Chapter 12: The Risk and Term Structure of Interest Rates Flashcards
risk structure of interest rates
The relationship of bonds with the same term to maturity with different interest rates
risk and liquidity both play a role in determining the risk structure
term structure of interest rates
the relationship among interest rates on bonds with different terms to maturity
A bond’s term to maturity that also affects its interest rate
risk of default
influences a bond’s interest rate
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
a corporation facing big losses has more or less chances of having bonds that have risk of default?
more
why do government bonds usually have no default risk?
the federal government can always increase taxes to pay off its obligations
default-free bonds
default-free bonds
bonds that have no default risk
bond risk premium
The spread between the interest rates on bonds with default risk and default-free bonds
indicates how much additional interest people must earn in order to be willing to hold that risky bond
what happens to the risk premium of a corporate bond if its default risk increases (because corporation is bugging or something like that)?
why?
an increase in its default risk will raise the risk premium
the expected return on the corporate bond falls relative to the expected return on the default-free government bond while its relative riskiness rises
the corporate bond is less desirable and demand for it will fall (shift to the left)
it will reduce the corporate bond price and raise interest
the expected return on default-free government bonds increases relative to the expected return on corporate bonds while their relative riskiness declines
the demand for government bonds increases (shift to the right)
it will increase the government bond price and decrease interest
the risk premium is the difference between corporate interest (which is now higher) ad the risk free government bods (which is ow lower)
a bond with a default risk will always have a positive or negative risk premium?
a bond with default risk will always have a positive 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
have a rating of BBB ad above
speculative-grade or junk bonds
Bonds with ratings below BBB
have higher default risk
why are speculative-grade or junk bonds also referred to as high-yield bonds
Because these bonds always have higher interest rates than investment-grade securities
fallen angels
Investment-grade securities whose rating has fallen to junk levels
liquid asset
one that can be quickly and cheaply converted into cash if the need arises
attributes that influence bond risk structures (the relationship among interest rates on bonds with the same maturity) and interest rates
default risk
liquidity
the income tax treatment of the bond s interest payments
true or false
The more liquid an asset is, the more desirable
true
which bonds are the most liquid of all long term bonds?
why?
Canada bonds
because they are so widely traded that they are the easiest to sell quickly and the cost of selling them is low
why are corporate bonds not that liquid?
because fewer bonds for any one corporation are traded
it can be costly to sell these bonds in an emergency because it may be hard to find buyers quickly
how does the liquidity of corporate bonds from a company bugging the interest premium? why?
harder to sell them since they lose liquidity
they become less desirable and governments bonds more desirable
corporate bond price will fall ad their interest will rise
government bond prices will rise and their interests will fall
the risk premium will increase
why is a risk premium more accurately defined as risk and liquidity premium?
he differences between interest rates on corporate bonds and Canada bonds (that is, the risk premiums) reflect not only the corporate bond’s default risk but its liquidity too
in canada, how are coupon payments on fixed-income securities taxed?
are taxed as ordinary income in the year they are received
how can taxes influence how desirable a bond can be?
if in canada, you got a bond that has a higher interest than an American one, but after tax its lower, you ill want the American one
how can bonds with identical risk, liquidity, and tax characteristics have different interest rates?
because the time remaining to maturity is different
yield curve
A graph of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations
it describes the term structure of interest rates for particular types of bonds, such as government bonds
inverted yield curve
downward- sloping yield curves
how can yield curves be classified?
upward-sloping
flat
downward- sloping
what does it mean when yield curves slope upward?
the long-term interest rates are above the short-term interest rates
what does it mean when yield curves are flat?
short- and long-term interest rates are the same
what does it mean when yield curves are inverted (downward sloping)?
long-term interest rates are below short-term interest rates
three important empirical facts of the term structure of interest rates
- interest rates on bonds of different maturities move together over time
- 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
- Yield curves almost always slope upward
Four theories have put forward to explain the term structure of interest rates
(1) the expectations theory
(2) the segmented markets theory
(3) the liquidity premium theory
(4) the preferred habitat theory
which facts does expectations theory explain
- interest rates on bonds of different maturities move together over time
- 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
vags on the third empirical fact
which facts does the segmented markets theory explain
can explain fact 3 (Yield curves almost always slope upward)
does not explain the other two empirical facts
which theories explain all three of the empirical rules of the term structure of interest rates
the liquidity premium theory
preferred habitat theory
The expectations theory of the term structure
the interest rate on a long-term bond will equal an average of short-term interest rates that people expect to occur over the life of the long-term bond
r example, if people expect that short-term interest rates will be 10% on average over the coming five years, the expectations theory predicts that the interest rate on bonds with five years to maturity will be 10% too
perfect substitute bonds
bonds with different maturities are perfect substitutes, the expected return on these bonds must be equal
what is the key assumption behind the expectations theory?
buyers of bonds do not prefer bonds of one maturity over another
they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity
what are is the formula for the yields of bonds that don’t have the same maturity under the expectations theory?
the formula for the term structure of bonds under the expectations theory
what does it explain?
i_n = ie_+(n-1)
n is the amount of periods
the n-period interest rate equals the average of the one-period interest rates expected to occur over the n-period life of the bond
segmented markets theory of the term structure
sees markets for different maturity bonds as completely separate and segmented
under the segmented markets theory, how is the interest rate for each bond with a different maturity determined?
by the supply of and demand for that bond with no effects from expected returns on other bonds with other maturities
what is the key assumption in the segmented markets theory?
bonds of different maturities are not substitutes at all
the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity
how would you compare the expectations theory and the segmented markets theory?
as complete opposites
how does the segmented markets theory explain that bonds of different maturities are not substitutes?
investors have very strong preferences for bonds of one maturity but not for another
they will be concerned with the expected returns only for bonds of the maturity they prefer
how is the return of a bond when the holding period equals the term to maturity?
the return is known for certain because it equals the yield exactly
there is no interest-rate risk
how does the segmented markets theory explain the third empirical fact?
investors generally prefer bonds with shorter maturities that have less interest-rate risk
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
hence the yield curve will typically slope upward
how does the the segmented markets theory fail to explain empirical facts 1 and 2?
