Suppose that on 01 April 2023 a cattle feeder in Lubbock bought 1,000 head of feeder cattle

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Question:

Suppose that on 01 April 2023 a cattle feeder in Lubbock bought 1,000 head of feeder cattle with the plan of feeding the animals until they reach an average weight of 1,200 pounds. She estimated that it would take approximately 6 months to finish the cattle and she planned to sell the fed cattle on 28 October 2023.

On 01 Apr. 2023, the closing price for fed cattle in the local cash market was 183.00 cents per pound. However, the cattle feeder is worried that the cash prices for live cattle will decrease during the Fall months because of increased supply of fed cattle in the market, and she may not be able to recover her costs (of purchasing feeder animals and feeding). She came to know that you went to Texas Tech to study Agricultural Economics and learned some strategies for price risk management. She called you and asked for your suggestion.

You took the Futures and Options class and learned that hedging with futures is one of the cash price risk minimization strategies. So, you wanted to explore the possibility of devising a hedging strategy for the cattle feeder. You have obtained some historical data on cash and futures prices for live cattle (see the spread sheet you have downloaded from Blackboard).

Q1. Write down the formula for calculating the variance, standard deviation, covariance, and correlation coefficient of the cash and futures price series. (2 6 = 12 points)

Q2. According to the above formula, calculate the variance, standard deviation, covariance, and correlation coefficient of the cash and futures price series provided in the spreadsheet (show your calculation both in the spread sheet and below). (2 6 = 12 points)

Q3. Given the data, what is the cattle feeder's cash price risk? What is the cattle feeder's futures price risk? (8 points)

Q4. What is the cattle feeder's basis risk? Write down the formula for calculating basis risk and calculate the basis risk according to the formula using the data in the spreadsheet (show your calculation both in the spread sheet and below). (8 points)

Q5. What is your anticipated hedging efficiency? Write down the formula for calculating hedging efficiency and calculate the hedging efficiency using the data in the spreadsheet (show your calculation in the spread sheet as well). Do you recommend hedging based on the calculated hedging efficiency? (10 points)

Q6. Write down the formula for calculating hedge ratio according to the nave and econometric methods. Calculate the nave and statistical hedge ratios using the data in the spreadsheet (show your calculation both in the spread sheet and below). (4 2 = 8 points)

Q7. The cattle feeder expects to have (1,0001200 =) 1,200,000 pounds of live cattle upon the completion of feeding the animals. Write down the formula for calculating the number of futures contracts to be used in hedging that minimizes risk (with the hedge ratio). The size of the CME live cattle futures contract is 40,000 pounds. Using the naive hedge ratio, calculate the number of futures contracts the cattle feeder needed to hedge her cash position. (6 points)

Q8. Using the calculated econometric hedge ratio, calculate the number of risk minimizing futures contracts the cattle feeder needed to hedge her cash position. (6 points)

Q9. Suppose that you recommend the cattle feeder to hedge her cash position by trading the risk minimizing number of December 2023 CME live cattle futures contract. Following your advice, on 09 April 2023, the cattle feeder placed hedge by selling the risk-minimizing number (NFC*, as calculated using the econometric hedge ratio) of December 2023 CME Live Cattle futures contract at 192.35 cents per pound. The local cash price for live cattle at the time of placing hedge was 183.00 cents per pound. Suppose that, on 28 October 2023, the closing price for fed cattle in the local cash market appears to be 179.40 cents per pound and the December 2023 live cattle futures settlement price appears to be 183.15 cents per pound. Show the hedging strategy in the following table and calculate the revenue from selling the live animals in the local cash market, gain/loss from the futures position, total revenue, and net realized price per pound of live animal. (10 points)

Date/Action	Cash Market	Futures Market
09 April 2023 Action	CP = 183.00 cents/lb.	FP = 192.35 cents/lb.
	____________ Dec. 2023 CME LC contracts @ __________ cents/lb.
28 Oct. 2023 Action	CP = 179.40 cents/lb.	FP = 183.15 cents/lb.
________1,000 cattle (1,200,000 lb.) @ ___________	___________Dec. 2023 CME LC contracts @ __________cents/lb.
Gain / Loss =
Return from Cash Market
Return from Futures Market
Net Return from Cash and Futures Markets
Net realized price of live cattle (cents/lb.)

Q10. What would have happened if you had suggested the feeder to hedge using the nave hedge ratio? Using the following table, calculate the revenue from selling the live animals in the local cash market, gain/loss from the futures position, total revenue, and net realized price per pound of live animal. Compare the results with the answers of the last question. (10 points)

Date/Action	Cash Market	Futures Market
09 April 2023 Action	CP = 183.00 cents/lb.	FP = 192.35 cents/lb.
	____________ Dec. 2023 CME LC contracts @ __________ cents/lb.
28 Oct. 2023 Action	CP = 179.40 cents/lb.	FP = 183.15 cents/lb.
________1,000 cattle (1,200,000 lb.) @ ___________	___________Dec. 2023 CME LC contracts @ __________cents/lb.
Gain / Loss =
Return from Cash Market
Return from Futures Market
Net Return from Cash and Futures Markets
Net realized price of live cattle (cents/lb.)

Q11. What would have happened if you had suggested the feeder to hedge the total expected cash position (full hedging)?Using the following table, calculate the revenue from selling the live animals in the local cash market, gain/loss from the futures position, total revenue, and net realized price per pound of live animal. Compare the results with the answers of questions 9 and 10. (10 points)

Date/Action	Cash Market	Futures Market
09 April 2023 Action	CP = 183.00 cents/lb.	FP = 192.35 cents/lb.
	____________ Dec. 2023 CME LC contracts @ __________ cents/lb.
28 Oct. 2023 Action	CP = 179.40 cents/lb.	FP = 183.15 cents/lb.
________1,000 cattle (1,200,000 lb.) @ ___________	___________Dec. 2023 CME LC contracts @ __________cents/lb.
Gain / Loss =
Return from Cash Market
Return from Futures Market
Net Return from Cash and Futures Markets
Net realized price of live cattle (cents/lb.)