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Chapter 3. The Level and Structure of Interest Rates. Historical Interest Rate Patterns. Over the last three decades interest rates have often followed patterns of persistent increases or persistent decreases with fluctuations around these trends.
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Chapter 3 The Level and Structure of Interest Rates
Historical Interest Rate Patterns Over the last three decades interest rates have often followed patterns of persistent increases or persistent decreases with fluctuations around these trends. In the 1970s and early 1980s the U.S.’s inflation led to increasing interest rates during that period. This period of increasing rates was particularly acute from the late 1970s through early 1980s when the U.S. Federal Reserve changed the direction of monetary policy by raising discount rates, increasing reserve requirements, and lowering monetary growth.
Historical Interest Rate Patterns This period of increasing rates was followed by a period of declining rates from the early 1980s to the late 1980s, then a period of gradually increasing rates for most of the 1990s, and finally a period of decreasing rates from 2000 through 2003. The different interest rates levels observed since the 1970s can be explained by such factors as economic growth, monetary and fiscal policy, and inflation.
Historical Interest Rate Patterns TREASURY BILL RATES, 1970-2003
Historical Interest Rate Spreads In addition to the observed fluctuations in interest rate levels, there have also been observed spreads between the interest rates on bonds of different categories and terms to maturity over this same period. For example, the spread between yields on Baa and AAA bonds is greater in the late 1980s and early 1990s when the U.S. economy was in recession compared to the differences in the mid to late 1990s when the U.S. economy was growing. In general, spreads can be explained by differences in each bond’s characteristics: risk, liquidity, and taxability.
Historical Interest Rate Spreads TREASURY BOND, Aaa CORPORATE, Baa CORPORATE, AND MORTAGE RATES, 1970-2002
Historical Interest Rate Spreads Interest rate differences can be observed between similar bonds with different maturities. The figures on the next slide shows two plots of the YTM on U.S. government bonds with different maturities for early 2002 and early 1981. The graphs are known as yield curves and they illustrate what is referred to as the term structure of interest rates. The lower graph shows a positively-sloped yield curve in early 2002 with rates on short-term government securities lower than intermediate-term and long-term ones. In contrast, the upper graph shows a negatively sloped curve in early 1981 with short-term rates higher than intermediate- and long-term ones.
Objective Understanding what determines both the overall level and structure of interest rates is an important subject in financial economics. Here, we examine the factors that are important in explaining the level and differences in interest rates. Examining the behavior of overall interest rates using basic supply and demand analysis Looking at how risk, liquidity, and taxes explain the differences in the rates on bonds of different categories. Looking at four well-known theories that explain the term structure on interest rates.
Supply and Demand Analysis One of the best ways to understand how market forces determine interest rates is to use fundamental supply and demand analysis. In determining the supply and demand for bonds, let us treat different bonds as being alike and simply assume the bond in question is a one-period, zero-coupon bond paying a principal of F equal to 100 at maturity and priced at P0 to yield a rate i. Given this type of bond, we want to determine the important factors that determine its supply and demand.
Bond Demand and Supply Analysis Bond Demand Curve: • Bond Demand Curve: The curve shows an inverse relationship between, bond demand, BD, and its price, P0, and a direct relation between BD interest rate, i, given other factors are constant. • Bond demand curve is also called the supply of loanable funds curve.
Bond Demand and Supply Analysis Bond Demand Curve: • The factors held constant include the overall wealth or economic state of the economy, as measured by real output, gdp, the bond’s risk relative to other assets, its liquidity relative to other assets, expected future interest rates, E(i) and inflation, and government policies:
Bond Demand and Supply Analysis Bond Demand Curve: • Bond demand is inversely related to its price and directly related to interest rate. • The bond demand curve showing bond demand and price relation is negatively-sloped. • This reflects the fundamental assumption that investors will demand more bonds the lower the price or equivalently the greater the interest rate. • Changes in the economy, futures interest rate and inflation expectations, risk, liquidity, and government policies lead to either rightward or leftward shifts in the demand curve, reflecting greater or less bond demand at each price or interest rate.
