Question

In: Finance

Suppose the spot price of a bushel of wheat is $2.00, the annual storage cost is...

Suppose the spot price of a bushel of wheat is $2.00, the annual storage cost is $0.30 per/bushel, the risk‐free rate is 8%, and the costs of transporting wheat from the destination point specified on the futures contract to a local grain elevator, or vice versa, is $0.01/bu.

a. Use the cost‐of‐carry model to determine the equilibrium price of a September wheat futures contract (expiration of T = 0.25).

b. Explain the arbitrage strategy an arbitrageur would pursue if the September wheat contract is trading at $2.16/bu.

Expert Solution

1.

Futures price refers to the price of financial or consumption asset which is computed as taking base of the spot price of such asset as well as taking into account of the other costs. Future price shall be computed by taking interest rate into account for the maturity period given in the case. If the computed future price is not equal to the actual price in the market then there is arbitrage opportunity available in the market.

Following is the formula for computation of futures price as follows:

Futures Price= (S₀+Storage Costs+Transportation Costs)*(1+r*0.25)

= ($2+($0.30*0.25)+$0.01)*(1+0.08*0.25)

= (2.085)*(1+0.02)

= $2.1267 per bushel

Thus the futures price has been computed above as $2.1267. But the actual price in the market is $2.16 per bushel which shows that there is arbitrage opportunity which needs to be exploited.

2. In the given case, actual price is $2.16 whereas computed price is $2.1267 which shows that future price of wheat is overvalued in the market. In order to exploit the opportunity, a strategy should be framed so that risk-less profit could be made out of it.

Following shall be the strategy to make the risk-less profit:

-Long the wheat in spot market at $2.00 per bushel

- Short futures contract of wheat at $2.16 per bushel

- At Maturity of contract, sell wheat in spot market

-Long wheat futures contract to cancel out the short futures position

Risk Less profit would be =$2.16-$2.1267

=$0.0333 per bushel

If you still have any doubt, then please ping me in the comment box, I would love to help you.

jeff jeffy answered 9 months ago

The spot price of corn is $17.2 per bushel. Storage costs are $0.32 per bushel per...

The spot price of corn is $17.2 per bushel. Storage costs are $0.32 per bushel per year. Payment of storage costs occurs in advance for the next three months. Assuming that interest rates are 7% per annum, calculate the forward price of corn for delivery in 12 months. Appreciate if you show me the calculation steps. Thank you!!

Suppose that the spot price of gold is $600. The total cost of insurance and storage...

Suppose that the spot price of gold is $600. The total cost of insurance and storage for gold is $30 per year, payable in advance. The rate of interest for borrowing or lending is 20%. If the forward price is $700, and you are interested in arbitrage, you would: (Hint: Check answer with an arbitrage table) Sell the spot commodity, lend money, and buy a forward contract Borrow money, buy the spot commodity, and buy a forward contract Borrow money,...

Suppose that the spot price of gold is $500. The total cost of insurance and storage for...

Suppose that the spot price of gold is $500. The total cost of insurance and storage for gold is $30 per year, payable in advance. The rate of interest for borrowing or lending is 20%. If the forward price is $650, how much money could you make from arbitrage at expiration of the forward? Hint: Use an arbitrage table after you figure out the appropriate arbitrage portfolio. 12 14 16 18 20

Suppose the futures price is $2.00, and spot price is $1.90. The interest rate is 3%,...

Suppose the futures price is $2.00, and spot price is $1.90. The interest rate is 3%, and cost of the storage is 1%. The future contract matures in 9 months. Calculate the convenience yield. Explain the possible reasons behind the calculated convenience yield.

Draw a graph with the following information: The world price of soybeans is $2.00 per bushel...

Draw a graph with the following information: The world price of soybeans is $2.00 per bushel with a domestic supply of 60 Q/million bushels and a domestic demand of Q/millions bushels. The importing country is small enough not to affect the world price. A. Suppose government puts a tariff of $0.25 per bushel on soybean imports. How much will the tariff reduce imports? Draw the new graph. B. Given a tariff of $0.25 per bushel on soybean imports, how much...

Farmer Jones is producing wheat and must accept the market price of $7.00 per bushel. At...

Farmer Jones is producing wheat and must accept the market price of $7.00 per bushel. At this time, her average total costs and her marginal costs both equal $9.50 per bushel. Her minimum average variable costs are $7.50 per bushel. In order to maximize profits or minimize losses in the short run, farmer Jones should A. increase output. B. continue producing, but reduce output. C. increase selling price. D. produce zero output and shut down.

The farmer produces 899 bushels of wheat at a total cost of $6 per bushel. He...

The farmer produces 899 bushels of wheat at a total cost of $6 per bushel. He sells all of the wheat to Firm F for $11 per bushel. Firm F produces 500 pounds of flour from the wheat at a total cost of $23 per pound (including the amount paid to the farmer for the wheat). Firm F sells 475 pounds of flour to consumers for $31 per pound. There are no other firms in this simple economy. What is...

A farmer grows a bushel of wheat and sells it to a miller for $1.00. The...

A farmer grows a bushel of wheat and sells it to a miller for $1.00. The miller turns the wheat into flour and then sells the flour to a baker for $3.00. The baker uses the flour to make bread and sells the bread to an engineer for $6.00. The engineer eats the bread. What is the value added by each person? What is GDP?

The spot price of oil is $54 per barrel and the the storage costs per barrel...

The spot price of oil is $54 per barrel and the the storage costs per barrel are a constant proportion, 2%, of the spot price. The risk-free interest rate is 5% per annum continuously compounded. If the one year futures price of oil is $55, estimate the convenience yield associated with holding oil. Current price of oil ($/bbl) $54.00 Storage costs (%/year) 2% Risk free rate (per annum) 5% time to maturity of contract (months) 12 Futures Price of oil...

). A farmer knows from experience that his wheat harvest Q (in bushel

). A farmer knows from experience that his wheat harvest Q (in bushels) has the probability distribution given by: Q = 150 with probability 0.30 , = 170 with probability 0.45, =200 with probability 0.25; note that the probabilities add up to 1 as they are required by a probability distribution. Suppose the demand function he faces in the market place is given by: p = 320 - 0.5 Q where p = price in dollars per bushel. Let R = total revenue = p x Q. [Note: You may find it convenient to first derive...