503Applied Macroeconomics

Chapter 2. The Behavior of Interest Rates2004 Kevin D. Hoover

Applied Intermediate Macroeconomics

Prof. M. El-SakkaProf. M. El-SakkaDept of EconomicsDept of Economics

Kuwait UniversityKuwait University

What can you figure out lookingat this graph. Is there a trend in the behavior of different rates of interest

• Five Questions About Interest RatesFive Questions About Interest Rates

1.1. First, why do interest rates tend to move together?First, why do interest rates tend to move together?

2.2. Second, why do they move only imperfectly together?Second, why do they move only imperfectly together?

3.3. Third, why do shorter maturity assets typically, but not uniformly, Third, why do shorter maturity assets typically, but not uniformly, yield lower rates of interest than longer maturity assets? yield lower rates of interest than longer maturity assets?

4.4. Fourth, why at each maturity do government assets yield lower Fourth, why at each maturity do government assets yield lower rates of interest than private sector assets?rates of interest than private sector assets?

5.5. Fifth, what determines the overall level of interest rates?Fifth, what determines the overall level of interest rates?

This chapter aims to answer these five questions.This chapter aims to answer these five questions.

• Similarity and ReplacementSimilarity and Replacement

• To one degree or another, all financial instruments are To one degree or another, all financial instruments are similarsimilar, , but generally they are but generally they are not identicalnot identical. Each is issued by a . Each is issued by a different borrower with different borrower with different chances different chances of paying back the of paying back the loan, each provides the lender with a loan, each provides the lender with a different stream different stream of of incomeincome, and each may have its , and each may have its own special characteristicsown special characteristics..

• Two financial assets are Two financial assets are SUBSTITUTESSUBSTITUTES when a when a fallfall in the yield in the yield or interest rate on the first asset (that is, a rise in its price) or interest rate on the first asset (that is, a rise in its price) reducesreduces the demand for that asset and the demand for that asset and raisesraises the demand for the the demand for the other asset.other asset.

• Supply and Demand of Financial InstrumentsSupply and Demand of Financial Instruments

• Consider two similar corporate bonds – say, bonds issued by Consider two similar corporate bonds – say, bonds issued by Proctor and Gamble Proctor and Gamble (P&G) and by (P&G) and by CloroxClorox. What determines . What determines their yields?their yields?

• Borrowers use funds and Borrowers use funds and supply the financial instrumentsupply the financial instrument; ; lenders are the source of funds and lenders are the source of funds and demand the financial demand the financial instrument. instrument. In the case of the two bonds, P&G and Clorox are In the case of the two bonds, P&G and Clorox are the the supplierssuppliers, and the public are the , and the public are the demandersdemanders..

• Reaching Equilibrium in a Financial MarketReaching Equilibrium in a Financial Market

• The interest rate is determined where supply equals demand in The interest rate is determined where supply equals demand in each market and the rate is initially shown the same (each market and the rate is initially shown the same (rr11) in each ) in each

market on the assumption that P&G bonds and Clorox bonds market on the assumption that P&G bonds and Clorox bonds are perfect substitutes.are perfect substitutes.

• If P&GIf P&G decides to fund a major investment project through decides to fund a major investment project through issuing new bonds. At each rate of interest its desire for funds issuing new bonds. At each rate of interest its desire for funds will be higher, shifting its supply curve rightward (shift 1). All will be higher, shifting its supply curve rightward (shift 1). All other things equal, the equilibrium would move from point other things equal, the equilibrium would move from point AA to point to point BB, and the interest rate would rise from , and the interest rate would rise from rr11 to to rr22. The . The

reason is that since more bonds are available, the only way the reason is that since more bonds are available, the only way the public can be public can be enticed to hold them is for them to become enticed to hold them is for them to become cheaper. As their price falls, their yields rise.cheaper. As their price falls, their yields rise.

• Notice that with the market for P&GNotice that with the market for P&G bonds at point bonds at point BB while while the market for Clorox bonds is still at point the market for Clorox bonds is still at point A’A’,, the yield on the the yield on the P&GP&G bonds is higher than the yield on Clorox bonds. Since bonds is higher than the yield on Clorox bonds. Since both bonds are assumed to be practically both bonds are assumed to be practically identicalidentical in the eyes in the eyes of the public, why would people remain content to hold lower of the public, why would people remain content to hold lower yielding Clorox bonds?yielding Clorox bonds?

