$3.$Devon Energy, a gas processing company, expects to pay for $400,000$ mmBtu of natural gas at the close of day on Friday, September $13.$ They want to hedge their position with Henry Hub$$s natural gas futures. Assume that they enter into the position at the close of day on Tuesday, September $10.$ The size of one natural gas futures is $10,000$ mmBtu. Futures and spot data are provided in the file HW$1\_$data.doc.

a$.$Describe the position they should enter $($long or short, contract month$).$

b$.$Compute the hedge ratio using data from Data$\_$hw$1.$xls file.

c$.$How many contracts do they need to buy or sell?

d$.$Document the price gain or loss every day that their position is open.

e$.$What is the total cost after they have closed out their futures position, and made their payment?

f$.$What is the effective cost per mmBtu?

Henry Hub Natural Gas Futures Data

Trade Date: Wednesday, $09/11/2024$

Month Open High Low Last Change Settle Estimated Volume Prior Day Open Interest

OCT $242\mathrm{.}391002\mathrm{.}436002\mathrm{.}307002\mathrm{.}31200-\mathrm{.}049002\mathrm{.}32400171,895139,098$

NOV $242\mathrm{.}645002\mathrm{.}691002\mathrm{.}603002\mathrm{.}60800-\mathrm{.}026002\mathrm{.}61300118,350288,736$

DEC $243\mathrm{.}071003\mathrm{.}111003\mathrm{.}041003\mathrm{.}04900$A $-\mathrm{.}017003\mathrm{.}0500042,592134,209$

Trade Date: Friday, $09/13/2024$

Month Open High Low Last Change Settle Estimated Volume Prior Day Open Interest

OCT $242\mathrm{.}363002\mathrm{.}407002\mathrm{.}294002\mathrm{.}29400$B $-\mathrm{.}052002\mathrm{.}30500173,713175,383$

NOV $242\mathrm{.}638002\mathrm{.}666002\mathrm{.}575002\mathrm{.}57700-\mathrm{.}044002\mathrm{.}58900109,159273,256$

DEC $243\mathrm{.}089003\mathrm{.}111003\mathrm{.}012003\mathrm{.}01500-\mathrm{.}063003\mathrm{.}0250047,851129,190$

Spot Data:

$09/10/20242\mathrm{.}23$

$09/11/20242\mathrm{.}13$

$09/12/20242\mathrm{.}13$

$09/13/20242\mathrm{.}25.$

Date Futures Price Spot Price

$1$ $$2,61$ $$2,50$

$2$ $$2,61$ $$2,53$

$3$ $$2,58$ $$2,45$

$4$ $$2,51$ $$2,49$

$5$ $$2,58$ $$2,60$

$6$ $$2,77$ $$2,70$

$7$ $$2,77$ $$2,56$

$8$ $$2,80$ $$2,48$

$9$ $$2,66$ $$2,50$

$10$ $$2,67$ $$2,60$

$11$ $$2,66$ $$2,46$

$12$ $$2,64$ $$2,42$

$13$ $$2,59$ $$2,60$

$14$ $$2,65$ $$2,58$

$15$ $$2,74$ $$2,60$

$16$ $$2,69$ $$2,44$

$17$ $$2,76$ $$2,56$

$18$ $$2,73$ $$2,55$

$19$ $$2,78$ $$2,65$

$20$ $$2,90$ $$2,74$