a. 5, 6, 7, 6, 5 (%)
b. 5, 4, 3, 4, 5 (%)
9). If a yield curve looks like the one shown in figure (b) below, what is the market predicting about the movement of future short-term interest rates? What might the yield curve indicate about the market's predictions about the inflation rate in the future?
Summary:
1. Bonds with the same maturity will have different interest rates because of three factors: default risk, liquidity, and tax considerations. The greater a bond's default risk, the higher its interest rate relative to other bonds; the greater a bond's liquidity, the lower the interest rate; and bonds with tax-exempt status will have lower interest rates than they otherwise would. The relationship among interest rates on bonds with the same maturity that arise because of these three factors is known as the risk structure of interest rates.
2. Four theories of the term structure provide explanations of how interest rates on bonds with different terms to maturity are related. The expectations theory views long-term interest rates as equaling the average of future short-term interest rates expected to occur over the life of the bond. By contrast, the segmented markets theory treats the determination of interest rates for each bond's maturity as the outcome of supply and demand in that market only. Neither of these theories by itself can explain the fact that interest rates on bonds of different maturities move together over time and that yield curves usually slope upward.
3. The liquidity premium and preferred habitat theories combine the features of the other two theories, and by so doing are able to explain the facts just mentioned. They view long-term interest rates as equaling the average of future short-term interest rates expected to occur over the life of the bond plus a liquidity premium. These theories allow us to infer the market's expectations about the movement of future short-term interest rates from the yield curve. A steeply upward-sloping curve indicates that future short-term rates are expected to rise, a mildly upward-sloping curve indicates that short-term rates are expected to stay the same, a flat curve indicates that short-term rates are expected to decline slightly, and an inverted yield curve indicates that a substantial decline in short-term rates is expected in the future.
-Relationship of various interest rates to one another
-Different interest rates on same maturity --> Risk structure of interest rates
-Different interest rates on different maturity --> Term Structure of interest rates
Risk Structure of Interest Rates:
I). What contribute to the different interest rates?
1. Default Risk
-Risk of default when the issuer is unable to make interest payments or pay off bond.
-The diffference between interest rates of default risk and default-free bonds (both with same maturity) is risk premium --> how much more additional interest people should get to be willing to hold that risky bond.
-A bond with default risk always have a positive risk premium and an increase in its default risk will raise the risk premium.
-Credit-rating agencies: low risk (investment-grade >BBB), high risk (junk bonds
The Enron Bankruptcy and the Baa-Aaa Spread
-Investors doubt the health of corporations that are less than Baa. increase in interest rates. More people want Aaa bonds and led to big gap between Aaa and Baa.
2. Liquidity
-The more liquid, the more desirable.
-Liquidity affect interest rate: less liquid, demand decrease, price fall, and interest rates rise.
3. Income Tax Considerations
-The behavior of municipal bond rates which are not default-free and not as liquid as T-bills.
-Municipal bonds have less interest rates than T-bills because interest payments on municipal bonds are exempt from federal income taxes --> increase in expected return.
-T-bills: 1000 face-value with coupon payment 100 (r=10%), income tax 35% --> earn only 6.5%
-Municipal bonds: " " with coupon payment 80 (r=8%), income tax 0% --> earn 8%
-With tax advantage, expected return increases, higher demand, higher prices, lower interest rates.
Effects of Bush tax cut on Bond Interest Rates
-39% to 35%: a decrease in income tax rate means that the after-tax expected return on tax-free municipal bonds relative to the T-bills are lower --> municipal less desirable --> demand decrease, lower price and higher interest rates. T-bills more desirable --> demand increase, higher price, and lower interest rates.
II). Term structure of interest rates
-Another factor that influences interest rate is its term to maturity.
-A plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations, is called a yield curve. It describes the term structure of interest rates for particular types of bonds, such as government bonds.
-Yield curve: upward, downward, or flat.
-Upward: the most usual; the long-term interest rates are above the short-term interest rates
-Flat: short- and long-term interest rates are the same.
-Downward: long-term interest rates are below short-term interest rates.
-Term structure must explain different shapes of yield curves and the following:
a. Interest rates on bonds of different maturities move together over time
b. 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.
c. Yield curves almost always slope upward.
-Three theories to explain term structure of interest rates: expectations theory, segmented market theory, and the liquidity premium theory.
-ET explains 12 not 3, SMT explains 3 not 12, LPT 123.
1. Expectations Theory
-The interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond.
-Example: average expected short-term interest rates the next 5 years= 10%, then interest rate on a five-year maturity bond=10%.
-Key assumption: buyers of bonds to 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 --> perfect substitutes --> expcected return on these bonds must be equal.
...137-138
-Expectations theory explains why the term structure of interest rates changes at different times. When yield curves is upward-sloping, the expectations theory suggests that short-term interest rates are expected to rise in the future. In this situation when the long-term rate is higher than the short-term rate, the average of future short-term rates is expected to be higher than the current short-term rate, which can only occur if short-term interest rates are expected to rise.
-Downward: short-term are expected to fall in the future.
-Also explains fact 1: historically, if short increase today, they are higher in future --> rise in short-term interest rates will raise people's expectations of future short-term rates --> raise in long-term rates --> short and long move together.
-Explains fact 2: when short are low, people expect them to rise to normal level in future --> avg of future expected short is higher than current short rate--> upward sloping
-Does not explain fact 3, suggests that yield curve should be flat.
2. Segmented Markets Theory
-Different maturity bonds have different markets
-Interest rate determined by the supply and demand of that bond independent of other bonds.
-Key assumption: bonds of different maturities are not substitutes so the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity.
-Investors have strong preferences for particular maturities.
-Investors have short desired holding periods --> demand for long is lower than short --> long have lower prices and higher interest rates --> upward sloping --> fact 3.
-Cannot explain why interest rates on bonds of different maturities tend to move together (fact 1).
-Not clear on how demand and supply for short vs. long change with short rate (fact 2).
3. Liquidity Premium and Preferred Habitat Theories
-The rate on a long will equal an average of short expected to occur over the life of long plus a liquidity premium that responds to supply and demand for the bond.
-Key assumption: bonds of different maturities are substitutes, but it allows investors to prefer one maturity over another --> substitutes but not perfect substitutes.
-Prefer short bonds so investors must offer a positive liquidity premium to induce them to hold long bonds.
-Preferred habitat theory: related to liquid premium theory
*Investors have preference for maturity: only buy different maturity if have higher expected return.
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