• They would not. Some people would sell their (expensive) They would not. Some people would sell their (expensive) Clorox bonds and use the proceeds to buy the (now cheaper) Clorox bonds and use the proceeds to buy the (now cheaper) P&GP&G bonds. As a result funds would leave the Clorox bond bonds. As a result funds would leave the Clorox bond market and enter the P&Gmarket and enter the P&G bond market. At each level of bond market. At each level of interest rates, the demand for Clorox bonds would fall. The interest rates, the demand for Clorox bonds would fall. The demand curve would shift leftward in the right-hand panel.demand curve would shift leftward in the right-hand panel.

• More P&GMore P&G bonds are outstanding at the new equilibrium bonds are outstanding at the new equilibrium ((BP&G BP&G increased to increased to BB′′P&G). There are two effects. First, the P&G). There are two effects. First, the rise in interest rates encouraged the rise in interest rates encouraged the public to buy more bonds. public to buy more bonds. Second, the incipient difference between the yields in the two Second, the incipient difference between the yields in the two markets (markets (rr22 > r > r11) encouraged the public to shift from Clorox to ) encouraged the public to shift from Clorox to

P&GP&G bonds bonds until the yields were brought back into equality (until the yields were brought back into equality (B B Clorox fell to Clorox B′ and both bonds Clorox fell to Clorox B′ and both bonds yield yield rr33). ).

• There are fewer Clorox bonds at the new equilibrium. Because of There are fewer Clorox bonds at the new equilibrium. Because of the higher the higher rates, Clorox prefers less debt and so would lower it rates, Clorox prefers less debt and so would lower it by not rolling over bonds that come mature and, even, by by not rolling over bonds that come mature and, even, by buying back outstanding bonds, which are now cheaper.buying back outstanding bonds, which are now cheaper.

• ArbitrageArbitrage

• The The simultaneoussimultaneous buying and selling of buying and selling of closelyclosely related goods or related goods or financial instruments in different markets to take advantage of financial instruments in different markets to take advantage of price differentialsprice differentials..

• Actual financial markets are more complicated than the simple Actual financial markets are more complicated than the simple example of the two bonds. In reality there are many financial example of the two bonds. In reality there are many financial assets. They are almost all substitutes – sometimes extremely assets. They are almost all substitutes – sometimes extremely close substitutes. As a result, what happens in any market close substitutes. As a result, what happens in any market affects every market to some degree. affects every market to some degree.

• The closer substitutes two assets are, the The closer substitutes two assets are, the closer closer arbitragearbitrage drives drives their their yieldsyields..

• EFFICIENT MARKETS: Inside and Outside Views of EFFICIENT MARKETS: Inside and Outside Views of Financial MarketsFinancial Markets

• The effectiveness of arbitrage allows us to see financial markets The effectiveness of arbitrage allows us to see financial markets from two perspectives. The first views the market from from two perspectives. The first views the market from insideinside in terms of process. Highly motivated traders look for fleeting in terms of process. Highly motivated traders look for fleeting opportunities and exploit them quickly before they disappear.opportunities and exploit them quickly before they disappear.

• The market can also be viewed from the The market can also be viewed from the outsideoutside in terms of in terms of outcomes. Since arbitrage is highly effective, it is reasonable outcomes. Since arbitrage is highly effective, it is reasonable for many purposes to assume that it is complete. All profit for many purposes to assume that it is complete. All profit opportunities are opportunities are competed away so quickly competed away so quickly that we can assume that we can assume that they do that they do not exist at allnot exist at all. .

• From this second perspective, financial markets can be thought From this second perspective, financial markets can be thought of as highly of as highly efficientefficient processors of information. processors of information.

• The Efficient Markets HypothesisThe Efficient Markets Hypothesis

• This view of the financial market as a highly effective processor This view of the financial market as a highly effective processor of information is the critical element of the of information is the critical element of the EFFICIENT-EFFICIENT-MARKETS HYPOTHESISMARKETS HYPOTHESIS, which states , which states there are no there are no systematically systematically exploitable arbitrage opportunitiesexploitable arbitrage opportunities based on based on information that is information that is publicly available publicly available to financial markets. to financial markets.

• Profiting from truly private information is consistent with the Profiting from truly private information is consistent with the efficient-markets hypothesis. Similarly, the efficient-markets efficient-markets hypothesis. Similarly, the efficient-markets hypothesis is consistent with some people hypothesis is consistent with some people beatingbeating the market the market and making enormous profits on financial trading. It does not and making enormous profits on financial trading. It does not rule out luck.rule out luck.