Bond Demand and Supply Analysis Bond Supply Curve: • The bond supply curve shows the quantity supplied of bonds, BS, by corporations, governments, and intermediaries is directly related to the bond’s price and inversely related interest rate, given other factors such as the state of the economy, government policy, and expected future inflation are constant: • Bond supply curve is also called the demand of loanable funds curve.
Bond Demand and Supply Analysis Bond Supply Curve: • The bond supply curve is positively sloped. • The positively sloped curve reflects the fundamental assumption that corporations, governments, and financial intermediaries will sell more bonds the greater the bond’s price or equivalently the lower the interest rate. • The bond supply curve will shift in response to changes in the state of the economy, government policy, and expected inflation.
Bond Demand and Supply Analysis Equilibrium: • The equilibrium rate, i* and price, P0*, are graphically defined by the intersection of the bond supply and bond demand curves.
Bond Demand and Supply Analysis Proof of Equilibrium: • If the bond price were below this equilibrium price (or equivalently the interest rate were above the equilibrium rate), then investors would want more bonds than issuers were willing to sell. • This excess demand would drive the price of the bonds up, decreasing the demand and increasing the supply until the excess was eliminated.
Bond Demand and Supply Analysis Proof of Equilibrium: • If the price on bonds were higher than its equilibrium (or interest rates lower that the equilibrium rate), then bondholders would want fewer bonds, while issuers would want to sell more bonds. • This excess supply in the market would lead to lower prices and higher interest rates, increasing bond demand and reducing bond supply until the excess supply was eliminated.
Cases Using Demand and Supply Analysis Expansionary Open Market Operation: • Central Bank buys bonds, decreasing the bond supply and shifting the bond supply curve to the left. • The impact would be an increase in bond prices and a decrease in interest rates. Intuitively, as the central bank buys bonds, they will push the price of bond up and interest rate down.
Cases Using Demand and Supply Analysis Economic Recession: • In an economic recession, there is less capital formation and therefore fewer bonds are sold. • This leads to a decrease in bond supply and a leftward shift in the bond supply curve. • The recession also lowers bond demand, shifting the bond demand curve to the left. • If the supply effect dominates the demand effect, then there will be an increase in bond prices and a decrease in interest rates.
Cases Using Demand and Supply Analysis Treasury Financing of a Deficit: • With a government deficit, the Treasury will have to sell more bonds to finance the shortfall. • Their sale of bonds will increase the supply of bonds, shifting the bond supply curve to the right, initially creating an excess supply of bonds. • This excess supply will force bond prices down and interest rates up.
Cases Using Demand and Supply Analysis Economic Expansion: • In a period of economic expansion, there is an increase in capital formation and therefore more bonds are being sold to finance the capital expansion. • This leads to an increase in bond supply and a rightward shift in the bond supply curve. • The expansion also increases bond demand, shifting the bond demand curve to the right. • If the supply effect dominates the demand effects, then there will be a decrease in bond prices and an increase in interest rates.
Risk and Risk Premium • Investment risk is the uncertainty that the actual rate of return realized from a security will differ from the expected rate. • In general, a riskier bond will trade in the market at a price that yields a greater YTM than a less risky bond. • The difference in the YTM of a risky bond and the YTM of less risky or risk-free bond is referred to as a risk spread or risk premium.
Risk and Risk Premium • The risk premium, RP, indicates how much additional return investors must earn in order to induce them to buy the riskier bond: • We can use the supply and demand model to show how the risk premium is positive. RP = YTM on Risky Bond - YTM on Risk-Free Bond
Risk and Risk Premium • Consider the equilibrium adjustment that would occur for two identical bonds (C and T) that are priced with the same yields, but events occur that make one of the bonds more risky.
Risk and Risk Premium • The increased riskiness on the one bond (Bond C) would cause its demand to decrease, shifting its bond demand curve to the left. That bond’s riskiness would also make the other bond (Bond T) more attractive, increasing its demand and shifting its demand curve to the right. • At the new equilibriums, the riskier bond’s price is lower and its rate greater than the other. • The different risk associated with bonds leads to a market adjustment in which at the new equilibriumthere is a positive risk premium.
