CHAPTER 6: RISK AND TERM STRUCTURE OF INTEREST RATES ...
CHAPTER 6: RISK AND TERM STRUCTURE OF INTEREST RATES (MISHKIN) - In our supply and demand analysis of interest-rate behavior in the previous chapter, we examined the determination of just one interest rate - There are many bonds on which the interest rates differ, and understanding why they differ from bond to bond can help people decide which bonds to purchase and which ones to sell - Risk Structure of Interest Rates: the relationship between interest rates for bonds that have the same term to maturity but have different interest rates - Term structure of Interest rates: the relationship among interest rates on bonds with different terms to maturity
6.1 – Risk Structure of Interest Rates (same maturity) - For bonds of the same maturity, interest rates on different categories of bonds differ from one another in any given year, and the spread (difference) between the interest rates varies over time - Bonds with the same maturity have different interest rates due to: Default risk Liquidity, and Tax considerations A. Default Risk Default Risk: 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 A corporation suffering big losses will be more likely to suspend interest payments on its bonds, thus the default risk on its bonds would be high On the other hand, Canadian government bonds are considered to have no default risk because the federal government can increase taxes to pay off its bonds (we call these defaultfree bonds) Risk Premium: the difference between the interest rates on bonds with default risk and default-free bonds of the same maturity, it tells us how much additional interest people must earn in order to be willing to hold that risky bond A bond with default risk always has a positive risk premium, the higher the default risk is, the larger the risk premium will be
-
Let us assume that initially corporate bonds have the same default risk as Canadian bonds In this case, these two bonds have the same attributes (identical risk and maturity) We can assume that their equilibrium prices and interest rates will initially be equal ( C
T
P1 =
P1
and
I C1 -
I T1
= 0)
C
I1
=
T
I 1 ) and the risk premium on corporate bonds will be zero (
If the risk default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease The theory of portfolio choice tells us that because the expected return on the corporate bond falls relative to the expected return on the default-free Canada bond while its relative riskiness rises, the corporate bond is less desirable and demand for it will fall At the same time, the expected return on default-free Canada bonds increases relative to the expected return on corporate bonds. So Canada bonds become more desirable and demand rises So now we see that the equilibrium price of corporate bonds has decreased, implying that the interest rate for corporate bonds has increased. We also see that the new equilibrium price of Canadian bonds has increased, causing the interest rate to fall -
Thus
I C1
>
I T1
, and
I C1
-
I T1
= Risk premium
So we can now conclude that a bond with default risk will always have appositive risk premium, and an increase in its default risk will raise the risk premium Credit-Rating Agencies: investment advisory firms that rate the quality of corporate and municipal bonds in terms of the probability of default Investment-grade securities: bonds with relatively low risk of default and have a rating of BBB and above Junk Bonds: bonds with ratings below BBB have higher default risk (speculative-grade) Fallen Angels: investment-grade securities whose rating has fallen to junk bond levels Corporate bonds always have higher interest rates than Canadian bonds because they always have some risk of default, whereas Canadian bonds do not Because corporate bonds have a greater default risk than Canadian bonds, their risk premium is greater, and the corporate bond rate therefore always exceeds the Canadian bond rate
Recession periods see a very high rate of business failures and defaults, thus there would be an increase in default risk for bonds issued by corporations, and the risk premium for corporate bonds would reach very high levels in this economic downturn B. Liquidity A liquid asset is one that can be quickly and cheaply converted into cash if the need arises The more liquid an asset is the more desirable it is, holding everything else constant Canadian bonds are the most liquid of all long-term bonds because they are so widely traded that they are the easiest to sell quickly and the cost of selling them is low Corporate bonds, on the other hand, are not as liquid because fewer bonds for any one corporation are traded, thus it can be costly to sell these bonds in an emergency because it may be hard to find buyers quickly The lower liquidity of corporate bonds relative to Canadian bonds increases the spread between the interest rates on these two bonds Once again, we assume that initially corporate and Canadian bonds are equally liquid and other attributes like maturity date are the same (so they will have the same price and interest rate) However, if corporate bond becomes less liquid than the Canadian bond because it is less widely traded, the theory of portfolio choice tells us that demand for corporate bonds will fall, while demand for Canadian bonds will rise, and thereby creating a spread between interest rates Therefore, the differences between interest rates on corporate bonds and Canadian bonds (that is the risk premiums) reflect not only the corporate bond’s default risk but its liquidity too
