior by depository institutions is simply insensitive to changes in the reserve accounting system.1 5 The Variability o f Interest Rates The AAPC was calculated for the federal funds, the three-month Treasuiy bill and the 30-day commercial paper rate for comparable 28-week periods before and after the implementation o f CRR. The results, which are reported in table 3, indicate a slight increase in the ,5Neither of these, however, rules out other potential gains from CRR See Goodfriend (1984). 30 This is illustrated in the accompanying charts, which show the level o f seasonally adjusted M l, by itself and relative to its mean level for the 28-week period following the implementation o f CRR. Charts 1 and 2 show that the largest (in absolute and relative terms) one-week change in M l oc curred on May 7, w hen the m oney supply increased by $5.3 billion. Because the absolute and relative (i.e., mean-adjusted) levels are only slightly above their respective means for the period, their respec tive contributions to the SD and the CV are small. Moreover, the smallest one-week change in M l oc curred on March 19. Because the levels are further from their mean, their contribution to the SD and the CV is larger than that o f the largest change. The average absolute percentage change (AAPC) is a measure o f relative variability that avoids the problem o f inappropriate weighting. Thus, it is a better measure o f the week-to-week variability with which this article is concerned.2 2Of course, if the growth rate is constant across time periods, then the AAPC will not necessarily be preferable to the SD of the growth rate. If there is variable growth or short periods of rapid growth preceded and followed by periods of approximately equal growth, as in the charts above, then the AAPC is likely to be a better measure of week-to-week variability. If the growth rates were constant over these periods, however, the CV of the growth rate might be a useful measure. AAPC for the federal funds rate for periods im m edi ately before and after the implementation o f CRR and a slight decrease for both the Treasury bill rate and the commercial paper rate; however, none o f these were Table 3 The Variability of Selected Interest Rates Federal1 Treasury Commercial Period funds bills paper 2/24/84 — 8/31/84 7/15/83 — 1/20/84 3/04/83 — 9/09/83 2.55% 2.33 1.99 1.13% 1.21 1.58 'For week ending two days earlier than date shown. 1.13% 1.27 1.56 OCTOBER 1984 FEDERAL RESERVE BANK OF ST. LOUIS C hart 1 Levels of M l FEB. MAR. APR. M AY JUNE JULY AUG . JUNE JULY AUG. SEPT. 1984 C hart 2 Ratio of M l to Sa m p le M e a n FEB. MAR. APR. M AY SEPT. 1984 31 FEDERAL RESERVE BANK OF ST. LOUIS P.O. BOX 442 ST. LOUIS, MISSOURI 63166 Subscriber: Please include address label with subscription inquiries or address changes. significant at the 5 percent level."1 Thus, the results suggest that the implementation o f CRR had little ef fect on the variability o f money or interest rates. The significant reduction in interest rate variability ap pears to correspond with the earlier change in operat ing procedures, not with the implementation o f CRR. CONCLUSIONS The purpose o f this article was to take an early look at the effect o f the Federal Reserve’s new system of contemporaneous reserve accounting on the variabil ity o f m oney and interest rates. Although the CRR system was adopted with the expectation that it w ould reduce the variability o f m oney under a reserve targeting procedure, it may not have that effect for two reasons. First, depositoiy institutions may behave in ways that reduce the short-run contemporaneous link between aggregate reserves and deposits even under CRR. Second, the change in operating procedures in October 1982 may have preem pted any potential benefits from the switch in accounting systems. The data for M l indicate that there was no signifi cant change in week-to-week variability following ei ther the change in operating procedure in October 1982 or the adoption o f CRR. The variability o f shortrun interest rates declined significantly after the change in operating procedures, but has been unaf fected by the im plem entation o f CRR. Thus, the change in the reserve accounting procedure had no ,6The relevant t-statistics for a comparison of periods immediately before and after the implementation of CRR for the federal funds rate, the three-month Treasury bill rate and the commercial paper rate are 0.30, 0.39 and 0.53, respectively. http://fraser.stlouisfed.org/ 32 Federal Reserve Bank of St. Louis statistically significant impact on the variability of m oney either because depository institutions’ lending and investment decisions are insensitive to the reserve accounting system, or because o f the change in oper ating procedures that occurred some year and a half earlier. Consequently, CRR’s potential usefulness in reducing the variability o f m oney can be determined for certain only if the Federal Reserve implements a strict reserve aggregate or monetary base target. REFERENCES Gilbert, R. Alton, and Michael E. Trebing. "The New System of Contemporaneous Reserve Requirements,” this Review (Decem ber 1982), pp. 3-7. Goodfriend, Marvin. “The Promises and Pitfalls of Contemporane ous Reserve Requirements for the Implementation of Monetary Policy," Federal Reserve Bank of Richmond Economic Review (May/June 1984), pp. 3-12. Hein, Scott E., and Mack Ott. "Seasonally Adjusting Money: Proce dures, Problems, Proposals," this Review (November 1983), pp. 16-25. Spindt, Paul A., and Vefa Tarhan. “Bank Reserve Adjustment Pro cess and the Use of Reserve Carryover as a Reserve Manage ment Tool: A Microeconometric Approach,” Journal of Banking and Finance (March 1984), pp. 5-20. Solomon, Anthony M. “Unresolved Issues in Monetary Policy,” Federal Reserve Bank of New York Quarterly Review (Spring 1984), pp. 1-6. Thornton, Daniel L. “Simple Analytics of the Money Supply Process and Monetary Control,” this Review (October 1982), pp. 22-39. _________ “The FOMCin 1982: De-emphasizing M1," this Review (June/July 1983a), pp. 26-35. ________. “Lagged and Contemporaneous Reserve Accounting: An Alternative View,” this Review (November 1983b), pp. 26-33. Wallich, Henry C. “Recent Techniques of Monetary Policy,” Fed eral Reserve Bank of Kansas City Economic Review (May 1984), pp. 21-30.