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. Japanese Yen Data

Daily Settlements for Japanese Yen Future $($FINAL$)$Trade Date: Wednesday, $09/11/2024$

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

SEP $24\mathrm{.}0070270\mathrm{.}0071120\mathrm{.}0070200\mathrm{.}0070285+\mathrm{.}0000060\mathrm{.}0070370302,854260,790$

OCT $24\mathrm{.}0070580\mathrm{.}0071400\mathrm{.}0070500\mathrm{.}0070555$A $+\mathrm{.}0000065\mathrm{.}00706552,067986$

NOV $24\mathrm{.}0071125\mathrm{.}0071740\mathrm{.}0070920$A $\mathrm{.}0071030$B $+\mathrm{.}0000065\mathrm{.}00709951,185343$

DEC $24\mathrm{.}0071135\mathrm{.}0072005\mathrm{.}0071085\mathrm{.}0071185$A $+\mathrm{.}0000075\mathrm{.}0071260165,465113,858$

JAN $25-\mathrm{.}0071535$B $-\mathrm{.}0071535$B $+\mathrm{.}0000075\mathrm{.}007149000$

MAR $25\mathrm{.}0071985\mathrm{.}0072745\mathrm{.}0071860$A $\mathrm{.}0072115$A $+\mathrm{.}0000090\mathrm{.}0072030443286$

Daily Settlements for Japanese Yen Futures $($FINAL$)$Trade Date: Friday, $09/13/2024$

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

SEP $24\mathrm{.}0070520\mathrm{.}0071285\mathrm{.}0070485\mathrm{.}0070980$B $+\mathrm{.}0000535\mathrm{.}007095527,516188,296$

OCT $24\mathrm{.}0070830\mathrm{.}0071565\mathrm{.}0070775\mathrm{.}0071240$B $+\mathrm{.}0000520\mathrm{.}00712251,684943$

NOV $24\mathrm{.}0071495\mathrm{.}0071890\mathrm{.}0071465\mathrm{.}0071575$B $+\mathrm{.}0000535\mathrm{.}0071575491158$

DEC $24\mathrm{.}0071380\mathrm{.}0072175\mathrm{.}0071355\mathrm{.}0071890+\mathrm{.}0000535\mathrm{.}0071835205,441192,597$

JAN $25-\mathrm{.}0071710$B $-\mathrm{.}0071710$B $+\mathrm{.}0000570\mathrm{.}007206500$

MAR $25\mathrm{.}0072135\mathrm{.}0072875\mathrm{.}0072125\mathrm{.}0072720$A $+\mathrm{.}0000525\mathrm{.}0072590389339$

Spot data:

$09/10/20240\mathrm{.}0070195$

$09/11/20240\mathrm{.}0070240$

$09/12/20240\mathrm{.}0070512$

$09/13/20240\mathrm{.}0071008$

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:

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

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

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

$09/13/20242\mathrm{.}25$ Compute the hedge ratio using data from Data