C. Income Tax Considerations In Canada, coupon payments on fixed-income securities are taxed as ordinary income in the year they are received (in the US, certain government bonds are not taxable) You earn more on a tax-exempt bond, so you are willing to hold the bond even though it has a lower interest rate than the taxable bond E.g. Option 1: Face value and purchase price of $1,000. Coupon and interest rate of 8%, tax free Option 2: FV and price of $1,000. Coupon and interest rate of 10%, 40% tax bracket We would pick Option 1 because our return would be $80 while Option 2 only gives us $60 Notice that the tax-exempt status of a bond becomes a significant advantage when income tax rates are very high D. Recap As a corporate bond’s default risk increases, the risk premium on that bond rises The greater the liquidity of Canadian bonds explains why their interest rates are lower than interest rates on less liquid corporate bond If a bond has favorable tax treatment, like interest payments are exempt from federal income taxes, its interest rate will be lower
6.2 – Term Structure of Interest Rates (different maturity) Bonds with identical risk, liquidity, and tax characteristics, may have different interest rates because the time remaining to maturity is different Yield Curve: plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations, describes the term structure of interest rates for bonds Yield curves can be upward sloping, flat, or downward sloping (inverted yield curve)
When the yield curves slope upward, the long-term interest rates are above the short-term rates When the yield curves are flat, short- and long-term interest rates are the same When the yield curves are inverted, long-term interest rates are below short-term interest rates There are 3 important facts about yield curves and term structure of interest rates: Fact 1: Interest rates on bonds of different maturities move together over time Fact 2: When short-term interest rates are low, yield curves have an upward slope; when short-term interest rates are high, yield curves are more likely to be inverted Fact 3: yield curves almost always slope upward There are 3 theories that explain these facts for the term structure of interest rates: Expectations theory (explains fact 1 & 2) Segmented markets theory (explains fact 3) Liquidity premium theory – combination of expectations and segmented (explains all 3 facts) These theories are important because they help us understand the shape of the yield curve, but also allow us to do 3 things: Forecast future interest rates Forecast future changes in economic activity and business cycle turning points Forecast future rates of inflation The Yield Curve:
A. Expectations Theory Expectations Theory: the interest rate on a long-term bond will be the average of shortterm interest rates that people expect to occur over the life of the long-term bond If people expect that short-term interest rates will be 10% on average over five years, the expectations theory says that the interest rate on bonds with five years to maturity will be 10% If short-term interest rates were expected to rise even higher after this 5-year period so that the average short-term interest rate over the coming 20 years is 11%, then the interest rate on 20-year bonds would be 11% and would be higher than the rate on 5-year bonds The expectations theory explains why interest rates on bond of different maturities differ; because short-term interest rates are expected to have different values at future dates The key assumption for 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 (perfect substitutes) If bonds with different maturities are perfect substitutes, the expected return on these bonds must be equal E.g. The 1-year interest rate over the next five years is expected to be 5%, 6%, 7%, 8%, and 9%. Given this, what are the interest rates on an equivalent two-year bond and five-year bond? The interest rate on the 2-year bond would be
And the interest rate on the 5-year bond would be We see that rising short-term interest rates produces an upward sloping yield curve along which interest rates rise as maturity lengthens And thus we have the general formula of The expectations theory explains why the term structure of interest rates changes at different times When the yield curve 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 currently above the short-term rate, the average of future short-term rates is expected to be higher than the current short-term rate When the yield curve is inverted, the average of future short-term interest rates is expected to be below the current short-term rate, implying that short-term interest rates are expected to fall, on average, in the future When the yield curve is flat, the expectations theory suggests that short-term interest rates are not expected to change, on average, in the future So how does the Expectations Theory help explain fact 1 and 2? i. Explaining Fact 1 (interest rates on bonds with different maturities move together) Historically, if short-term interest rates increase today, they tend to be higher in the future Hence, a rise in short-term rates will raise people’s expectations of future shortterm rates Since long-term rates are the average of expected future short-term rates, a rise in short-term rates will also raise long-term rates, both short- and long-term rates to move together ii. Explaining Fact 2 (yield curves have an upward slope when short-term interest rates are low) When short-term rates are low, people generally expect them to rise to some normal level in the future, and the average of future expected short-term rates is high relative to the current short-term rate. Therefore long-term interest rates will be substantially above current short-term rates, and the yield curve would then have an upward slope Conversely, if short-term rates are high, people usually expect them to come back down. So long-term rates would then drop below short-term rates because the average of expected future short-term rates would be below current short-term rates, and the yield curve would slope downward and be inverted B. Segmented Markets Theory Segmented Markets theory: markets for different-maturity bonds are separate and segmented. The interest rate for each bond with a different maturity is determined by the supply and demand for that bond with no effects from expected returns on other bonds with other maturities The key assumption for this theory is that bonds of different maturities are not substitutes at all, so the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity (the complete opposite of the expectations theory) The argument for why bonds of different maturities are not substitutes is that investors have very strong preferences for bonds of one maturity but not for another, so they will be concerned with the expected returns only for bonds of the maturity they prefer This might occur because they have a particular holding period in mind and if they match the maturity of the bond to the desired holding period, they can obtain a certain return with no
