Review questions

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Review questions

• 1. Discuss the factors that determine the shape
  and level of a yield curve. How do term to
  maturity, credit risk, and tax treatment affect
  the interest rate on a particular asset?

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• A yield curve is a graphic representation of the
  relationship between interest rates (yields) on a
  particular security and its term to maturity. The
  time to maturity is measured on the horizontal
  axis and the interest rate (yield) on the
  vertical axis. The relationship between the term
  to maturity and interest rate is what determines
  the shape and level of a yield curve.
• Term to maturity, credit risk, and tax treatment
  are all determinants of the interest rate on a
  particular asset. If credit risk, interest
  rates, or tax treatment change, the yield curve
  shifts.

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• 2.Explain why a yield curve can be negatively
  sloped. Would interest rates be abnormally high
  or low? What would be the overall expectation of
  the direction of future short-term interest
  rates?

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• A yield curve can be negatively sloped when the
  yield declines as the term to maturity increases.
  In this case, interest rates are generally
  abnormally high and short-term interest rates are
  expected to decline in the future.

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• 3.According to the expectations theory, how is
  the long-term interest rate determined? Why is
  the geometric average used instead of the simpler
  arithmetic average?

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• According to the expectations theory, the
  long-term interest rate is the geometric average
  of the current short-term rate and the expected
  future short-term rate expected to prevail over
  the term to maturity of the longer-term security.
  The geometric average is used instead of the
  simpler arithmetic average in order to take
  account of the effects of compounding.

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• 4.BBB-rated corporate bonds are riskier than
  AAA-rated bonds. Explain where the two yield
  curves will lie relative to each other. What
  could cause the spread to widen?

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• The yield curve for BBB-rated bonds would lie
  higher than the yield curve for AAA-rated
  corporate bonds. The spread could widen if
  BBB-rated bonds became riskier relative to AAA
  corporate bonds or if AAA corporate bonds became
  safer relative to BBB bonds.

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• 5.What determines expectations? Are expectations
  about future prices independent of expectations
  about future money supply growth rates? Why or
  why not?

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• Interest rate expectations are determined by
  expectations about the money supply, national
  income or gross domestic product, and inflation.
  Expectations about future prices are not
  independent of expectations about future money
  supply growth rate because the larger the supply
  of money, the more prices will be expected to
  rise.

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• 6.Could the yield curve for municipals ever lie
  above the yield curve for government securities?
  (Hint Consider all tax rates.) What effect
  would an increase in marginal tax rates have on
  the position of the yield curve for municipals?

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• Under normal circumstances, the yield curve for
  municipals lies below the yield curve for
  government securities because the interest earned
  on municipals is tax free. If the interest
  earned on municipals were taxed at the same rates
  as interest on government securities, then the
  yield curve for municipals could lie above the
  yield curve for government securities because
  municipals are less liquid (have less developed
  secondary markets) than government securities. An
  increase in marginal tax rates could lower the
  position of the yield curve for municipals and
  widen the spread between the yield curve for
  municipals and government securities.

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• 7.Use the liquidity premium to give an
  explanation for why yield curves have most often
  been upward sloping over the past 50 years.
  Could a yield curve be upward sloping even if
  short-term rates were expected to remain
  constant? If interest rates are expected to fall
  dramatically, under what conditions would the
  yield curve still be upward sloping?

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• Yield curves have most often been upward sloping
  over the past forty-five years because lenders
  have required a higher return to lend long term
  rather than short term. This extra sweetener is
  called the liquidity premium.
• A yield curve could be upward sloping even if
  short-term rates were expected to remain constant
  because of the liquidity premium that lenders
  require to lend long term rather than short term.
• If interest rates are expected to fall
  dramatically, the yield curve would be upward
  sloping only if the liquidity premium was large
  enough to offset the expectations of lower
  interest rates in the future.

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• 8.Define preferred habitats. Explain how this
  modification affects the expectations theory.
  What could cause market segmentation based on
  preferred habitats to break down? How is the
  market segmentation hypothesis different from the
  expectations theory?

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• "Preferred habitats" is the name given to the
  theory that borrowers and lenders have preferred
  maturities in which they wish to borrow and lend.
  While the expectation theory suggests that
  lenders and borrowers have no preference between
  long- and short-term securities, preferred
  habitats suggests differently.
• Market segmentation based on preferred habitats
  could break down due to changes in liquidity
  premiums or if rate spreads widen enough to
  entice(??) borrowers and lenders to leave their
  traditional borrowing and lending markets.

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• 9.Discuss the following statements Over a
  typical cycle, the movement of the yield curve is
  like the wagging of a dogs tail. The entire
  tail wags, but short-term rates wag more than
  long-term rates.

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• According to the expectations theory, the
  long-run rate is the geometric average of the
  current short rate and the future short rates
  expected to prevail over the term to maturity of
  the longer-term security. It is reasonable to
  conclude that short-term rates will vary more
  than long-term rates because long-term rates are
  averaged so they dont tend to be
  scattered(???,???)as much as short-term rates.

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• 10.If yield curves became flatter (steeper), what
  does this say about expectations of future
  interest rates?

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• Flatter yield curves for certain years suggest
  that the spread between present short-term and
  expected future short-term rates has narrowed.
  Flatter yield curves suggest that short-term
  interest rate expectations have been revised
  downward. If yield curves becomes steeper, this
  suggests that expectations about future
  short-term rates have been revised upward.

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• 11.What would happen to the risk premium if the
  economy went into a strong expansion? A deep
  recession?

