503 Applied Macroeconomics Chapter 7. The Behavior of Interest Rates Prof. M. El-Sakka Dept of Economics Kuwait University What can you figure out looking at this graph. Is there a trend in the behavior of different rates of interest
Five Questions About Interest Rates 1. First, why do interest rates tend to move together? 2. Second, why do they move only imperfectly together? 3. Third, why do shorter maturity assets typically, but not uniformly, yield lower rates of interest than longer maturity assets? 4. Fourth, why at each maturity do government assets yield lower rates of interest than private sector assets? 5. Fifth, what determines the overall level of interest rates? This chapter aims to answer these five questions.
Similarity and Replacement To one degree or another, all financial instruments are similar, but generally they are not identical. Each is issued by a different borrower with different chances of paying back the loan, each provides the lender with a different stream of income, and each may have its own special characteristics. Two financial assets are SUBSTITUTES when a fall in the yield or interest rate on the first asset (that is, a rise in its price) reduces the demand for that asset and raises the demand for the other asset.
Supply and Demand of Financial Instruments Consider two similar corporate bonds say, bonds issued by Proctor and Gamble (P&G) and by Clorox. What determines their yields? Borrowers use funds and supply the financial instrument; lenders are the source of funds and demand the financial instrument. In the case of the two bonds, P&G and Clorox are the suppliers, and the public are the demanders. Reaching Equilibrium in a Financial Market The interest rate is determined where supply equals demand in each market and the rate is initially shown the same (r1) in each
market on the assumption that P&G bonds and Clorox bonds are perfect substitutes. If P&G decides to fund a major investment project through issuing new bonds. At each rate of interest its desire for funds will be higher, shifting its supply curve rightward (shift 1). All other things equal, the equilibrium would move from point A to point B, and the interest rate would rise from r1 to r2. The reason is that since more bonds are available, the only way the public can be enticed to hold them is for them to become cheaper. As their price falls, their yields rise.
Notice that with the market for P&G bonds at point B while the market for Clorox bonds is still at point A, the yield on the P&G bonds is higher than the yield on Clorox bonds. Since both bonds are assumed to be practically identical in the eyes of the public, why would people remain content to hold lower yielding Clorox bonds? They would not. Some people would sell their (expensive) Clorox bonds and use the proceeds to buy the (now cheaper) P&G bonds. As a result funds would leave the Clorox bond market and enter the P&G bond market. At each level of
interest rates, the demand for Clorox bonds would fall. The demand curve would shift leftward in the right-hand panel. More P&G bonds are outstanding at the new equilibrium (BP&G increased to BP&G). There are two effects. First, the rise in interest rates encouraged the public to buy more bonds. Second, the incipient difference between the yields in the two markets (r2 > r1) encouraged the public to shift from Clorox to P&G bonds until the yields were brought back into equality (B Clorox fell to Clorox B and both bonds yield r3). There are fewer Clorox bonds at the new equilibrium. Because of
the higher rates, Clorox prefers less debt and so would lower it by not rolling over bonds that come mature and, even, by buying back outstanding bonds, which are now cheaper. Arbitrage The simultaneous buying and selling of closely related goods or financial instruments in different markets to take advantage of price differentials. Actual financial markets are more complicated than the simple example of the two bonds. In reality there are many financial assets. They are almost all substitutes sometimes extremely close substitutes. As a result, what happens in any market
affects every market to some degree. The closer substitutes two assets are, the closer arbitrage drives their yields. EFFICIENT MARKETS: Inside and Outside Views of Financial Markets The effectiveness of arbitrage allows us to see financial markets from two perspectives. The first views the market from inside in terms of process. Highly motivated traders look for fleeting opportunities and exploit them quickly before they disappear. The market can also be viewed from the outside in terms of
outcomes. Since arbitrage is highly effective, it is reasonable for many purposes to assume that it is complete. All profit opportunities are competed away so quickly that we can assume that they do not exist at all. From this second perspective, financial markets can be thought of as highly efficient processors of information. The Efficient Markets Hypothesis This view of the financial market as a highly effective processor of information is the critical element of the EFFICIENTMARKETS HYPOTHESIS, which states there are no systematically exploitable arbitrage opportunities based on
information that is publicly available to financial markets. Profiting from truly private information is consistent with the efficient-markets hypothesis. Similarly, the efficient-markets hypothesis is consistent with some people beating the market and making enormous profits on financial trading. It does not rule out luck. Many traders, managers of mutual funds, and financial advisers believe that they can systematically outperform the market and can cite evidence of successive years of above average returns.