• Many traders, managers of mutual funds, and financial Many traders, managers of mutual funds, and financial advisers believe that they can systematically advisers believe that they can systematically outperformoutperform the the market and can cite evidence of successive years of above market and can cite evidence of successive years of above average returns. average returns.

• How could we tell if this were How could we tell if this were skill or luckskill or luck? For any individual, ? For any individual, it is impossible. The real test is: it is impossible. The real test is: will the luck continuewill the luck continue??

• One test would be to divide the market into One test would be to divide the market into above-averageabove-average and and below-averagebelow-average performers for, say, one year and then to see performers for, say, one year and then to see whether the above-average continue to beat the average in the whether the above-average continue to beat the average in the next year. Many careful studies have shown that an above-next year. Many careful studies have shown that an above-average performance one year average performance one year does not does not predict an above-predict an above-average performance the next year.average performance the next year.

• The efficient-markets hypothesis does not say that no one can The efficient-markets hypothesis does not say that no one can make their living from such arbitrage activity. Rather, it says make their living from such arbitrage activity. Rather, it says that the returns to such activity that the returns to such activity ccannot on average exceed annot on average exceed the the amount that makes it just worth the tradersamount that makes it just worth the traders’ ’ while to continue it.while to continue it.

• The efficient-markets hypothesis is the The efficient-markets hypothesis is the dominantdominant theory of the theory of the functioning of financial markets, but there are many people functioning of financial markets, but there are many people who who do not believe do not believe it. They point to people who have made it. They point to people who have made millions, to statistical evidence of millions, to statistical evidence of systematic unexploited profit systematic unexploited profit opportunities, and to opportunities, and to psychological theories of herd behaviorpsychological theories of herd behavior..

• Two AnswersTwo Answers

• We now have initial answers to the first two questions posed We now have initial answers to the first two questions posed above:above:

1.1. Interest rates tend to move together because financial assets Interest rates tend to move together because financial assets are are substitutes substitutes and profit-seeking traders engage in effective and profit-seeking traders engage in effective arbitragearbitrage;;

2.2. Interest rates do not move perfectly together because financial Interest rates do not move perfectly together because financial assets are not assets are not perfect substitutesperfect substitutes..

• Imperfect substitutability can be regarded as just a name for Imperfect substitutability can be regarded as just a name for the fact that arbitrage is the fact that arbitrage is ineffectiveineffective in removing all differences in removing all differences in yields. It remains to explain why it is ineffective.in yields. It remains to explain why it is ineffective.

• Risk:Risk:

• Risk is a complex business. We focus on two key elements: Risk is a complex business. We focus on two key elements: default risk and price or interest-rate risk.default risk and price or interest-rate risk.

• DEFAULT RISKDEFAULT RISK

• Risk and ReturnRisk and Return

• Those who borrow funds through issuing a bond or taking out Those who borrow funds through issuing a bond or taking out a loan might go a loan might go bankruptbankrupt. In that case, the lender or bond . In that case, the lender or bond holders face holders face DEFAULT RISKDEFAULT RISK: they might not get paid.: they might not get paid.

• The chances of default on any particular The chances of default on any particular bondbond are typically are typically quite low. The chances of default on quite low. The chances of default on personal loans personal loans are are generally much higher. Only a fool would choose a bond with a generally much higher. Only a fool would choose a bond with a high risk of default over one with the same yield and a lower high risk of default over one with the same yield and a lower risk of default.risk of default.

• If the high-risk bond were If the high-risk bond were cheap enough cheap enough – that is, if its yield – that is, if its yield were enough larger than that on the were enough larger than that on the low risk bond low risk bond – it might – it might become worthwhile to become worthwhile to hold ithold it. The additional yield or risk . The additional yield or risk premium compensates for the higher risk. The risk premium premium compensates for the higher risk. The risk premium can be thought of as the can be thought of as the price of riskprice of risk. .

• Federal Government BondsFederal Government Bonds

• JunkJunk bonds stand at one extreme of the risk spectrum. U.S. bonds stand at one extreme of the risk spectrum. U.S. federalfederal government bonds stand at the other. They are virtually government bonds stand at the other. They are virtually free of default risk. Governments have a monopoly on taxation free of default risk. Governments have a monopoly on taxation and, therefore, and, therefore, a ready source of funds a ready source of funds to repay their debt.to repay their debt.

• Effectively a government agency – can create as many dollars Effectively a government agency – can create as many dollars as necessary to fund its debt, it never has as necessary to fund its debt, it never has any reason to defaultany reason to default. . The key to its freedom from default risk is that federal The key to its freedom from default risk is that federal government debt is denominated in dollars, which are within government debt is denominated in dollars, which are within its controlits control..