Risk Premium The riskiness of Bond C increases the demand for Bond T, shifting its bond demand curve to the right. Impact: A Lower Interest Rate on Bond T The riskiness of Bond C decreases its demand, shifting its bond demand curve to the left. Impact: A Higher Interest Rate on Bond C
Risk Premiums and Investors’ Return-Risk Premiums • The size of the risk premium depends on investors’ attitudes toward risk. • To see this relation, suppose there are only two bonds available in the market: a risk-free bond and a risky bond.
Risk Premiums and Investors’ Return-Risk Premiums • Suppose the risk-free bond is a zero-coupon bond promising to pay $1,000 at the end of one year and currently is trading for $909.09 to yield a one-year risk-free rate, Rf, of 10%:
Risk Premiums and Investors’ Return-Risk Premiums • Suppose the risky bond is a one-year zero coupon bond with a principal of $1,000. • Suppose there is a .8 probability the bond would pay its principal of $1,000 and a .2 probability it would pay nothing. • The expected dollar return from the risky bond is therefore $800: E(Return) = .8($1,000) + .2(0) = $800
Risk Premiums and Investors’ Return-Risk Premiums • Given the choice of two securities, suppose that the market were characterized by investors who were willing to pay $727.27 for the risky bond, in turn yielding them an expected rate of return of 10%: • In this case, investors would be willing to receive an expected return from the risky investment that is equal to the risk-free rate of 10%, and the risk premium, E(R) - Rf, would be equal to zero. • In finance terminology, such a market is described as risk neutral. RP = 0 → Risk-Neutral Market
Risk Premiums and Investors’ Return-Risk Premiums • Instead of paying $727.27, suppose investors like the chance of obtaining returns greater than 10% (even though there is a chance of losing their investment), and as a result are willing to pay $750 for the risky bond. In this case, the expected return on the bond would be 6.67% and the risk premium would be negative: • By definition, markets in which the risk premium is negative are called risk loving. RP < 0 → Risk-Loving Market
Risk Premiums and Investors’ Return-Risk Premiums • Risk loving markets can be described as ones in which investors enjoy the excitement of the gamble and are willing to pay for it by accepting an expected return from the risky investment that is less than the risk-free rate. • Even though there are some investors who are risk loving, a risk loving market is an aberration, with the exceptions being casinos, sports gambling markets, lotteries, and racetracks.
Risk Premiums and Investors’ Return-Risk Premiums • Suppose most of the investors making up our market were unwilling to pay $727.27 or more for the risky bond. • In this case, if the price of the risky bond were $727.27 and the price of the risk-free were $909.09, then there would be little demand for the risky bond and a high demand for the risk-free one. • Holders of the risky bonds who wanted to sell would therefore have to lower their price, increasing the expected return. On the other hand, the high demand for the risk-free bond would tend to increase its price and lower its rate.
Risk Premiums and Investors’ Return-Risk Premiums • Suppose the markets cleared when the price of the risky bond dropped to $701.75 to yield 14%, and the price of the risk-free bond increased to $917.43 to yield 9%: • In this case, the risk premium would be 5%:
Risk Premiums and Investors’ Return-Risk Premiums • By definition, markets in which the risk premium is positive are called risk-averse markets. • In a risk-averse market, investors require compensation in the form of a positive risk premium to pay them for the risk they are assuming. • Risk-averse investors view risk as a disutility, not a utility as risk-loving investors do. RP > 0 → Risk-Averse Market
Risk Premiums and Investors’ Return-Risk Premiums • Historically, security markets such as the stock and corporate bond markets have generated rates of return that, on average, have exceeded the rates on Treasury securities. • This would suggest that such markets are risk averse. • Since most markets are risk averse, a relevant question is the degree of risk aversion. • The degree of risk aversion can be measured in terms of the size of the risk premium. The greater investors’ risk aversion, the greater the demand for risk-free securities and the lower the demand for risky ones, and thus the larger the risk premium.
Liquidity and Liquidity Premium • Liquid securities are those that can be easily traded and in the short-run are absent of risk. • In general, we can say that a less liquid bond will trade in the market at a price that yields a greater YTM than a more liquid one.
Liquidity and Liquidity Premium • The difference in the YTM of a less liquid bond and the YTM of a more liquid one is defined as the liquidity premium, LP: LP = YTM on Less Liquid Bond - YTM on More-Liquid Bond
