《货币金融学cha》PPT课件.pptVIP

chapter 5 The Risk and Term Structure of Interest Rates Instructor: Xiajing Dai preview uIn our supply and demand analysis of interest -rate behavior in Chapter 5, we examined the determination of just one interest rate. Yet we saw earlier that there are enormous numbers of bonds on which the interest rates can and do differ. uIn this chapter, we complete the interest- rate picture by examining the relationship of the various interest rates to one another uFigure 1 shows the yields to maturity for several categories of long-term bonds from 1919 to 2002. uIt shows us two important features of interest-rate behavior for bonds of the same maturity: u(1)Interest rates on different categories of bonds differ from one another in any given year u(2)the spread (or difference) between the interest rates varies over time. Default risk uOne attribute of a bond that influences its interest rate is its risk of default, which occurs when the issuer of the bond is unable or unwilling to make interest payments when promised or pay off the face value when the bond matures. uBy contrast, U.S. Treasury bonds have usually been considered to have no default risk because the federal government can always increase taxes to pay off its obligations. Bonds like these with no default risk are called default-free bonds. uThe spread between the interest rates on bonds with default risk and default-free bonds, called the risk premium, indicates how much additional interest people must earn in order to be willing to hold that risky bond Conclusion uA bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium. uBecause default risk is so important to the size of the risk premium, purchasers of bonds need to know whether a corporation is likely to default on its bonds. uTwo major investment advisory firms, Moodys Investors Service and Standard and Poors Corporation, provide default risk information by rating the quality of corporate and municipal bonds in terms of the probability of default uLiquidity uThe differences between interest rates on corporate bonds and Treasury bonds (that is, the risk premiums) reflect not only the corporate bonds default risk but its liquidity, too. uThis is why a risk premium is more accurately a “risk and liquidity premium,” but convention dictates that it is called a risk premium. Income Tax Considerations Why is it, then, that these bonds have had lower interest rates than U.S. Treasury bonds for at least 40 years, as indicated in Figure 1? The explanation lies in the fact that interest payments on municipal bonds are exempt from federal income taxes, a factor that has the same effect on the demand for municipal bonds as an increase in their expected return. Summary uThe risk structure of interest rates is explained by three factors: default risk, liquidity, and the income tax treatment of the bonds interest payments. uAs a bonds default risk increases, the risk premium on that bond (the spread between its interest rate and the interest rate on a default-free Treasury bond) rises. uThe greater liquidity of Treasury bonds also explains why their interest rates are lower than interest rates on less liquid bonds. uIf a bond has a favorable tax treatment, its interest rate will be lower. Term Structure of Interest Rates uA plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations is called a yield curve, and it describes the term structure of interest rates for particular types of bonds. uYield curves can be classified as upward-sloping, flat, and downward-sloping (the last sort is often referred to as an inverted yield curve). A good theory of the term structure of interest rates must explain the following three important empirical facts: u1. As we see in Figure 4, interest rates on bonds of different maturities move together over time. u2. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term interest rates are high, yield curves are more likely to slope downward and be inverted. u3. Yield curves almost always slope upward, as in the “Following the Financial News” box. Three theories have been put forward to explain the term structure of interest rates; that is, the relationship among interest rates on bonds of different maturities reflected in yield curve patterns: u(1) the expectations theory u(2) the segmented markets theory u(3) the liquidity premium theory Expectation Theory uThe expectations theory of the term structure states the following commonsense proposition: The interest rate on a long-term bond will equal an average of short-term. uThe key assumption behind this theory is that buyers of bonds do not prefer bonds of one maturity over another, so they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity. Bonds that have this characteristic are said to be perfect substitutes let us consider the following two investment strategies: u1. Purchase a one-year bond, and when it matures in one year, purchase another one-year bond. u2. Purchase a two-year bond and hold it until maturity Expected return from strategy 2 (1 + i2t)(1 + i2t) 1 1 + 2(i2t) + (i2t)2 1 = 11 Since (i2t)2 is extremely small, expected return is approximately 2(i2t) 2006 Pearson Addison-Wesley. All rights reserved (1 + it)(1 + iet+1) 11 + it + iet+1 + it(iet+1) 1 = 1 1 Since it(iet+1) is also extremely small, expected return is approximately it + iet+1 From implication above expected returns of two strategies are equal: Therefore 2(i2t) = it + iet+1 Solving for i2t it + iet+1 i2t = 2 2006 Pearson Addison-Wesley. All rights reserved More generally for n-period bond: it + iet+1 + iet+2 + . + iet+(n1) int = n In words: Interest rate on long bond = average short rates expected to occur over life of long bond Numerical example: One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9%: Interest rate on two-year bond: (5% + 6%)/2 = 5.5% Interest rate for five-year bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Interest rate for one to five year bonds: 5%, 5.5%, 6%, 6.5% and 7%. 