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.