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• If the economy went into a strong expansion,
  there would be less risk of default, and risk
  premiums would decrease. In this case, the spread
  between government default risk-free securities
  and other securities would narrow. If on the
  other hand the economy went into a deep
  recession, default risk would increase and so
  would risk premiums. The spread between
  government default risk-free securities and other
  securities would widen.

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Analytical Questions

• 12.If the current short-term rate is 5 percent
  and the expected short-term rate is 8 percent,
  what is the long-term interest rate? (Use the
  expectations theory.)

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• Based on the expectations theory, the long-term
  rate is the geometric average of the current
  short-term rate and the expected future
  short-term rate (il (1 is)(1 ise)1/2
  1). Solving for the geometric average in this
  case, we get that the long-term rate is 6.58
  percent.

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• 13.If the current short-term rate is 5 percent
  and the current long-term rate is 4 percent, what
  is the expected short-term interest rate? (Use
  the expectations theory.)

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• Based on the expectations theory, if we know the
  current short-term rate and the current long-term
  rate, we can solve for the expected short-term
  interest rate by plugging the long-term and
  short-term rates into the formula (il (1
  is)(1 ise)1/2 1) and solving for ise. In
  this case, the expected short-term rate is 3.01
  percent.

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• 14.Rework questions 12 and 13 assuming that there
  is no compounding. (Hint Use the simple
  arithmetic average instead of the geometric
  average.)

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• Using the simple arithmetic average that ignores
  the effects of compounding, the long-term rate is
  6.5 percent ((5 percent 8 percent)/2 13
  percent/2 6.5 percent)).
• Using the simple arithmetic average, the expected
  short-term interest rate is 3 percent. This can
  be found by solving for the expected short-term
  rate in the following equation ((is ise)/2
  il). Substituting for the short and long-term
  rates and solving for ise, we get ise 3 percent
  ((5 percent ise)/2 4 percent)).

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• 15.Assume that current interest rates on
  government securities are as follows one-year
  rate, 5 percent two-year rate, 6 percent
  three-year rate, 6.5 percent four-year rate, 7
  percent. Graph the yield curve.

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• 16.Given the yield curve in question 15, what is
  the expected direction of future one-year rates?
  Under what circumstances would one-year rates be
  expected to decline?

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• According to the pure expectations theory,
  short-term rates are expected to rise.
• However, we are not certain that this is the case
  because we don't know the magnitude of the
  liquidity premium. If the liquidity premium is
  larger than the difference between current
  long-term rates and the current short-term rates,
  then expected short-term rates would actually be
  expected to fall. If the liquidity premium is
  equal to the difference between current long-term
  and current short-term rates, then short-term
  interest rates would be expected to remain the
  same. If the liquidity premium is smaller than
  the difference between current long and current
  short-term rates, then indeed short-term rates
  are expected to rise.

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• 17.If a taxpayers marginal tax rate is 33
  percent, what is the after-tax yield on a
  corporate bond that pays 5 percent interest? If
  the average marginal tax rate of all taxpayers is
  50 percent, will the taxpayer with the 33 percent
  marginal tax rate prefer a corporate or a
  municipal security? Assume equivalent safety and
  maturity.

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• If a taxpayer's marginal tax rate is 33 percent,
  the after tax yield on a corporate bond that pays
  5 percent interest is 3.35 percent interest (5
  percent (5 percent x .33 percent) 3.35
  percent). The rate on municipal securities will
  gravitate to the rate where the average taxpayer
  is indifferent between a municipal security and a
  corporate security of equivalent safety and
  maturity. If the marginal tax rate of all
  taxpayers is 50 percent, the municipal security
  will pay 2.5 percent (5 percent (5 percent x 50
  percent) 2.5 percent). A taxpayer with a 33
  percent marginal tax rate will prefer a corporate
  security because it has a higher after-tax return
  of 3.35 percent.

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• 18.Go to the Wall Street Journal and gather data
  on interest rates for government securities of
  various maturities for today. Graph the yield
  curve. (Hint Check your answer by looking at
  the yield curve for Treasury securities that the
  Journal publishes daily in Part C.)
• This answer will vary depending on the dates the
  students choose.

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• 19.What would happen to interest rates, given
  each of the following scenarios?
• a. The government increases marginal tax rates.
• b. The tax exemption on municipals is
  eliminated.
• c. Corporate profits fall severely.
• d. The federal government guarantees that the
  interest and principal on corporate bonds will be
  paid.
• e. A broader secondary market for government
  agency securities develops.

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• a. The rate on municipal securities will fall so
  that the taxpayer in the average marginal tax
  bracket is indifferent between municipals and
  other securities of equivalent risk and maturity.
  
• b. The rate on municipal securities will increase
  until the after-tax return on municipals is the
  same as other securities of equivalent risk and
  maturity.
• c. The default risk for corporate securities will
  increase and the spread between the yield curves
  for corporate and other municipal and government
  securities will widen.
• d. The default risk for corporate securities will
  decrease. The spreads between corporate
  securities and other government and municipal
  securities will decrease.
• e. The spread between the yield curve for
  government securities and government agency
  securities will narrow.

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• 20.Draw the yield curve assuming future
  short-term rates are expected to remain constant
  and the liquidity premium is positive. Now
  assume that net lenders increase their preference
  for short-term securities. Show what happens to
  the yield curve.

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The Role of Liquidity Premiums
Yield to Maturity (percent)
Term to Maturity
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When net lenders increase their preference for
short-term securities, the yield curve becomes
steeper as short-term rate decrease relative to
long term rates.
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When net lenders increase their preference for
short-term securities, the yield curve becomes
steeper as long term rates increase relative to
short-term rate.
Yield to Maturity (percent)
original yield curve
5.99
5
1
2
Term to Maturity