risk at all (because if the term to maturity equals the holding period, the return is equal to the yield) E.g. if you were putting funds away for your child to go to college, your desired holding period will be longer, so you would want to hold longer-term bonds, and won’t care about shortterm If investors have short desired holding periods and generally prefer bonds with shorter maturities that have less interest-rate risk, the segmented markets theory can explain why yield curves typically slope upward In the typical situation where the demand for long-term bonds is relatively lower than that for short-term bonds, long-term bonds will have lower prices and higher interest rates, and hence the yield curve will typically slope upward C. Liquidity Premium and Preferred Habitat Theories Liquidity Premium Theory: the interest rate on a long-term bond will be an average of short-term interest rates expected to occur over the life of the long-term bond plus a liquidity/term premium that responds to supply and demand conditions for that bond The key assumption for this theory is that bonds of different maturities are substitutes in the sense that the expected return on one bond influences the expected return on a bond of a different maturity, but it also allows investors to prefer one bond maturity over another In other words, bonds of different maturities are assumed to be substitutes but not perfect Investors tend to prefer short-term bonds because these bonds bear less interest-rate risk
int =
it + ite+1 + ite+ 2 + ... + ite+( n −1) n
+ lnt
For these reasons, investors must be offered a positive liquidity premium to entice them to hold longer-term bonds. Thus, the liquidity premium theory is written as The liquidity/term premium is always positive and rises with the term to maturity of the bond (this is because the longer the term, the greater the interest-rate risk is, so the greater the compensation must be to hold on to the long-term bond) Preferred Habitat Theory: investors have a preference for bonds of one maturity over another, a particular bond maturity (preferred habitat) in which they prefer to invest Because they prefer the habitat of shorter-term bonds to that of longer-term bonds, they are willing to hold long-term bonds only if they have higher expected returns Since the liquidity premium is always positive and grows as the term to maturity increases, the yield curve implied by the liquidity premium theory is always above the yield curve implied by the expectations theory and has a steeper slope E.g. suppose that the one-year interest rate over the next 5 years is expected to be 5%, 6%, 7%, 8%, and 9%. Investors’ preference for holding short-term bonds have the liquidity premiums for one to five-year bonds as 0%, 0.25%, 0.5%, 0.75%, and 1%. What is the interest rate on an equivalent two-year bond and a five-year bond? Solution:
So how does the Liquidity Premium Theory explain all 3 facts? i. Fact 1 (Interest rates on different-maturity bonds move together over time) A rise in short-term interest rates indicates that short-term interest rates will, on average, be higher in the future, which implies that long-term interest rates will rise as well, since long-term interest rates are determined based on the expected future short-term rates ii. Fact 2 (Yield curves have an upward slope when short-term interest rates are low) If investors expect short-term interest rates to rise when they are low, the average of future expected short-term rates will be high relative to the current short-term rate With a positive liquidity premium, the long-term interest rates will be substantially above current short-term rates, and the yield curve would then have an upward slope Conversely, if short-term rates are high, people expect them to come back down. Tus long-term rates would drop below short-term rates because the average of expected future short-term rates would be below current short-term rates, and the curve will slope downward iii. Fact 3 (Yield curves typically slope upward) The liquidity premium rises with a bond’s maturity because of investors’ preferences for short-term bonds Even if short-term interest rates are expected to stay the same on average in the future, long-term interest rates will be above short-term interest rates and yield curves will typically slope upward because of the liquidity/term premium Liquidity Premium and Preferred habitat theories also tell us what the market is predicting about future short-term interest rates based on the slope of the yield curve: A steeply rising yield curve indicates that short-term interest rates are expected to rise in the future (figure a) A moderately steep yield curve indicates that short-term interest rates are not expected to rise or fall much in the future (figure b) A flat yield curve indicates that short-term rates are expected to fall moderately in the future (figure c) An inverted yield curve indicates that short-term interest rates are expected to fall sharply in the future (figure d)
D.
