Q$8.$ Suppose that a beef packer was planning on $03$ January $2024$ to purchase $400$ Live Cattle $29$ Apr $2024.$ The expected weight of fed cattle is $1600$ lbs$.$ per animal. On $03$ Jan $2024,$ the cash price of fed cattle was $170\mathrm{.}25$ cents$/$lb$.,$ and the price of Aug $2024$ CME Live Cattle futures was $180\mathrm{.}25$ cents$/$lb$.$ The beef packer was worried that cash price of fed cattle might increase in April$-$May and considered hedging using a Call option. A Call option on Aug $2024$ CME Live Cattle with SP $=165$ cents$/$lb$.$ was trading at $10\mathrm{.}40$ cents$/$lb$.03$ Jan $2024.$ The beef packer placed the hedge on $03$ Jan $2023$ and lifted the hedge on $29$ April $2024$ while purchasing the fed animals from the cash market at the same time. As reported, the cash price of live cattle and the Aug $2023$ CME Live Cattle futures on $29$ Apr $2024$ were $181\mathrm{.}00$ cents$/$lb$.$ and $175\mathrm{.}68$ cents$/$lb$.,$ respectively. Consider two long hedging strategies $(1)$ full hedging with a Call option $($with SP $=168$ cent$/$lb$.)$ on Aug $2023$ CME Live Cattle futures; and $(2)$ delta hedging with the same Call option $($with SP $=168$ cent$/$lb$.)$ on Aug $2023$ CME Live Cattle futures.

If the beef packer hedged her full cash position, how many Call option contracts did she use? The size of fed cattle futures is $40,000$ lbs$.(3$ Points$)$

Answer: NFCF $=$

Using the following table to calculate the beef packer$$s net price paid per pound of fed cattle from full hedging. Use the Jan $03$ and May $02$ cash prices, futures prices, and Call premiums as listed above. Fill in the gaps, calculate cash cost, gain$/$loss from hedging, and net price paid. $(7$ Pts$)$

Date$/$Action Cash Market Futures Market

Jan $03,2024$

Action CP $=\_\_\_\_\_\_\_$ cents$/$lb$.$ Aug. $24$ CME LC$,$ FP $=\_\_\_\_\_\_\_\_$ c$/$lb$.$

None Long$/$Short $\_\_\_\_$Call with SP$=165$ c$/$lb$.$ at Cf $=\_\_\_\_\_$ c$/$lb$.$

Apr $29,2024$

Action CP $=\_\_\_\_\_\_\_$ cents$/$lb$.$ FP $=\_\_\_\_\_\_\_\_\_\_\_\_$ cents$/$lb$.$

$\_\_\_\_\_\_\_\_400$ fed animals @

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ Exercise$/$Do not Exercise $($cross one$)$

Gain $/$ Loss $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ c$/$lb$.$

Cost of purchasing cattle $=$ Total Gain$/$Loss $=$

Net Payment $=$ Cash Cost $$ Gains from hedging $=$

Net price paid $($cents$/$lb$.)=$

The $3$rd page of the spread sheet $($titled Call$)$ lists daily futures prices $($cents$/$lb$.)$ of Aug $2024$ CME Live Cattle futures contract and the premiums of a call option with SP $=165$ cents$/$lb$.$ For each day, calculate the call option$$s delta and hedge ratio in the spread sheet and list the average delta and the hedge ratio based on the average delta here. If you find an undefined value, replace that with a period. $(4$ Points$)$

Answer: Average $\backslash$delta $=$ HR$\backslash$delta $=$

If the beef packer used delta hedging based on the average delta hedge ratio $($that you calculated in Part C$),$ how many Call option contracts did she use? $(3$ Points$)$

Answer: NFC$\backslash$delta $=$

Using the following table, calculate the beef packer$$s net price per pound of fed cattle from delta hedging. Use the Jan $03$ and May $02$ cash prices, futures prices, and option premiums as listed in the beginning of this question. Fill in the gaps, calculate cash cost, gain$/$loss from hedging, and net price paid. $(8$ Points$)$

Date$/$Action Cash Market Futures Market

Jan $03,2024$

Action CP $=\_\_\_\_\_\_\_$ cents$/$lb$.$ Aug. $24$ CME LC$,$ FP $=\_\_\_\_\_\_\_\_$ c$/$lb$.$

None $\backslash$delta $=\_\_\_\_\_\_$; HR$\backslash$delta $=\_\_\_\_$; NFC$\backslash$delta $=\_\_\_\_\_$

Long$/$Short $\_\_\_\_$Call with SP$=165$ c$/$lb$.$ at Cf $=\_\_\_\_\_$ c$/$lb$.$

Apr $29,2023$

Action CP $=\_\_\_\_\_\_\_$ cents$/$lb$.$ FP $=\_\_\_\_\_\_\_\_\_\_\_\_$ cents$/$lb$.$

$\_\_\_\_\_\_\_\_400$ fed animals @

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ Exercise$/$Do not Exercise $($cross one$)$

Gain $/$ Loss $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ c$/$lb$.$

Cost of purchasing cattle $=$ Total Gain$/$Loss $=$

Net Payment $=$ Cash Cost $$ Gains from hedging $=$

Net price paid $($cents$/$lb$.)=$