• Many developing countries find that they cannot borrow on Many developing countries find that they cannot borrow on international markets in their own currencies. Mexico, for international markets in their own currencies. Mexico, for instance, does not find it easy to sell peso-denominated bonds instance, does not find it easy to sell peso-denominated bonds to foreigners, who usually prefer dollars, yen, or euros. Since to foreigners, who usually prefer dollars, yen, or euros. Since Mexico Mexico cannot print dollarscannot print dollars, its dollar-denominated bonds are , its dollar-denominated bonds are just as subject to default risk as a corporate or municipal bond just as subject to default risk as a corporate or municipal bond in the United Statesin the United States

• Rating RiskRating Risk

• Banks try to screen their personal and corporate borrowers to Banks try to screen their personal and corporate borrowers to limit defaultlimit default. This is the reason that banks require borrowers to . This is the reason that banks require borrowers to provide extensive information on their assets and liabilities and provide extensive information on their assets and liabilities and why they check borrowers’ payment histories with credit why they check borrowers’ payment histories with credit information agencies such as Trans Union, Equifax, and information agencies such as Trans Union, Equifax, and Experian. Riskier customers pay Experian. Riskier customers pay higher interest rates higher interest rates on loans.on loans.

• Firms and government agencies who wish to sell bonds on Firms and government agencies who wish to sell bonds on organized markets are able to do so effectively only if they pay organized markets are able to do so effectively only if they pay a a bond rating agency bond rating agency to rank the riskiness of their debt.to rank the riskiness of their debt.

• These agencies (the three most important are These agencies (the three most important are Moody’s, Moody’s, Standard & Poor’s , and FitchStandard & Poor’s , and Fitch) use information – partly ) use information – partly gathered from the firms themselves – to assign ratings similar gathered from the firms themselves – to assign ratings similar to letter grades to letter grades

• Bonds with ratings in the Bonds with ratings in the upper-half upper-half of the rating scale of the rating scale (relatively (relatively low default risklow default risk) are ) are referredreferred to as investment grade to as investment grade and those in the and those in the lower half lower half ((high default riskhigh default risk) as speculative. ) as speculative. The term The term junk bond junk bond became familiar starting in the 1980s. became familiar starting in the 1980s. Although it sounds like a synonym for “worthless” junk bonds Although it sounds like a synonym for “worthless” junk bonds are just bonds are just bonds below investment grade.below investment grade.

• PRICE OR INTEREST-RATE RISKPRICE OR INTEREST-RATE RISK

• We learned that the price or market value of a bond moves We learned that the price or market value of a bond moves inverselyinversely with its yield. The PRICE (or INTEREST-RATE) with its yield. The PRICE (or INTEREST-RATE) RISK RISK of holding a bond is the risk of capital gains or losses as a of holding a bond is the risk of capital gains or losses as a result of changes in interest rates between the point of purchase result of changes in interest rates between the point of purchase and the point of saleand the point of sale. . Price risk is greater for debt of greater Price risk is greater for debt of greater maturity.maturity.

• All bondsAll bonds, including federal government bonds, face price risk. , including federal government bonds, face price risk. Price risk explains at least some of the Price risk explains at least some of the difference in yields difference in yields for for bonds of different maturities. Long bonds face greater price bonds of different maturities. Long bonds face greater price risk and, therefore, must earn a risk premium compared to risk and, therefore, must earn a risk premium compared to short bonds. The short bonds. The longer the bondlonger the bond, the , the higherhigher the risk premium. the risk premium.

• Risk premia – whether they compensate for default risk or for Risk premia – whether they compensate for default risk or for price risk – ensure that the returns to holding risky price risk – ensure that the returns to holding risky assets are assets are higher than the returns to holding safer assetshigher than the returns to holding safer assets..

• If one is willing to hold a portfolio that is If one is willing to hold a portfolio that is more risky more risky than the than the average market portfolio, then one can earn returns average market portfolio, then one can earn returns systematically systematically higherhigher than those enjoyed by the market in than those enjoyed by the market in general.general.

• Such returns do not Such returns do not violate the efficient-markets hypothesisviolate the efficient-markets hypothesis. . They are not the result of unexploited arbitrage opportunities. They are not the result of unexploited arbitrage opportunities. Rather they reflect the “price” of risk.Rather they reflect the “price” of risk.

