1. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.
$100 par of a 0.5-year 10%-coupon bond has a price of $102.
$100 par of a 1-year 12%-coupon bond has a price of $105.
a. What is the price of $1 par of a 0.5-year zero?
b. What is the price of $1 par of a 1-year zero?
c. Suppose $100 of a 1-year 8%-coupon bond has a price of $99. Is there an arbitrage opportunity? If so, how?
d. What is the 0.5-year zero rate?
e. What is the 1-year zero rate?
f. What is the 1-year par rate, i.e., what coupon rate would make the price of a 1-year
coupon bond equal to par?
g. Considering the shape of the yield curve, should the yield on the 1-year 12%-coupon bond be higher or lower than the 1-year par rate?
2. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.
The 0.5-year zero rate is 6% and the 1-year zero rate is 8%.
a. What is the price of:
b. What is the dollar duration of:
c. What is the duration of:
d. Use dollar duration to estimate the change in value of $1,000 par of the 1-year 8%-
i. $1 par of a 0.5-year zero?
ii. $1 par of a 1-year zero?
iii. $100 par of a 1-year 8%-coupon bond, in the absence of arbitrage?
i. $1 par of a 0.5-year zero?
ii. $1 par of a 1-year zero?
iii. 100 par of a 1-year 8%-coupon bond?
i. $1 par of a 0.5-year zero
ii. $1 par of a 1-year zero?
iii. $100 par of a 1-year 8%-coupon bond?
coupon bond if all zero rates rise 100 basis points.