The Predictive Power of the Yield Curve
People often think that the slope of the yield curve can be used to forecast future shortterm interest rates The yield curve only has this use if it is determined by the expectations theory of the term structure that views long-term interest rates as the average of future short-term rates If there are liquidity/term premiums in the term structure then it will be difficult to extract a reliable forecast of future short-term interest rates without good measures of the premiums
6.3 – Using Term Structure to Forecast Interest Rates - Our discussion of the term structure of interest rates indicated that the slope of the yield curve tells us about the market’s prediction of the future path of interest rates - For example, a steeply upward-sloping yield curve tells us that short-term interest rates are predicted to rise in the future - However, a financial institution manager needs more specific information on interest-rate forecasts - So here, we show you how to generate specific forecasts of interest rates using the term structure - Recall that because bonds of different maturities are considered perfect substitutes, we assumed that the expected return over two periods from investing $1 in a two-period bond is and it must equal the expected return from investing $1 in one-period bonds
-
i et+1 is called the forward rate because it is the one-period interest rate that the pure
expectations theory indicates is expected to prevail one period in the future
-
However, since we are using the liquidity premium theory, the adjusted forward-rate forecast for one period in the future is
-
And the adjusted forward-rate forecast for n periods in the future is
2
(1+i 2t )
–1
6.1 – Risk Structure of Interest Rates (same maturity) - For bonds of the same maturity, interest rates on different categories of bonds differ from one another in any given year, and the spread (difference) between the interest rates varies over time - Bonds with the same maturity have different interest rates due to: Default risk Liquidity, and Tax considerations A. Default Risk Default Risk: 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 A corporation suffering big losses will be more likely to suspend interest payments on its bonds, thus the default risk on its bonds would be high On the other hand, Canadian government bonds are considered to have no default risk because the federal government can increase taxes to pay off its bonds (we call these defaultfree bonds) Risk Premium: the difference between the interest rates on bonds with default risk and default-free bonds of the same maturity, it tells us how much additional interest people must earn in order to be willing to hold that risky bond A bond with default risk always has a positive risk premium, the higher the default risk is, the larger the risk premium will be
-
Let us assume that initially corporate bonds have the same default risk as Canadian bonds In this case, these two bonds have the same attributes (identical risk and maturity) We can assume that their equilibrium prices and interest rates will initially be equal ( C
T
P1 =
P1
and
I C1 -
I T1
= 0)
C
I1
=
T
I 1 ) and the risk premium on corporate bonds will be zero (
If the risk default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease The theory of portfolio choice tells us that because the expected return on the corporate bond falls relative to the expected return on the default-free Canada bond while its relative riskiness rises, the corporate bond is less desirable and demand for it will fall At the same time, the expected return on default-free Canada bonds increases relative to the expected return on corporate bonds. So Canada bonds become more desirable and demand rises So now we see that the equilibrium price of corporate bonds has decreased, implying that the interest rate for corporate bonds has increased. We also see that the new equilibrium price of Canadian bonds has increased, causing the interest rate to fall -
Thus
I C1
>
I T1
, and
I C1
-
I T1
= Risk premium
So we can now conclude that a bond with default risk will always have appositive risk premium, and an increase in its default risk will raise the risk premium Credit-Rating Agencies: investment advisory firms that rate the quality of corporate and municipal bonds in terms of the probability of default Investment-grade securities: bonds with relatively low risk of default and have a rating of BBB and above Junk Bonds: bonds with ratings below BBB have higher default risk (speculative-grade) Fallen Angels: investment-grade securities whose rating has fallen to junk bond levels Corporate bonds always have higher interest rates than Canadian bonds because they always have some risk of default, whereas Canadian bonds do not Because corporate bonds have a greater default risk than Canadian bonds, their risk premium is greater, and the corporate bond rate therefore always exceeds the Canadian bond rate
