Determine the optimal hedge ratio for Treasury bonds worth $1,000,000 with a duration of 12.45 yielding 11.9% if the futures has a price of $90,000, a duration of 8.5 years and an implied yield of 9.5%.

a. 16.27

b. 16.63

c. 7.42

d. 11.11

e. cannot be determined

Determine the optimal hedge ratio for Treasury bonds worth $1,000,000 with a modified duration of 12.45 if the futures contract has a price of $90,000 and a modified duration of 8.5 years.

a. 16.27

b. 15.93

c. 7.42

d. 11.11

e. none of the above