• The Term Structure of Interest RatesThe Term Structure of Interest Rates

• THE RELATIONSHIP OF INTEREST RATES OF DIFFERENT THE RELATIONSHIP OF INTEREST RATES OF DIFFERENT MATURITIESMATURITIES

• The smooth line connecting the various points on the graph is The smooth line connecting the various points on the graph is known as a known as a YIELD CURVEYIELD CURVE. The fact that the 10-year bond . The fact that the 10-year bond rate is above the 3-month Treasury bill rate and, more rate is above the 3-month Treasury bill rate and, more generally, that longer rates exceed shorter rates is reflected in generally, that longer rates exceed shorter rates is reflected in the fact that the the fact that the yieldyield curve slopes upcurve slopes up. The relationship among . The relationship among the returns on bonds of different maturities is called the the returns on bonds of different maturities is called the TERMTERM STRUCTURE OF INTEREST RATESSTRUCTURE OF INTEREST RATES. The yield curve is one, . The yield curve is one, particularly useful, way of visualizing the term structureparticularly useful, way of visualizing the term structure

THE EXPECTATIONS THEORY OF THE TERM STRUCTURE.

• Arbitrage Across Different Maturities Arbitrage Across Different Maturities

• How might we account for the term structure of interest rates? How might we account for the term structure of interest rates? What explains the shape of the yield curve?What explains the shape of the yield curve?

• In general, the yield on an In general, the yield on an m-period bond over its life should m-period bond over its life should equal the expected yields of m 1-period bondsequal the expected yields of m 1-period bonds::

• Solving for Solving for rrmm,,tt,,

• In words: the gross yield on an In words: the gross yield on an m-period bond (that is, 1 + rm,t ) m-period bond (that is, 1 + rm,t ) is the geometric is the geometric average of the gross yield on the average of the gross yield on the m current and m current and expected future 1-period bonds.expected future 1-period bonds.

• Equation (11.2) can be simplified for easier calculation. Taking Equation (11.2) can be simplified for easier calculation. Taking logarithms of both sides and recalling that log(1 + logarithms of both sides and recalling that log(1 + x) ≈ x, when x) ≈ x, when x is x is small, equation (11.1) can be written assmall, equation (11.1) can be written as

• oror

• THE ROLE OF RISKTHE ROLE OF RISK

• price risk is greater the longer the maturity of a bond and that price risk is greater the longer the maturity of a bond and that generally markets require higher returns, a term premium (a generally markets require higher returns, a term premium (a kind of risk premium), to compensate for higher risk. The term kind of risk premium), to compensate for higher risk. The term premium is shown as a function of maturity since longer premium is shown as a function of maturity since longer maturity bonds face greater price risk. We can therefore maturity bonds face greater price risk. We can therefore modify the above equation to add in the term premium:modify the above equation to add in the term premium:

Inflation and Interest Rates

• THE EFFECT OF INFLATION ON THE SUPPLY AND THE EFFECT OF INFLATION ON THE SUPPLY AND DEMAND FOR BONDSDEMAND FOR BONDS

• market rate can be decomposed into the sum of a market rate can be decomposed into the sum of a real rate real rate of of interest and the rate of interest and the rate of inflationinflation. Since inflation rates have . Since inflation rates have varied considerably over time, it would be interesting to know varied considerably over time, it would be interesting to know how that variation might have affected interest rates. At first how that variation might have affected interest rates. At first blush, you might think that the question is answered already in blush, you might think that the question is answered already in knowing the decompositionknowing the decomposition

r = rr + pˆe.r = rr + pˆe.

• An increase in expected inflation An increase in expected inflation increasesincreases the market rate of the market rate of interest. But that moves too quickly. We cannot know how any interest. But that moves too quickly. We cannot know how any change in inflation affects nominal rates of interest until we change in inflation affects nominal rates of interest until we know how it affects real rates of interest.know how it affects real rates of interest.

• The key point is that rational people should not care about the The key point is that rational people should not care about the nominalnominal values of prices or interest rates. They should care values of prices or interest rates. They should care about the about the real valuesreal values, what their money will actually buy or , what their money will actually buy or what their savings will earnwhat their savings will earn

• What happens if the expected rate of inflation increases to What happens if the expected rate of inflation increases to pˆe pˆe = 4%? Since = 4%? Since the users of funds care about the users of funds care about real ratesreal rates, they , they should be should be willing to supply exactly the same amounts willing to supply exactly the same amounts at the at the same real rates. But now each real rate corresponds to a higher same real rates. But now each real rate corresponds to a higher nominal rate. A nominal rate of 8% (= nominal rate. A nominal rate of 8% (= rr + pˆe = 4 + 4) rr + pˆe = 4 + 4) corresponds to a real rate of 4corresponds to a real rate of 4%, and a nominal rate of 6 %, and a nominal rate of 6 percent corresponds to a real rate of 2 percent.percent corresponds to a real rate of 2 percent.