Recession periods see a very high rate of business failures and defaults, thus there would be an increase in default risk for bonds issued by corporations, and the risk premium for corporate bonds would reach very high levels in this economic downturn B. Liquidity A liquid asset is one that can be quickly and cheaply converted into cash if the need arises The more liquid an asset is the more desirable it is, holding everything else constant Canadian bonds are the most liquid of all long-term bonds because they are so widely traded that they are the easiest to sell quickly and the cost of selling them is low Corporate bonds, on the other hand, are not as liquid because fewer bonds for any one corporation are traded, thus it can be costly to sell these bonds in an emergency because it may be hard to find buyers quickly The lower liquidity of corporate bonds relative to Canadian bonds increases the spread between the interest rates on these two bonds Once again, we assume that initially corporate and Canadian bonds are equally liquid and other attributes like maturity date are the same (so they will have the same price and interest rate) However, if corporate bond becomes less liquid than the Canadian bond because it is less widely traded, the theory of portfolio choice tells us that demand for corporate bonds will fall, while demand for Canadian bonds will rise, and thereby creating a spread between interest rates Therefore, the differences between interest rates on corporate bonds and Canadian bonds (that is the risk premiums) reflect not only the corporate bond’s default risk but its liquidity too
C. Income Tax Considerations In Canada, coupon payments on fixed-income securities are taxed as ordinary income in the year they are received (in the US, certain government bonds are not taxable) You earn more on a tax-exempt bond, so you are willing to hold the bond even though it has a lower interest rate than the taxable bond E.g. Option 1: Face value and purchase price of $1,000. Coupon and interest rate of 8%, tax free Option 2: FV and price of $1,000. Coupon and interest rate of 10%, 40% tax bracket We would pick Option 1 because our return would be $80 while Option 2 only gives us $60 Notice that the tax-exempt status of a bond becomes a significant advantage when income tax rates are very high D. Recap As a corporate bond’s default risk increases, the risk premium on that bond rises The greater the liquidity of Canadian bonds explains why their interest rates are lower than interest rates on less liquid corporate bond If a bond has favorable tax treatment, like interest payments are exempt from federal income taxes, its interest rate will be lower
6.2 – Term Structure of Interest Rates (different maturity) Bonds with identical risk, liquidity, and tax characteristics, may have different interest rates because the time remaining to maturity is different Yield Curve: plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations, describes the term structure of interest rates for bonds Yield curves can be upward sloping, flat, or downward sloping (inverted yield curve)
When the yield curves slope upward, the long-term interest rates are above the short-term rates When the yield curves are flat, short- and long-term interest rates are the same When the yield curves are inverted, long-term interest rates are below short-term interest rates There are 3 important facts about yield curves and term structure of interest rates: Fact 1: Interest rates on bonds of different maturities move together over time Fact 2: When short-term interest rates are low, yield curves have an upward slope; when short-term interest rates are high, yield curves are more likely to be inverted Fact 3: yield curves almost always slope upward There are 3 theories that explain these facts for the term structure of interest rates: Expectations theory (explains fact 1 & 2) Segmented markets theory (explains fact 3) Liquidity premium theory – combination of expectations and segmented (explains all 3 facts) These theories are important because they help us understand the shape of the yield curve, but also allow us to do 3 things: Forecast future interest rates Forecast future changes in economic activity and business cycle turning points Forecast future rates of inflation The Yield Curve:
A. Expectations Theory Expectations Theory: the interest rate on a long-term bond will be the average of shortterm interest rates that people expect to occur over the life of the long-term bond If people expect that short-term interest rates will be 10% on average over five years, the expectations theory says that the interest rate on bonds with five years to maturity will be 10% If short-term interest rates were expected to rise even higher after this 5-year period so that the average short-term interest rate over the coming 20 years is 11%, then the interest rate on 20-year bonds would be 11% and would be higher than the rate on 5-year bonds The expectations theory explains why interest rates on bond of different maturities differ; because short-term interest rates are expected to have different values at future dates The key assumption for 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 (perfect substitutes) If bonds with different maturities are perfect substitutes, the expected return on these bonds must be equal E.g. The 1-year interest rate over the next five years is expected to be 5%, 6%, 7%, 8%, and 9%. Given this, what are the interest rates on an equivalent two-year bond and five-year bond? The interest rate on the 2-year bond would be
