Suppose you have access to a 3-month futures contract on a 20-year zero coupon bond with face value of $1 million. Describe the position you need to take in these futures to duration hedge your net worth. (You need to explain how many contracts and whether you are short or long.)

Solution:

The length of the potential (or revised length) is the term (or adjusted term) of the underlying contract, then the revised length of the futures contract:

                    =20/1.05 = 19.048 years

Currently, we will determine how many contracts (NF) to offset the loss of net value:

∆E should be equal to decline in the value of F:

∆F = -0.828 m = - MD

∆r = -19.048 * (0.382 m.)

NF* 0.005

==> NF = -0.828 / [-19.048 * (0.382 m)*0.005]

           = 22.76 contracts

Therefore, in 22,76 potential contracts we also have to take a long place with the 20-year zero coupon bond as the reference.

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this