Assume that the portfolio manager sells the bonds at a price of 87-05/32, and that she closes out the futures hedge position at a price of 81-17/32. What will be the net gain or loss on the entire bond transaction from the time that the hedge was placed?
A)Gain of $2,583,125.
B)Loss of $93,750.
C)Loss of $2,583,125.
D)Gain of $93,750.
E)Gain of $812,700.

Question

Quizplus · Accepted Answer

First, we need to calculate the initial value of the bond portfolio:

200,000 bonds x $1,000 face value x 98.125% = $19,625,000

Next, we need to calculate how much we received from selling the bonds:

87 - 5/32 = (87 x 32 + 5)/32 = 2,783/32
2,783/32 x $1,000 x 200,000 = $55,660,937.50

We received $55,660,937.50 from selling the bonds, which means we have a gain of:

$55,660,937.50 - $19,625,000 = $36,035,937.50

Now, let's calculate the gain or loss on the futures hedge:

The futures price declined from 87-07/32 to 81-17/32, which is a decline of 5-14/32 = (5 x 32 + 14)/32 = 174/32 points.

Each point in the T-bond futures contract is worth $1,000, so the change in the futures price resulted in a gain on the hedge of:

$1,000 x 32 x 174 = $5,568,000

However, we need to subtract the initial margin requirement of $3,750,000 to get the net gain on the futures hedge:

$5,568,000 - $3,750,000 = $1,818,000

Finally, we need to subtract the cost of the hedge (the premium paid for the put option) from the net gain on the futures hedge:

$1,818,000 - $1,911,750 = -$93,750

Therefore, the net gain or loss on the entire bond transaction is:

$36,035,937.50 - $93,750 = $35,942,187.50

This is a loss of $93,750, so the best choice is B.

Assume That the Portfolio Manager Sells the Bonds at a Price