And the interest rate on the 5-year bond would be We see that rising short-term interest rates produces an upward sloping yield curve along which interest rates rise as maturity lengthens And thus we have the general formula of The expectations theory explains why the term structure of interest rates changes at different times When the yield curve 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 currently above the short-term rate, the average of future short-term rates is expected to be higher than the current short-term rate When the yield curve is inverted, the average of future short-term interest rates is expected to be below the current short-term rate, implying that short-term interest rates are expected to fall, on average, in the future When the yield curve is flat, the expectations theory suggests that short-term interest rates are not expected to change, on average, in the future So how does the Expectations Theory help explain fact 1 and 2? i. Explaining Fact 1 (interest rates on bonds with different maturities move together) Historically, if short-term interest rates increase today, they tend to be higher in the future Hence, a rise in short-term rates will raise people’s expectations of future shortterm rates Since long-term rates are the average of expected future short-term rates, a rise in short-term rates will also raise long-term rates, both short- and long-term rates to move together ii. Explaining Fact 2 (yield curves have an upward slope when short-term interest rates are low) When short-term rates are low, people generally expect them to rise to some normal level in the future, and the average of future expected short-term rates is high relative to the current short-term rate. Therefore long-term interest rates will be substantially above current short-term rates, and the yield curve would then have an upward slope Conversely, if short-term rates are high, people usually expect them to come back down. So long-term rates would then drop below short-term rates because the average of expected future short-term rates would be below current short-term rates, and the yield curve would slope downward and be inverted B. Segmented Markets Theory Segmented Markets theory: markets for different-maturity bonds are separate and segmented. The interest rate for each bond with a different maturity is determined by the supply and demand for that bond with no effects from expected returns on other bonds with other maturities The key assumption for this theory is that bonds of different maturities are not substitutes at all, so the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity (the complete opposite of the expectations theory) The argument for why bonds of different maturities are not substitutes is that investors have very strong preferences for bonds of one maturity but not for another, so they will be concerned with the expected returns only for bonds of the maturity they prefer This might occur because they have a particular holding period in mind and if they match the maturity of the bond to the desired holding period, they can obtain a certain return with no
risk at all (because if the term to maturity equals the holding period, the return is equal to the yield) E.g. if you were putting funds away for your child to go to college, your desired holding period will be longer, so you would want to hold longer-term bonds, and won’t care about shortterm If investors have short desired holding periods and generally prefer bonds with shorter maturities that have less interest-rate risk, the segmented markets theory can explain why yield curves typically slope upward In the typical situation where the demand for long-term bonds is relatively lower than that for short-term bonds, long-term bonds will have lower prices and higher interest rates, and hence the yield curve will typically slope upward C. Liquidity Premium and Preferred Habitat Theories Liquidity Premium Theory: the interest rate on a long-term bond will be an average of short-term interest rates expected to occur over the life of the long-term bond plus a liquidity/term premium that responds to supply and demand conditions for that bond The key assumption for this theory is that bonds of different maturities are substitutes in the sense that the expected return on one bond influences the expected return on a bond of a different maturity, but it also allows investors to prefer one bond maturity over another In other words, bonds of different maturities are assumed to be substitutes but not perfect Investors tend to prefer short-term bonds because these bonds bear less interest-rate risk
int =
it + ite+1 + ite+ 2 + ... + ite+( n −1) n
+ lnt
