Homework #2 - FIU Faculty Websites

Homework Assignment #2
ECO 3223, Summer 2015
Instructions: Answer each of the following questions, showing your work where
appropriate.
Due: Wednesday, June 3rd at the beginning of class.
1. According to the theory of portfolio choice (see chapter 5 of the textbook), what are
the four primary determinants of demand for an asset? Which of those
determinants would be affected by an increase in the current price of an asset, all
else equal? What would happen to the quantity of the asset demanded as a
consequence? Explain.
2. Use the textbook’s supply/demand model of the bond market to predict how each
of the following shocks would likely affect bond prices and the overall level of
interest rates, all else equal. In each case, be sure to (1) clearly state the predicted
direction of change for both bond prices and interest rates, (2) depict the impact of
the shock on bond prices with a supply/demand diagram, and (3) explain your
predictions intuitively in words.
a. The price of gold (an alternative investment for potential bondholders) suddenly
becomes more volatile.
b. A central bank announcement increases the future level of interest rates expected
by investors.
c. Federal income tax rates are increased.
d. An economic upturn results in rising real GDP and expanded fixed investment
opportunities for businesses.
3. At the onset of recessions, the “spread” between corporate bond yields and
Treasury bond yields typically increases (i.e. – the yield to maturity offered by
corporate bonds rises relative to the yield to maturity offered by T-bonds). Use the
textbook’s supply/demand model of the bond market to explain this observation.
Hint: a recession affects the probability of corporate bond defaults.
4. What is meant by “money demand” in Keynes’ Liquidity Preference Theory?
According to that theory, what determines a nation’s aggregate money demand?
Explain.
5. Use the Keynesian model of “Liquidity Preference Theory” to predict how each of
the following shocks would likely affect a nation’s overall level of interest rates in
the short run, all else equal. In each case, be sure to (1) clearly state the predicted
direction of change for interest rates, (2) depict the impact of the shock with a
supply/demand diagram, and (3) explain your predictions intuitively in words.
a. An economic downturn causes real aggregate income to fall
b. The central bank reduces the size of the money supply
c. An energy price shock increases the overall level of prices for goods and services
6. What is a “yield curve”? Do yield curves normally slope up or down? Why?
7. Suppose that 1-year bonds currently offer a nominal yield to maturity of 4%
(𝑖1,0 = 0.04), otherwise comparable 2-year bonds currently offer a yield to maturity of
3% (𝑖2,0 = 0.03), and 3 year bonds currently offer a yield to maturity of 2.5% (𝑖3,0 =
0.025).
a. Based on the Expectations Theory of term structure, what do investors expect the
𝑒
yield on 1 year bonds to be next year (i.e. - 𝑖1,1
)?
𝑒
b. What do investors expect to be the yield on 1 year bonds in two years (i.e. - 𝑖1,2
)?
𝑒
c. What do investors expect to be the yield on 2 year bonds, next year (i.e. - 𝑖2,1
)?
8. According to the Expectations Theory of term structure, interest rates will always
settle at values that equate the gross return on a two year bond (i.e. – (1 + 𝑖2,0 )2) with
𝑒
the gross return on a sequence of two 1 year bonds (i.e. - (1 + 𝑖1,0 )(1 + 𝑖1,1
)). Show
that this condition will be met if and only if the expected 1 year holding period rates of
return on 1 year and 2 year zero coupon bonds are equal.
9. What is “interest rate arbitrage”? Why don’t interest rate arbitrage opportunities last
long?
10. Suppose that today’s interest rate on 1-year bonds is 4% (i1, 0 = 0.04). Interest rates
on 1-year bonds next year, in two years, and in three years are expected to be 5%, 6%,
and 6%.
a. According to the Expectations Theory of term structure, what are the equilibrium
interest rates today on otherwise comparable 2-year, 3-year, and 4-year bonds?
b. Draw the yield curve for that case.
c. Now suppose that investors require a “risk premium” of rp(n) = (n/2)%, where n
denotes the term to maturity in years, to hold bonds with a term to maturity greater
than 1. What would today’s interest rates be for 2-year, 3-year, and 4-year bonds in
that case?
d. Draw the corresponding yield curve.
11. If inflation and interest rates become more volatile, what would you expect to happen
to the slope of the yield curve (up, down, or no change)? Explain.
12. Suppose you know for sure that interest rates are going to fall over the upcoming year.
Which would you rather hold: a long term bond or a short term bond? Why? Assume the
bonds are comparable in all other respects (face value, coupon rate, yield to maturity,
default risk, etc.) and that you only plan to hold the bond for 1 year. Now suppose you
know interest rates will change over the upcoming year, but you don’t know whether
they will rise or fall. Which would you rather hold if you are “risk averse”: a long term
bond or a short term bond? Why?
13. Suppose that bond A and bond B have equal face values, equal coupon rates, and equal
terms to maturity, but that bond A has a higher default risk than bond B. Which bond
will sell at a higher price? Which bond will offer a higher interest rate? Explain.
14. What is the “default risk” on a bond? What sort of bond has the lowest default risk?
What is the “interest rate risk” on a bond? What sort of bond has the lowest interest
rate risk?
15. Bond A is a 4 year coupon bond with a 60% coupon rate, a $1000 face value, and a 2%
yield to maturity. Bond B is a comparable (i.e. – with similar liquidity, default risk, and
tax treatment) 3 year coupon bond with a 60% coupon rate, a $1000 face value, and 2%
yield to maturity. Bond C is a comparable 3 year, zero coupon bond with a $1000 face
value and a 2% yield to maturity.
a. Calculate the “duration” of all three bonds.
b. Which bond is the most risky? Explain.
c. Which bond is the least risky? Explain.
16. Suppose that your local government, threatened by bankruptcy, decides to tax the
interest income on its own bonds as part of an effort to rectify its budgetary woes. If
bondholders care about their after-tax returns, what would you expect to happen to the
prices of local municipal bonds? To their yields? Explain.