Question

Mr. Adam sold short 100 units of a bond at $1,100 per unit a few weeks ago. Today the price per bond is $1,050 per unit. Mr. Adam is concerned that the price of the bond may rise, shrinking his current gains and he wants to hedge his short position.

Suppose he buys 80 units of the bond today at S1,050 per unit. Calculate his profit (loss) at a future date t from his total portfolio position at each of the following levels of the bond price: (a) S1,000, (b) $1,100 and (c) S1,150. By buying 80 units of the bond today, does Mr. Adam get full hedge of his short position. Explain.

Answer 1

Given details in the question:

Sold short of the bonds=100 units at $1100/unit.

Total consideration of selling=100*1100=$110000.

Solution:

Short hedging is a risk aversion strategy used to protect against the declining prices of the assets in the future.It also refers to shorting an asset which mitigates the risk against the potential losses of the investments by selling at a specified price.

If Mr. Adam buys 80 unties of the bond at $1050 per unit, the total consideration paid would be $84000.

The total profit which Mr.Adam made by selling the bonds at $1100 for 100 units and buying 80 units at &1050 =$110000-$84000=$26000.

Calculation of the bonds profit or loss:

a)$1000

Assuming that Mr.Adam Brought 80 units at $1000,

Total consideration=$80000

Total consideration when he brought today for 80 units of the bonds at $1050=$84000

total profit/Loss=total consideration at future price- Total consideration on today's price

Total loss for A=80000-84000= -$4000

b)$1100

Assuming that Mr.Adam brought 80 units at $1100 per unit.

the total consideration=$88000

Total profit=$88000-$84000=$4000

c)$1150

Assuming that Mr.Adam brought 80 shares at $1150 per share,

Total consideration= 1150*80=92000

Total profit= $92000-$84000=$8000

Hence to summarize:

a) if Mr Adam Brought bonds at $1000/unit in the future, he would make a loss of $4000.

b)If Mr Adam Brought Bonds at $1100, then he would have made a profit of $4000

c) If Mr.Adam brought bonds at $1150, he would make profit of $8000