How could we tell if this were skill or luck? For any individual, it is impossible. The real test is: will the luck continue? One test would be to divide the market into above-average and below-average performers for, say, one year and then to see whether the above-average continue to beat the average in the next year. Many careful studies have shown that an aboveaverage performance one year does not predict an aboveaverage performance the next year. The efficient-markets hypothesis does not say that no one can make their living from such arbitrage activity. Rather, it says that the returns to such activity cannot on average exceed the amount that makes it just worth the traders while to continue it.
The efficient-markets hypothesis is the dominant theory of the functioning of financial markets, but there are many people who do not believe it. They point to people who have made millions, to statistical evidence of systematic unexploited profit opportunities, and to psychological theories of herd behavior. Two Answers We now have initial answers to the first two questions posed above: 1. Interest rates tend to move together because financial assets are substitutes and profit-seeking traders engage in effective
arbitrage; 2. Interest rates do not move perfectly together because financial assets are not perfect substitutes. Imperfect substitutability can be regarded as just a name for the fact that arbitrage is ineffective in removing all differences in yields. It remains to explain why it is ineffective. Risk: Risk is a complex business. We focus on two key elements: default risk and price or interest-rate risk. DEFAULT RISK
Risk and Return Those who borrow funds through issuing a bond or taking out a loan might go bankrupt. In that case, the lender or bond holders face DEFAULT RISK: they might not get paid. The chances of default on any particular bond are typically quite low. The chances of default on personal loans are 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 risk of default. If the high-risk bond were cheap enough that is, if its yield
were enough larger than that on the low risk bond it might become worthwhile to hold it. The additional yield or risk premium compensates for the higher risk. The risk premium can be thought of as the price of risk. Federal Government Bonds Junk bonds stand at one extreme of the risk spectrum. U.S. federal government bonds stand at the other. They are virtually free of default risk. Governments have a monopoly on taxation and, therefore, a ready source of funds to repay their debt. Effectively a government agency can create as many dollars
as necessary to fund its debt, it never has any reason to default. The key to its freedom from default risk is that federal government debt is denominated in dollars, which are within its control. Many developing countries find that they cannot borrow on international markets in their own currencies. Mexico, for instance, does not find it easy to sell peso-denominated bonds to foreigners, who usually prefer dollars, yen, or euros. Since Mexico cannot print dollars, its dollar-denominated bonds are just as subject to default risk as a corporate or municipal bond in the United States
Rating Risk Banks try to screen their personal and corporate borrowers to limit default. This is the reason that banks require borrowers to provide extensive information on their assets and liabilities and why they check borrowers payment histories with credit information agencies such as Trans Union, Equifax, and Experian. Riskier customers pay higher interest rates on loans. Firms and government agencies who wish to sell bonds on organized markets are able to do so effectively only if they pay a bond rating agency to rank the riskiness of their debt.
These agencies (the three most important are Moodys, Standard & Poors , and Fitch) use information partly gathered from the firms themselves to assign ratings similar to letter grades Bonds with ratings in the upper-half of the rating scale (relatively low default risk) are referred to as investment grade and those in the lower half (high default risk) as speculative. The term junk bond became familiar starting in the 1980s. Although it sounds like a synonym for worthless junk bonds are just bonds below investment grade.
PRICE OR INTEREST-RATE RISK We learned that the price or market value of a bond moves inversely with its yield. The PRICE (or INTEREST-RATE) RISK 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 and the point of sale. Price risk is greater for debt of greater maturity. All bonds, including federal government bonds, face price risk. Price risk explains at least some of the difference in yields for bonds of different maturities. Long bonds face greater price
risk and, therefore, must earn a risk premium compared to short bonds. The longer the bond, the higher the risk premium. Risk premia whether they compensate for default risk or for price risk ensure that the returns to holding risky assets are higher than the returns to holding safer assets. If one is willing to hold a portfolio that is more risky than the average market portfolio, then one can earn returns systematically higher than those enjoyed by the market in general. Such returns do not violate the efficient-markets hypothesis.
