1. 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
7. Suppose that 1-year bonds currently offer a nominal yield to maturity of 4% (??1,0=0.04), otherwise comparable 2-year bonds currently offer a yield to maturity of 3% (??2,0=0.03), and 3 year bonds currently offer a yield to maturity of 2.5% (??3,0=0.025).
a. Based on the Expectations Theory of term structure, what do investors expect the yield on 1 year bonds to be next year (i.e. –??^e1,1)?
b. What do investors expect to be the yield on 1 year bonds in two years (i.e. –??^e1,2)?
c. What do investors expect to be the yield on 2 year bonds, next year (i.e. –??^e2,1)?
3 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+??2,0)2) with the gross return on a sequence of two 1 year bonds (i.e. -(1+??1,0)(1+??1,1??)). 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.
4. 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.
5. 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 couponbond 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.
6. 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.
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