Problem 1:Now is t = 0. You have $20,000 that you are willing to investing for 3 years. You are considering three different potential strategies. They are:
Strategy 1: Invest in a 3 year zero with a current (i.e., t = 0) yield to maturity of 3 percent.
Strategy 2: Invest in a 1-year zero with a current (i.e., t = 0) yield to maturity of 1 percent; then next year (when the current 1-year zero matures) invest in a two year zero at whatever the yield to maturity on two-year zeros are then (at t = 1).
Strategy 3: Invest in a 5 year zero with a current yield to maturity of 3.5 percent and sell these bonds in three years (at t = 3).
If the yield curves at t = 1 and t = 3are as shown below, which of these three strategies will turn out the best? That is, after 3 years, which strategy will generate the largest amount of money?
t = 1 Yield Curve: t = 3 Yield Curve: .
Time to maturity YTM Time to Maturity YTM
(in years) (in years)
1 .02 1 .02
2 .022 2 .025
3 .025 3 .035
4 .030 4 .045
Problem 2:The default-free yield curve on zero-coupon U.S. Government Treasury securities is given below.
Maturity (in years) Rate
1 .01
2 .015
3 .02
4 .025
5 .0275
6 .03
Currently you can buy a corporate bond sold by a company that has some chance of defaulting in the future. This corporate bond matures in 5 years, pays a 5 percent coupon once a year, and has a face value of $1000
a. If there is no chance of default what would be the price of this corporate bond? Hint: if there is no chance of default, then the required rates of return for money at various horizons is given by the Treasury zero yield curve above. Given these rates, what would be the price of the corporate bond?
b. If there was a default-free bond with the same cash flows as the corporate bond described above, what would its price be? What would its yield to maturity be? Hint: Use goal seek to figure out the single rate YTM when applied to the cash flows implied a present value equal to the price you just derived.
c. The current price of the corporate bond with default risk is $1075 per $1000 in face value. What is the YTM on this bond? What is the annualized default risk premium on this bond (that is, what is the extra return per annum that this bond would return over a default free bond with the same payment stream)?