• The whole The whole supply curve, then, must shift vertically supply curve, then, must shift vertically upward by upward by exactly the change in the exactly the change in the expected rate of inflation expected rate of inflation (that is, by 3 (that is, by 3 percentage points), so that it lies parallel to original curve. At percentage points), so that it lies parallel to original curve. At point E the nominal interest rate is higher than at point A, but point E the nominal interest rate is higher than at point A, but since the real rate has not changed, the supply of bonds since the real rate has not changed, the supply of bonds remains at remains at BB00. Similarly, the supply of . Similarly, the supply of bonds remains bonds remains

unchanged between points C and F. The issuer of the bond is unchanged between points C and F. The issuer of the bond is willing to pay higher rates of interest for the same funds, willing to pay higher rates of interest for the same funds, because he can pay them back with money that is losing its because he can pay them back with money that is losing its value faster because of the higher inflation.value faster because of the higher inflation.

• An exactly parallel argument suggests that the demand curve An exactly parallel argument suggests that the demand curve should also shift vertically at every point by an amount equal should also shift vertically at every point by an amount equal to the change in the rate of inflation. The lender must charge to the change in the rate of inflation. The lender must charge higher rates of interest for the same loan in order to ensure higher rates of interest for the same loan in order to ensure that the real return remains the same in the face of money that that the real return remains the same in the face of money that is losing its value faster.is losing its value faster.

• The combined effect of these two adaptations to higher rates of The combined effect of these two adaptations to higher rates of inflation is that both the supply and demand curves shift inflation is that both the supply and demand curves shift vertically by vertically by the same amountthe same amount, so that that the equilibrium , so that that the equilibrium (right-hand panel), which had been at 4 percent (point G), also (right-hand panel), which had been at 4 percent (point G), also shifts vertically to 7 %(point H), and the equilibrium quantity shifts vertically to 7 %(point H), and the equilibrium quantity of bonds (of bonds (B*) remains B*) remains constant.constant.

THE FISHER EFFECT AND THE FISHER HYPOTHESIS

• The relationship between inflation rates and interest rates is The relationship between inflation rates and interest rates is known as the known as the Fisher effectFisher effect, in honor of the great American , in honor of the great American economist economist Irving Fisher Irving Fisher (1867-1947) who emphasized it in his (1867-1947) who emphasized it in his analysis of interest rates. It may be useful to distinguish the analysis of interest rates. It may be useful to distinguish the Fisher effect from the Fisher hypothesis.Fisher effect from the Fisher hypothesis.

• The FISHER EFFECT The FISHER EFFECT can be defined as can be defined as a point-for-point a point-for-point increase in the market rate of interest that results, ceteris increase in the market rate of interest that results, ceteris paribus, from an increase in the expected rate of inflationparibus, from an increase in the expected rate of inflation. The . The ceteris paribus clause is important. The Fisher effect is ceteris paribus clause is important. The Fisher effect is a a theoretical claimtheoretical claim that may be difficult to observe in the world that may be difficult to observe in the world because other things are not always equal.because other things are not always equal.

• The FISHER HYPOTHESIS can be defined as The FISHER HYPOTHESIS can be defined as the empirical the empirical phenomenon in which a change in market rates of interest is phenomenon in which a change in market rates of interest is associated approximately point for point with a change in the associated approximately point for point with a change in the actual rate of inflationactual rate of inflation. . The Fisher hypothesis is clearly The Fisher hypothesis is clearly true to true to a first approximationa first approximation. .

• The Fisher hypothesis – as Fisher himself was well aware – The Fisher hypothesis – as Fisher himself was well aware – does does notnot hold exactlyhold exactly. One reason is that no inflation measure, . One reason is that no inflation measure, such as the CPI, represents such as the CPI, represents exactly the bundle exactly the bundle that is relevant that is relevant to the players in financial markets. Borrowers and lenders to the players in financial markets. Borrowers and lenders might have might have systematically different consumption bundlessystematically different consumption bundles. . Indeed, the relevant bundles need not be the same for all Indeed, the relevant bundles need not be the same for all borrowers or all lenders.borrowers or all lenders.

