The spot price of corn is $8.00/bu., and the futures price of the July contract is $8.25/bu. This…

The spot price of corn is $8.00/bu., and the futures price of the July contract is $8.25/bu. This contract expires in three months. Suppose that storage costs for corn for 3 months are $0.15/bu., payable in advance. The continuously compounded 3-month risk-free rate is 1% per year. Is there an arbitrage opportunity? If so, what is the arbitrage strategy? (Assume that the strategy is designed so that net cash flows today are zero.) In your analysis, treat corn as a true consumption commodity. Hint: first calculate the no-arbitrage futures price.

A. Take a short position in July corn futures, sell yellow corn short in the spot market today, save on storage costs, and invest sales proceeds at the risk-free rate until July.
B. No arbitrage opportunity exists.
C. Take a long position in July corn futures, buy yellow corn in the spot market today, arrange to pay storage costs, and borrow at the risk-free rate until July.
D. Take a long position in July corn futures, sell yellow corn short in the spot market today, save on storage costs, and invest sales proceeds at the risk-free rate until July.
E. Take a short position in July corn futures, buy yellow corn in the spot market today, arrange to pay storage costs, and borrow at the risk-free rate until July.

2)

The spot price of light, sweet crude oil is $78.50 per bbl., and the futures price of the NYMEX August light, sweet crude oil futures contract is $80.95 per bbl. This contract expires in 6 months. The continuously compounded 6-month risk-free rate is 1.25% per year. The storage cost is $1.50 per barrel for 6 months, payable in advance.

Is there an arbitrage opportunity? If so, what is the arbitrage strategy? (Assume that the strategy is designed so that net cash flows today are zero.) In your analysis, treat crude oil as a true consumption commodity.

A. Take a long position in the August light, sweet crude oil futures; sell light, sweet crude oil; and invest the sales proceeds for 6 months at the risk-free rate.
B. Take a short position in the August light, sweet crude oil futures; buy light, sweet crude oil; and borrow for 6 months at the risk-free rate.
C. Take a short position in the August light, sweet crude oil futures; sell light, sweet crude oil; and invest the sales proceeds for 6 months at the risk-free rate.
D. No arbitrage opportunity exists.
E. Take a long position in the August light, sweet crude oil futures; buy light, sweet crude oil; and borrow for 6 months at the risk-free rate.

3)

“Today” is late March. Your company, Falcon Refining Inc., buys 1,000,000 barrels of crude oil at the end of each month to produce a variety of petroleum products. You have the following market data.

  • Spot price of light, sweet crude oil: S0 = $49.00/bbl.

  • Futures price of May NYMEX light, sweet crude oil contract: F0 = $50.88/bbl.

  • Trading in a NYMEX crude oil futures contract ceases shortly before the contract month begins. Delivery can be as early as the first calendar day of the contract month. For this analysis, assume that time to expiration of the May contract (more precisely, time until the start of the delivery month) is T = 1/12 year.

  • Your storage cost for crude oil is $0.125 per barrel per month. Assume that you must pay in advance.

  • Continuously compounded one-month risk-free rate: r = 1% per year.

Given current spot and futures prices, should your company hedge its late April purchase with crude oil futures? If yes, what hedging strategy should you adopt?

A. Do not hedge with crude oil futures.
B. Hedge: take a short position in 1,000 May crude oil futures contracts. Close out your futures position in late April.
C. Hedge: take a long position in 1,000 May crude oil futures contracts. Close out your futures position in late April.
D. Hedge: take a short position in 100 April crude oil futures contracts. Close out your futures position in late April.
E. Hedge: take a long position in 100 April crude oil futures contracts. Close out your futures position in late April.

4)

“Today” is late March. Your company, Mesquite Bush Refining Inc., produces 42,000,000 gallons of ultra low sulfur diesel (ULSD) fuel at the end of each month. You have the following market data.

  • Spot price of ULSD diesel fuel: S0 = $2.00/gal.
  • Futures price of June NYMEX New York Harbor ULSD futures: F0 = $1.84/gal.
  • Size of the underlying for this futures contract: 42,000 gallons
  • Trading in a NYMEX New York Harbor ULSD contract ceases shortly before the contract month begins. For this analysis, assume that time to expiration of the June contract (more precisely, time until the start of the delivery month) is T = 2/12 year.
  • Your storage cost for ULSD diesel is $0.125 per barrel per month. Assume that you must pay in advance.
  • Continuously compounded one-month risk-free rate: r = 2% per year.

Given current spot and futures prices, should your company hedge its late May sale with ULSD futures? If yes, what hedging strategy should you adopt? (Assume that your company is willing to hedge only at a “fair” price or better.)

A. Hedge: take a short position in 100 May ULSD futures contracts. Close out your futures position in late May.
B. Do not hedge with USLD futures.
C. Hedge: take a long position in 1,000 June ULSD futures contracts. Close out your futures position in late May.
D. Hedge: take a long position in 100 May ULSD futures contracts. Close out your futures position in late May.
E. Hedge: take a short position in 1,000 June ULSD futures contracts. Close out your futures position in late May.

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