For these reasons, investors must be offered a positive liquidity premium to entice them to hold longer-term bonds. Thus, the liquidity premium theory is written as The liquidity/term premium is always positive and rises with the term to maturity of the bond (this is because the longer the term, the greater the interest-rate risk is, so the greater the compensation must be to hold on to the long-term bond) Preferred Habitat Theory: investors have a preference for bonds of one maturity over another, a particular bond maturity (preferred habitat) in which they prefer to invest Because they prefer the habitat of shorter-term bonds to that of longer-term bonds, they are willing to hold long-term bonds only if they have higher expected returns Since the liquidity premium is always positive and grows as the term to maturity increases, the yield curve implied by the liquidity premium theory is always above the yield curve implied by the expectations theory and has a steeper slope E.g. suppose that the one-year interest rate over the next 5 years is expected to be 5%, 6%, 7%, 8%, and 9%. Investors’ preference for holding short-term bonds have the liquidity premiums for one to five-year bonds as 0%, 0.25%, 0.5%, 0.75%, and 1%. What is the interest rate on an equivalent two-year bond and a five-year bond? Solution:
So how does the Liquidity Premium Theory explain all 3 facts? i. Fact 1 (Interest rates on different-maturity bonds move together over time) A rise in short-term interest rates indicates that short-term interest rates will, on average, be higher in the future, which implies that long-term interest rates will rise as well, since long-term interest rates are determined based on the expected future short-term rates ii. Fact 2 (Yield curves have an upward slope when short-term interest rates are low) If investors expect short-term interest rates to rise when they are low, the average of future expected short-term rates will be high relative to the current short-term rate With a positive liquidity premium, the long-term interest rates will be substantially above current short-term rates, and the yield curve would then have an upward slope Conversely, if short-term rates are high, people expect them to come back down. Tus long-term rates would drop below short-term rates because the average of expected future short-term rates would be below current short-term rates, and the curve will slope downward iii. Fact 3 (Yield curves typically slope upward) The liquidity premium rises with a bond’s maturity because of investors’ preferences for short-term bonds Even if short-term interest rates are expected to stay the same on average in the future, long-term interest rates will be above short-term interest rates and yield curves will typically slope upward because of the liquidity/term premium Liquidity Premium and Preferred habitat theories also tell us what the market is predicting about future short-term interest rates based on the slope of the yield curve: A steeply rising yield curve indicates that short-term interest rates are expected to rise in the future (figure a) A moderately steep yield curve indicates that short-term interest rates are not expected to rise or fall much in the future (figure b) A flat yield curve indicates that short-term rates are expected to fall moderately in the future (figure c) An inverted yield curve indicates that short-term interest rates are expected to fall sharply in the future (figure d)
D.
The Predictive Power of the Yield Curve
People often think that the slope of the yield curve can be used to forecast future shortterm interest rates The yield curve only has this use if it is determined by the expectations theory of the term structure that views long-term interest rates as the average of future short-term rates If there are liquidity/term premiums in the term structure then it will be difficult to extract a reliable forecast of future short-term interest rates without good measures of the premiums
6.3 – Using Term Structure to Forecast Interest Rates - Our discussion of the term structure of interest rates indicated that the slope of the yield curve tells us about the market’s prediction of the future path of interest rates - For example, a steeply upward-sloping yield curve tells us that short-term interest rates are predicted to rise in the future - However, a financial institution manager needs more specific information on interest-rate forecasts - So here, we show you how to generate specific forecasts of interest rates using the term structure - Recall that because bonds of different maturities are considered perfect substitutes, we assumed that the expected return over two periods from investing $1 in a two-period bond is and it must equal the expected return from investing $1 in one-period bonds
-
i et+1 is called the forward rate because it is the one-period interest rate that the pure
expectations theory indicates is expected to prevail one period in the future
-
However, since we are using the liquidity premium theory, the adjusted forward-rate forecast for one period in the future is
-
And the adjusted forward-rate forecast for n periods in the future is
2
(1+i 2t )
–1