• A second reason is that A second reason is that taxestaxes are levied on nominal interest are levied on nominal interest payments. Higher interest rates, even if they are merely payments. Higher interest rates, even if they are merely compensation for higher inflation rates, compensation for higher inflation rates, generate higher tax generate higher tax liabilitiesliabilities. Lenders would, therefore, . Lenders would, therefore, require an extra require an extra increase increase in nominal interest rates to compensate for the loss of in nominal interest rates to compensate for the loss of purchasing power due to inflation-induced tax-rate increases.purchasing power due to inflation-induced tax-rate increases.

• Finally, and probably most important, there is no reason to Finally, and probably most important, there is no reason to believe that expectations of future believe that expectations of future inflationinflation are are formedformed perfectlyperfectly or are captured by the or are captured by the past behavior of inflationpast behavior of inflation. It . It may take some time to adjust expectations to an unexpected may take some time to adjust expectations to an unexpected increase or decrease in actual inflation. During the adjustment increase or decrease in actual inflation. During the adjustment period, period, realreal, rather than nominal, rates , rather than nominal, rates would be affectedwould be affected..

• The Level of Real Interest RatesThe Level of Real Interest Rates

• If we had a starting place (that is if we knew one real rate of If we had a starting place (that is if we knew one real rate of interest) we should be able in principle to use information interest) we should be able in principle to use information about the about the maturity, coupon structure, risk, tax rates, and maturity, coupon structure, risk, tax rates, and expected inflation ratesexpected inflation rates to deduce the rates on all other bonds. to deduce the rates on all other bonds. But where do we find the starting place – the one real rate? Or, But where do we find the starting place – the one real rate? Or, what determines the level of the real yield what determines the level of the real yield on any particular on any particular financial asset? There are two answers to this question, financial asset? There are two answers to this question, depending on whether we concentrate on depending on whether we concentrate on short rates or long short rates or long rates.rates.

• MONETARY POLICY AND SHORT RATESMONETARY POLICY AND SHORT RATES

• At the short end of the market, the interaction of monetary At the short end of the market, the interaction of monetary policy and expected inflation rates determines the real rate policy and expected inflation rates determines the real rate Central banks Central banks typically buy and sell short-term assets (largely typically buy and sell short-term assets (largely Treasury bills) on the open market. When the central bank Treasury bills) on the open market. When the central bank buys, it pays by crediting funds to the accounts that buys, it pays by crediting funds to the accounts that commercial banks hold with it. When it sells, it deducts funds commercial banks hold with it. When it sells, it deducts funds from these accounts, eliminating from these accounts, eliminating reservesreserves. In the United States, . In the United States, these these reserves are known reserves are known to financial markets as to financial markets as Federal fundsFederal funds..

• Commercial banks are required to Commercial banks are required to hold reserves hold reserves in a certain in a certain proportion to their deposit liabilities. There is an active proportion to their deposit liabilities. There is an active overnight market, the overnight market, the Federal funds marketFederal funds market, in which banks , in which banks with an with an excessexcess of reserves over their requirements lend to of reserves over their requirements lend to banks with a banks with a shortageshortage. The . The Federal Reserve setFederal Reserve set the interest the interest rate in this market, known as the rate in this market, known as the Federal funds rateFederal funds rate, by raising , by raising or lowering the stock of available reserves through purchases or lowering the stock of available reserves through purchases or sales of short-term financial assets. Monetary policy today or sales of short-term financial assets. Monetary policy today largely consists of setting a target for the largely consists of setting a target for the Federal funds rateFederal funds rate..

ARBITRAGE TO REAL RETURNS

• At At longerlonger maturities, maturities, bonds are substitutes with shares bonds are substitutes with shares in in corporations. If the corporations. If the real returns on bondsreal returns on bonds, after accounting for , after accounting for risk, are greater than the returns on risk, are greater than the returns on stocksstocks, then arbitrageurs , then arbitrageurs will direct funds towards bonds driving their rates down. will direct funds towards bonds driving their rates down. Similarly, if the real returns on bonds are Similarly, if the real returns on bonds are smallersmaller, arbitrage , arbitrage will drive their will drive their rates uprates up. The yields on stocks and bonds might . The yields on stocks and bonds might be very different on average, but they be very different on average, but they should tend to move should tend to move together over timetogether over time..

• Ultimately, the real yield on stocks – and, therefore, through Ultimately, the real yield on stocks – and, therefore, through arbitrage, the real yield on longer bonds – is determined by the arbitrage, the real yield on longer bonds – is determined by the profitability of corporations profitability of corporations and the real return they earn on and the real return they earn on their capital. It is useful to distinguish between physical and their capital. It is useful to distinguish between physical and financial returns. financial returns.

