$2.$ Suppose that today is Tuesday, October $1,2024,$ and you have a loan of $$5,000,000$ outstanding, on which you will have to make a floating$-$rate interest rate payment on Monday, October $7.$ The interest payment is determined based on a $3-$month SOFR rate on that day. You fear that in the next several days the rate might rise. So$,$ you hedge yourself by trading $3-$month SOFR futures. Assume that you enter the position at the close of day on Tuesday, October $1,$ and you trade AUG $24$ contract.

a$.$ In order to hedge yourself, which position in AUG $243-$month SOFR futures will you take $($i$.$e$.$ buy or sell, and the number of contracts$)?$

b$.$ What is your daily gain or loss on your futures position $($on Wednesday, Thursday, Friday, and Monday$)?$

c$.$ What is the interest rate payment that you have to make on Monday, October $7,$ on your $$5,000,000$ loan?

d$.$ What is the net cost to you, taking into account the gains$/$losses on your hedge, plus the interest payment on the loan $($ignore the time value of money$)?$ Daily Settlements for $3-$month SOFR Futures $($FINAL$)$ Trade Date: $10/02/2024($Wednesday$)$

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

JLY $24-----\mathrm{.}002594\mathrm{.}7725015,537$

AUG $2495\mathrm{.}012595\mathrm{.}012595\mathrm{.}012595\mathrm{.}0125-\mathrm{.}002595\mathrm{.}012517,230$

SEP $2495\mathrm{.}265095\mathrm{.}267595\mathrm{.}257595\mathrm{.}2625-\mathrm{.}002595\mathrm{.}2625142,7071,312,916$

OCT $24-95\mathrm{.}4800$B $95\mathrm{.}4700$A $95\mathrm{.}4800$B $-\mathrm{.}002595\mathrm{.}472513,628$

NOV $24--95\mathrm{.}7600$A $95\mathrm{.}7600$A $-\mathrm{.}005095\mathrm{.}76500752$

Daily Settlements for $3-$month SOFR Futures $($FINAL$)$ Trade Date: $10/04/2024($Friday$)$

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

JLY $2494\mathrm{.}772594\mathrm{.}772594\mathrm{.}772594\mathrm{.}7725\mathrm{.}000094\mathrm{.}772517415,532$

AUG $2495\mathrm{.}002595\mathrm{.}002595\mathrm{.}002595\mathrm{.}0025-\mathrm{.}010095\mathrm{.}0025407,363$

SEP $2495\mathrm{.}265095\mathrm{.}267595\mathrm{.}215095\mathrm{.}2250-\mathrm{.}035095\mathrm{.}2275187,6961,307,335$

OCT $2495\mathrm{.}415095\mathrm{.}415095\mathrm{.}3800$A $95\mathrm{.}3825$A $-\mathrm{.}077595\mathrm{.}3875633,909$

NOV $2495\mathrm{.}715095\mathrm{.}715095\mathrm{.}6050$A $95\mathrm{.}7150$B $-\mathrm{.}125095\mathrm{.}615095752$

Daily Settlements for $3-$month SOFR Futures $($FINAL$)$ Trade Date: $10/07/2024($Monday$)$

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

JLY $2494\mathrm{.}772594\mathrm{.}775094\mathrm{.}772594\mathrm{.}7725\mathrm{.}000094\mathrm{.}77252615,388$

AUG $2494\mathrm{.}995094\mathrm{.}997594\mathrm{.}995094\mathrm{.}9975-\mathrm{.}005094\mathrm{.}99752157,403$

SEP $2495\mathrm{.}225095\mathrm{.}225095\mathrm{.}200095\mathrm{.}2075-\mathrm{.}017595\mathrm{.}2100153,9861,283,233$

OCT $2495\mathrm{.}360095\mathrm{.}365095\mathrm{.}3400$A $95\mathrm{.}3475$B $-\mathrm{.}032595\mathrm{.}35503363,897$

NOV $2495\mathrm{.}560095\mathrm{.}560095\mathrm{.}525095\mathrm{.}5500$B $-\mathrm{.}065095\mathrm{.}5500769845$

$3-$month SOFR rate $(90-$day average$)$:

October $1,20245\mathrm{.}30501\%$

October $2,20245\mathrm{.}30186\%$

October $3,20245\mathrm{.}29725\%$

October $4,20245\mathrm{.}29197\%$

October $7,20245\mathrm{.}27541\%$