Because it views the market for bonds of different maturities as completely segmented, there is no reason for a rise in interest rates on a bond of one maturity to affect the interest rate on a bond of another maturity
Therefore, it cannot explain why interest rates on bonds of different maturities tend to move together (fact 1)
the theory cannot explain why yield curves tend to slope upward when short-term interest rates are low and to be inverted when short-term interest rates are high (fact 2)
because it is not clear how demand and supply for short- versus long-term bonds change with the level of short-term interest rates
The liquidity premium theory of the term structure
states that the interest rate on a long-term bond will equal an average of short-term interest rates expected to occur over the life of the long-term bond plus a liquidity premium that responds to supply and demand conditions for that bond
liquidity premium also referred to as a term premium
The liquidity premium theory’s key assumption
bonds of different maturities are substitutes
this means that the expected return on one bond does influence the expected return on a bond of a different maturity
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 substitutes
The liquidity premium theory
induces investors to hold longer-term bonds because they tend to prefer shorter-term
The liquidity premium theory formula
i_nt = i_t+(n-1) + l_nt
l_nt = the liquidity (term) premium for the n-period bond at time t
l_nt is always positive and rises with the term to maturity of the bond
n = the term to maturity of the bond
the preferred habitat theory
assumes that investors have a preference for bonds of one maturity over another
a particular bond maturity (preferred) in which they prefer to invest
the preferred habitat theory, when will investors invest in a bond that does not have the preferred maturity (habitat)?
only if they earn a somewhat higher expected return
under the preferred habitat theory, when will investors invest in a long term bond? why’
only if they have higher expected returns
because investors are likely to prefer the habitat of short-term bonds to that of longer-term bonds
why is the yield curve implied by the liquidity premium and preferred habitat theories always above the yield curve implied by the expectations theory and why does it have a steeper slope?
because the liquidity premium is always positive and typically grows as the term to maturity increases
how do the liquidity premium and preferred habitat theories explain fact 1
(that 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
i_nt = i_t+(n-1) + l_nt
i_t+(n-1) implies that long-term interest rates will rise along with them
how do the liquidity premium and preferred habitat theories explain fact 2
(yield curves tend to have an especially steep upward slope when short-term interest rates are low and to be inverted when short-term rates are high)
Because investors generally expect short-term interest rates to rise to some normal level when they are low, the average of future expected short-term rates will be high relative to the current short-term rate
long-term interest rates will be substantially above current short-term rates, and the yield curve would then have a steep upward slope with the additional boost of a positive liquidity premium
if short-term rates are high, people usually expect them to come back down
Long-term rates would then drop below short-term rates because the average of expected future short-term rates would be so far below current short-term rates that despite positive liquidity premiums, the yield curve would slope downward
how do the liquidity premium and preferred habitat theories explain fact 3
(yield curves typically slope upward)
it recognizes that 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
How can the liquidity premium and preferred habitat theories explain the occasional appearance of inverted yield curves if the liquidity premium is positive?
at times short-term interest rates are expected to fall so much in the future that the average of the expected short-term rates is well below the current short-term rate
Even when the positive liquidity premium is added to this average, the resulting long-term rate will still be below the current short-term interest rate
according to the liquidity premium and preferred habitat theories, what does a steeply rising yield curve indicate?
indicates that short-term interest rates are expected to rise in the future
according to the liquidity premium and preferred habitat theories, what does a moderately steep rising yield curve indicate?
indicates that short-term interest rates are not expected to rise or fall much in the future
according to the liquidity premium and preferred habitat theories, what does a flat yield curve indicate?
indicates that short-term rates are expected to fall moderately in the future
according to the liquidity premium and preferred habitat theories, what does an inverted yield curve indicate?
indicates that short-term interest rates
are expected to fall sharply in the future
why should yield curves also forecast inflation and real output fluctuations? how?
Because the yield curve contains information about future expected interest rates
the yield curve contains information not only about the future path of nominal interest rates, but about future inflation as well
what are rising interest rates associated with? economic booms or recessions
economic booms
what are falling interest rates associated with? economic booms or recessions
recessions
what does a lat or negatively sloped yield curve indicate when talking about inflation and economic situation?
the economy is more likely to enter a recession
a future fall in inflation
the forward rate
ie_+1
the one-period interest rate that the pure expectations theory of the term structure indicates is expected to prevail one period in the future
the settlement price of a transaction that will not take place until a predetermined date
it is forward-looking
spot rates
the price for a commodity being traded immediately, or “on the spot”
the current market value of an asset at the moment of the quote
adjusted forward-rate forecast
ie_t+n
this is the equivalent to the formula to allow for liquidity premiums
The difference between the expectations and liquidity premium theories’ formulas
They are practically the same, but the liquidity premium theory adds l_nt
l_nt is the liquidity premium for the n period bond at time t (when you buy it)
l_nt is always positive and increases the longer the term to maturity
Why is the yield curve implied by the liquidity premium theory always steeper than the expectations theory?
Because of the former’s liquidity premium, which only grows the longer the term to maturity of the bond