They are not the result of unexploited arbitrage opportunities. Rather they reflect the price of risk. The Term Structure of Interest Rates THE RELATIONSHIP OF INTEREST RATES OF DIFFERENT MATURITIES The smooth line connecting the various points on the graph is known as a YIELD CURVE. The fact that the 10-year bond rate is above the 3-month Treasury bill rate and, more generally, that longer rates exceed shorter rates is reflected in the fact that the yield curve slopes up. The relationship among
the returns on bonds of different maturities is called the TERM STRUCTURE OF INTEREST RATES. The yield curve is one, particularly useful, way of visualizing the term structure THE EXPECTATIONS THEORY OF THE TERM STRUCTURE. Arbitrage Across Different Maturities How might we account for the term structure of interest rates? What explains the shape of the yield curve? In general, the yield on an m-period bond over its life should equal the expected yields of m 1-period bonds:
Solving for rm,t, In words: the gross yield on an m-period bond (that is, 1 + rm,t) is the geometric average of the gross yield on the m current and expected future 1-period bonds. Equation (11.2) can be simplified for easier calculation. Taking logarithms of both sides and recalling that log(1 + x) x, when x is small, equation (11.1) can be written as or
THE ROLE OF RISK price risk is greater the longer the maturity of a bond and that generally markets require higher returns, a term premium (a kind of risk premium), to compensate for higher risk. The term premium is shown as a function of maturity since longer maturity bonds face greater price risk. We can therefore modify the above equation to add in the term premium: Inflation and Interest Rates THE EFFECT OF INFLATION ON THE SUPPLY AND DEMAND FOR BONDS
market rate can be decomposed into the sum of a real rate of interest and the rate of inflation. Since inflation rates have varied considerably over time, it would be interesting to know how that variation might have affected interest rates. At first blush, you might think that the question is answered already in knowing the decomposition r = rr + pet. An increase in expected inflation increases the market rate of interest. But that moves too quickly. We cannot know how any change in inflation affects nominal rates of interest until we know how it affects real rates of interest.
The key point is that rational people should not care about the nominal values of prices or interest rates. They should care about the real values, what their money will actually buy or what their savings will earn What happens if the expected rate of inflation increases to pe = 4%? Since the users of funds care about real rates, they should be willing to supply exactly the same amounts at the same real rates. But now each real rate corresponds to a higher nominal rate. A nominal rate of 8% (= rr + pe = 4 + 4) corresponds to a real rate of 4%, and a nominal rate of 6
percent corresponds to a real rate of 2 percent. The whole supply curve, then, must shift vertically upward by exactly the change in the expected rate of inflation (that is, by 3 percentage points), so that it lies parallel to original curve. At point E the nominal interest rate is higher than at point A, but since the real rate has not changed, the supply of bonds remains at B0. Similarly, the supply of bonds remains unchanged between points C and F. The issuer of the bond is willing to pay higher rates of interest for the same funds, because he can pay them back with money that is losing its
value faster because of the higher inflation. An exactly parallel argument suggests that the demand curve should also shift vertically at every point by an amount equal to the change in the rate of inflation. The lender must charge 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 is losing its value faster. The combined effect of these two adaptations to higher rates of inflation is that both the supply and demand curves shift vertically by the same amount, so that that the equilibrium
(right-hand panel), which had been at 4 percent (point G), also shifts vertically to 7 %(point H), and the equilibrium quantity of bonds (B*) remains constant. THE FISHER EFFECT AND THE FISHER HYPOTHESIS The relationship between inflation rates and interest rates is known as the Fisher effect, in honor of the great American economist Irving Fisher (1867-1947) who emphasized it in his analysis of interest rates. It may be useful to distinguish the Fisher effect from the Fisher hypothesis. The FISHER EFFECT can be defined as a point-for-point
increase in the market rate of interest that results, ceteris paribus, from an increase in the expected rate of inflation. The ceteris paribus clause is important. The Fisher effect is a theoretical claim that may be difficult to observe in the world because other things are not always equal. The FISHER HYPOTHESIS can be defined as the empirical phenomenon in which a change in market rates of interest is associated approximately point for point with a change in the actual rate of inflation. The Fisher hypothesis is clearly true to a first approximation.