• Sometimes financial returns may differ substantially from the Sometimes financial returns may differ substantially from the underlying physical returns on capital. In such a case, one underlying physical returns on capital. In such a case, one would expect would expect arbitragearbitrage to drive their returns to drive their returns togethertogether. Unlike . Unlike arbitrage among financial assets, arbitrage between physical arbitrage among financial assets, arbitrage between physical capital and financial instruments capital and financial instruments can be slowcan be slow, especially if it , especially if it involves investment and the expansion of the corporation. involves investment and the expansion of the corporation.

The Five Questions About Interest Rates Revisited

First, why do interest rates tend to move together?First, why do interest rates tend to move together?

• Traders in financial markets seek the highest return on their Traders in financial markets seek the highest return on their available funds. All financial assets are, to some degree, available funds. All financial assets are, to some degree, substitutessubstitutes. As a result any movement in the price or yield of . As a result any movement in the price or yield of any one financial asset opens up profit opportunities that areany one financial asset opens up profit opportunities that are quickly arbitraged away. In the process of arbitrage, funds quickly arbitraged away. In the process of arbitrage, funds flow from low yielding assets (raising their yield) toward high flow from low yielding assets (raising their yield) toward high yielding assets (lowering their yield). Upward or downward yielding assets (lowering their yield). Upward or downward movements of the yields of any one asset tend to draw the movements of the yields of any one asset tend to draw the yields on other assets along in the same direction.yields on other assets along in the same direction.

Second, why do they move only imperfectly together?Second, why do they move only imperfectly together?

• Although all financial assets are substitutes, they are not Although all financial assets are substitutes, they are not perfect substitutesperfect substitutes. Even when the markets have taken . Even when the markets have taken advantage of every profit opportunity, differences in maturity, advantage of every profit opportunity, differences in maturity, coupon structure, risk, and other features ensure that coupon structure, risk, and other features ensure that differences in yield differences in yield usually remainusually remain. Changing economic . Changing economic circumstances may change the importance of these differences circumstances may change the importance of these differences over time, so that the yield differentials are not necessarily over time, so that the yield differentials are not necessarily constant.constant.

Third, why do shorter maturity assets typically, but not uniformly, Third, why do shorter maturity assets typically, but not uniformly, yield lower rates of interest than longer maturity assets? yield lower rates of interest than longer maturity assets?

• Differences in maturity are a particularly important example Differences in maturity are a particularly important example of the imperfect substitutability of financial assets. Long rates of the imperfect substitutability of financial assets. Long rates are higher than short rates whenever short rates are expected are higher than short rates whenever short rates are expected to rise or whenever an expected fall in short rates is not large to rise or whenever an expected fall in short rates is not large enough to offset the risk premia.enough to offset the risk premia.

Fourth, why at each maturity do government assets yield lower rates Fourth, why at each maturity do government assets yield lower rates of interest than private sector assets?of interest than private sector assets?

• Governments whose debt is denominated in their Governments whose debt is denominated in their own own currenciescurrencies, have no reason to default on that debt, because they , have no reason to default on that debt, because they are always able to create the money necessary to pay the are always able to create the money necessary to pay the interest and principal. Any interest and principal. Any organization that cannot create its organization that cannot create its own money own money – state and local governments, agencies, and – state and local governments, agencies, and corporations – or whose debts are not denominated in its own corporations – or whose debts are not denominated in its own currency currency faces some risk of bankruptcyfaces some risk of bankruptcy, and its debt carries , and its debt carries some default risk. A premium in the form of a higher yield some default risk. A premium in the form of a higher yield must be paid to reflect this default risk.must be paid to reflect this default risk.

Fifth, what determines the overall level of interest rates?Fifth, what determines the overall level of interest rates?

• The two principal influences on real interest rates are The two principal influences on real interest rates are monetary policy at the short end of the maturity monetary policy at the short end of the maturity spectrum and spectrum and arbitrage with the yields on physical assets at the long endarbitrage with the yields on physical assets at the long end. . Monetary policy typically targets nominal interest rates, but Monetary policy typically targets nominal interest rates, but does so with an eye to the inflation rate and hence to real rates. does so with an eye to the inflation rate and hence to real rates. To a first approximation, the Fisher effect determines nominal To a first approximation, the Fisher effect determines nominal rates as the sum of the real rate and the expected rate of rates as the sum of the real rate and the expected rate of inflation.inflation.