Q$7.$ Suppose that a cattle feeder placed $200$ feeder cattle on $03$ Jan $2024$ and planned to sell the fed cattle on $29$ 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 cattle feeder was worried that the cash price of fed cattle might fall in April$-$May and considered hedging with Put options. A put option on Aug $2024$ CME Live Cattle with SP $=180$ cents$/$lb$.$ was trading at $8\mathrm{.}50$ cents$/$lb$.03$ Jan $2024.$ The feeder placed the hedge on $03$ Jan $2024$ and lifted the hedge on $29$ April $2024$ while selling the fed animals in 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 short hedging strategies $(1)$ full hedging with a Put option $($with SP $=180$ cent$/$lb$.)$ on Aug $2024$ CME Live Cattle futures; and $(2)$ delta hedging with the same Put option $($with SP $=180$ cent$/$lb$.)$ on Aug $2022$ CME Live Cattle futures.

A$.$ If the cattle feeder hedged her full cash position, how many put option contracts did she use? The size of fed cattle futures is $40,000$ lbs$.(4$ Points$)$

Answer: NFCF $=$

B$.$ Using the following table, calculate the cattle feeder$$s net realized price per pound of fed cattle from full hedging. Use the Jan $03$ and May $02$ cash prices, futures prices, and option premiums as listed above. Fill in the gaps, calculate cash revenue, gain$/$loss from hedging, and net realized price. $(8$ Points$)$

Date$/$Action Cash Market Futures Market

Jan $03,2024$

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

None Long$/$Short $\_\_\_\_$ Put with SP $=180$ c$/$lb$.$at Pf $=\_\_\_\_\_$ cents$/$lb$.$

Apr $29,2023$

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

$\_\_\_\_\_\_\_\_200$ fed animals @

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

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

Revenue from selling cattle $=$ Total Gain$/$Loss $=$

Net proceeds $=$ Cash revenue $+$ Gains from hedging $=$

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

C$.$ If the cattle feeder used delta hedging based on the average delta hedge ratio $($that you calculated in question $6),$ how many put option contracts did she use? $(3$ Points$)$

Answer: NFC$\backslash$delta $=$

D$.$ Using the following table, calculate the cattle feeder$$s net realized price per pound of fed cattle from delta hedging. Use the Jan $03$ and Apr $29$ cash prices, futures prices, and option premiums as listed in the beginning of this question. Fill in the gaps, calculate revenue, gain$/$loss$,$ and net realized price. $(8$ 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 $\_\_\_\_$ Put with SP $=180$ c$/$lb$.$at Pf $=\_\_\_\_\_$ cents$/$lb$.$

Apr $29,2024$

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

$\_\_\_\_\_\_\_\_200$ fed animals @

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

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

Revenue from selling cattle $=$ Total Gain$/$Loss $=$

Net proceeds $=$ Cash revenue $+$ Gains from hedging $=$

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