The Fisher hypothesis as Fisher himself was well aware does not hold exactly. One reason is that no inflation measure, such as the CPI, represents exactly the bundle that is relevant to the players in financial markets. Borrowers and lenders might have systematically different consumption bundles. Indeed, the relevant bundles need not be the same for all borrowers or all lenders. A second reason is that taxes are levied on nominal interest payments. Higher interest rates, even if they are merely compensation for higher inflation rates, generate higher tax
liabilities. Lenders would, therefore, require an extra increase in nominal interest rates to compensate for the loss of purchasing power due to inflation-induced tax-rate increases. Finally, and probably most important, there is no reason to believe that expectations of future inflation are formed perfectly or are captured by the past behavior of inflation. It may take some time to adjust expectations to an unexpected increase or decrease in actual inflation. During the adjustment period, real, rather than nominal, rates would be affected. The Level of Real Interest Rates
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 about the maturity, coupon structure, risk, tax rates, and expected inflation rates to deduce the rates on all other bonds. But where do we find the starting place the one real rate? Or, what determines the level of the real yield on any particular financial asset? There are two answers to this question, depending on whether we concentrate on short rates or long rates. MONETARY POLICY AND SHORT RATES
At the short end of the market, the interaction of monetary policy and expected inflation rates determines the real rate Central banks typically buy and sell short-term assets (largely Treasury bills) on the open market. When the central bank buys, it pays by crediting funds to the accounts that commercial banks hold with it. When it sells, it deducts funds from these accounts, eliminating reserves. In the United States, these reserves are known to financial markets as Federal funds. Commercial banks are required to hold reserves in a certain proportion to their deposit liabilities. There is an active
overnight market, the Federal funds market, in which banks with an excess of reserves over their requirements lend to banks with a shortage. The Federal Reserve set the interest rate in this market, known as the Federal funds rate, by raising or lowering the stock of available reserves through purchases or sales of short-term financial assets. Monetary policy today largely consists of setting a target for the Federal funds rate. ARBITRAGE TO REAL RETURNS At longer maturities, bonds are substitutes with shares in corporations. If the real returns on bonds, after accounting for
risk, are greater than the returns on stocks, then arbitrageurs will direct funds towards bonds driving their rates down. Similarly, if the real returns on bonds are smaller, arbitrage will drive their rates up. The yields on stocks and bonds might be very different on average, but they should tend to move together over time. Ultimately, the real yield on stocks and, therefore, through arbitrage, the real yield on longer bonds is determined by the profitability of corporations and the real return they earn on their capital. It is useful to distinguish between physical and financial returns.
Sometimes financial returns may differ substantially from the underlying physical returns on capital. In such a case, one would expect arbitrage to drive their returns together. Unlike arbitrage among financial assets, arbitrage between physical capital and financial instruments can be slow, especially if it involves investment and the expansion of the corporation. The Five Questions About Interest Rates Revisited First, why do interest rates tend to move together? Traders in financial markets seek the highest return on their
available funds. All financial assets are, to some degree, substitutes. As a result any movement in the price or yield of any one financial asset opens up profit opportunities that are quickly arbitraged away. In the process of arbitrage, funds flow from low yielding assets (raising their yield) toward high yielding assets (lowering their yield). Upward or downward movements of the yields of any one asset tend to draw the yields on other assets along in the same direction. Second, why do they move only imperfectly together? Although all financial assets are substitutes, they are not
perfect substitutes. Even when the markets have taken advantage of every profit opportunity, differences in maturity, coupon structure, risk, and other features ensure that differences in yield usually remain. Changing economic circumstances may change the importance of these differences over time, so that the yield differentials are not necessarily constant. Third, why do shorter maturity assets typically, but not uniformly, yield lower rates of interest than longer maturity assets? Differences in maturity are a particularly important example
of the imperfect substitutability of financial assets. Long rates are higher than short rates whenever short rates are expected to rise or whenever an expected fall in short rates is not large enough to offset the risk premia. Fourth, why at each maturity do government assets yield lower rates of interest than private sector assets? Governments whose debt is denominated in their own currencies, have no reason to default on that debt, because they are always able to create the money necessary to pay the interest and principal. Any organization that cannot create its
own money state and local governments, agencies, and corporations or whose debts are not denominated in its own currency faces some risk of bankruptcy, and its debt carries some default risk. A premium in the form of a higher yield must be paid to reflect this default risk. Fifth, what determines the overall level of interest rates? The two principal influences on real interest rates are monetary policy at the short end of the maturity spectrum and arbitrage with the yields on physical assets at the long end. Monetary policy typically targets nominal interest rates, but
does so with an eye to the inflation rate and hence to real rates. To a first approximation, the Fisher effect determines nominal rates as the sum of the real rate and the expected rate of inflation. Kevin D. Hoover Applied Intermediate Macroeconomics 2012
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