24 Expectations Hypothesis explains Fact 1 that short and long rates move together 1.Short rate rises are persistent 2.If it today, iet+1, iet+2 etc. average of future rates int 3.Therefore: it int , i.e., short and long rates move together 2006 Pearson Addison-Wesley. All rights reserved 1. When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above todays short rate: yield curve will have steep upward slope 2. When short rates are high, they will be expected to fall in future, and long rate will be below current short rate: yield curve will have downward slope Doesnt explain Fact 3 that yield curve usually has upward slope Short rates as likely to fall in future as rise, so average of future short rates will not usually be higher than current short rate: therefore, yield curve will not usually slope upward Explains Fact 2 2006 Pearson Addison-Wesley. All rights reserved Segmented Markets Theory Key Assumption: Bonds of different maturities are not substitutes at all Implication: Markets are completely segmented: interest rate at each maturity determined separately Explains Fact 3 that yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have lower interest rates than long bonds Does not explain Fact 1 or Fact 2 because assumes long and short rates determined independently 2006 Pearson Addison-Wesley. All rights reserved Liquidity Premium (Preferred Habitat) Theories Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes Implication: Modifies Expectations Theory with features of Segmented Markets Theory Investors prefer short rather than long bonds must be paid positive liquidity (term) premium, lnt, to hold long-term bonds Results in following modification of Expectations Theory it + iet+1 + iet+2 + . + iet+(n1) int = + lnt n 2006 Pearson Addison-Wesley. All rights reserved Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theories 2006 Pearson Addison-Wesley. All rights reserved The implication of figure 5 The liquidity premium is always positive and typically grows as the term to maturity increases 2006 Pearson Addison-Wesley. All rights reserved Numerical Example 1. One-year interest rate over the next five years: 5%, 6%, 7%, 8% and 9% 2. Investors preferences for holding short-term bonds, liquidity premiums for one to five-year bonds: 0%, 0.25%, 0.5%, 0.75% and 1.0%. Interest rate on the two-year bond: (5% + 6%)/2 + 0.25% = 5.75% Interest rate on the five-year bond: (5% + 6% + 7% + 8% + 9%)/5 + 1.0% = 8% Interest rates on one to five-year bonds: 5%, 5.75%, 6.5%, 7.25% and 8%. 2006 Pearson Addison-Wesley. All rights reserved Liquidity Premium (Preferred Habitat) Theories: Term Structure Facts Explains all 3 Facts Explains Fact 3 of usual upward sloped yield curve by investors preferences for short-term bonds Explains Fact 1 and Fact 2 using same explanations as expectations hypothesis because it has average of future short rates as determinant of long rate 2006 Pearson Addison-Wesley. All rights reserved Market Predictions of Future Short Rates 2006 Pearson Addison-Wesley. All rights reserved Answers in brief 1. bond with a C rating should have a higher interest rate because it has a higher default risk, which reduces its demand and raises its interest rate relative to that on the Baa bond. 2006 Pearson Addison-Wesley. All rights reserved 3. During business cycle booms, fewer corporations go bankrupt and there is less default risk on corporate bonds, which lowers their risk premium. Similarly, during recessions, default risk on corporate bonds increases and their risk premium increases. 2006 Pearson Addison-Wesley. All rights reserved 5. If yield curves on average were flat, this would suggest that the risk premium on longterm relative to shortterm bonds would equal zero and we would be more willing to accept the expectations hypothesis. 2006 Pearson Addison-Wesley. All rights reserved 7. (a) yield curve would be upward- and then downwardsloping (b) yield curve would be downward- and then up wardsloping If people prefer shorter-term bonds over longer-term bonds, the yield curve tend to be even more upward sloping because longterm bonds would then have a positive risk premium. 2006 Pearson Addison-Wesley. All rights reserved 9. The steep upwardsloping yield curve at shorter maturities suggests that shortterm interest rates are expected to rise in the near future . The downward slope for longer maturities indicates that shortterm interest rates are e