Economics 437

Problem Solutions to Assignment Number 1

1.3: The farmer faces the risk that the price of pigs will drop between now and the time of delivery three months from now. The farmer can sell three futures contracts (short three contracts) for 30,000 pounds of pigs each. The benefit of this strategy is that if the price of hogs goes down, the farmer will be compensated for the drop in price by the increased value of the futures position. The downside of course occurs if the price goes up. The farmer will benefit from selling the hogs at the high price, but the futures position will offset these gains dollar for dollar.

1.6: The holder of the put option has a right to sell the asset for $60. A gain occurs if the price of the asset falls enough below the strike price to compensate the holder for the $4.00 option premium. Thus, a gain will occur if the price of the asset in June is less than $56. If the price of the asset falls is below $60 in June, the holder will exercise the option because even though there is not an overall gain for prices between $56 and $60, the loss is minimized by exercising the option.

1.7: The seller of the call option has given the buyer the write to buy the stock at $20 in September. Thus, if the price is $25 in September, the seller of the call option must buy the stock at $25 and sell the stock to the holder of the call option for $20, for a net loss of $5.00 in September. Subtracting the $2 option premium that is received in May, , and the cash flow is a loss of $3.00 to the investor.

1.9: A cap on the average interest will pay to the borrower no more than a cap on the rate itself, hence a cap on the rate itself over a given period of time is more valuable than a cap on the average rate.

1.12: For each ounce of gold, borrow $500 and buy an ounce and sell the ounce in the future for $700 by taking a short futures position. Take the $700 per ounce and pay back the principal of the loan ($500) and the interest ($50) for a net profit of $150 per ounce.

1.14: Given that most people cannot tell what the future will hold for them, the executive may be correct but that does not mean that his company should not hedge against the risk of an upturn in oil prices. If the negative profit consequences from an upturn in oil prices are greater than the positive profit consequences of a downturn in oil prices, then the company might come out ahead, on average, from a hedge.

1.16: A zero sum game means that the gains to the winner exactly offset the losses to the loser. With options and futures, this is exactly what happens. The losses (gains) to a hort position exactly offset the gains (losses) to a long pposition.

Does this farmer have a long or short position in corn and soybeans? Please explain.

This farmer is long in corn and soybeans because his position is equivalent to a person who bought corn and soybeans.

Is this farmer a hedger or a speculator with respect to his position in corn and soybeans? Please explain.

Given that the farmer is long in corn and soybeans he is a speculator because the farmer has taken a position in the market and is exposed to downside risk.

If the farmer signs a contract to deliver 50,000 bushels of corn in May for $1.85/bu and 20,000 bushels of soybeans in May for $4.40/bu to the local elevator, is the farmer a hedger or a speculator? Please explain. (For now assume that the government LDP program does not exist.)

If the farmer takes a short position to offset his long position, then the farmer is a hedger. The farmer is fully protected against any downside price moves.

With the delivery contracts described in Part B in place, calculate the cash position of the farmer on June 1 if the cash prices for corn and soybeans turn out to be $2.20/bu and $5.00/bu in May. What if the prices turn out to be $1.60/bu and $4.00/bu? What can you conclude about the effects of the contract that the farmer signed?

Regardless of what the price of corn and soybeans turns out to be, the farmer receives $1.85/bu for corn and $4.40/bu for soybeans. The contract fully protects the farmer from any downside price risk and the farmer has no chance of enjoying any benefits from upside price movements. The farmer will receive a total of $180,500.

Now suppose that the farmer did not sign the delivery contracts. Instead the farmer signs a contract that gives the farmer the right (but not the obligation) to deliver corn in May for $1.85/bu. The contract costs the farmer 12.5 cents per bushel. The farmer also signs a contract gives him the right to deliver soybeans in May for $4.40/bu. The contract costs the farmer 33 cents per bushel. After signing these contracts, is the farmer a hedger or a speculator? Please explain.

The farmer is now a hedger because he is largely protected from any downside price movements. Regardless of what price does, the farmer receives at least $1.85/bu fopr corn and $4.40/bu for soybeans (less the cost of the options).

With the delivery contracts described in Part B in place, calculate the cash position of the farmer on June 1 if the cash prices for corn and soybeans turn out to be $2.20/bu and $5.00/bu in May. What if the prices turn out to be $1.60/bu and $4.00/bu? What can you conclude about the effects of the contract that the farmer signed?

At $2.20 and $5.00, the farmer will receive $210,000 for the corn and soybeans by selling at the market prices. The options cost $12,850 for a net cash position of $197,150. At $1.60 and $4.00 the farmer receives $180,500 for the corn and soybeans (exercise the options to sell at $1.85 and $4.40). The cost of the options is $12,850, for a net position of $167,650. The contracts put a floor on revenue, but allow the farmer to enjoy any upside potential.

If you were the farmer in January would you have entered into the contracts in Part C above, the contracts in Part E above, or continued to store the grain? What additional information might you need to answer this question?

It depends on a lot of factors that we will discuss in class including the probably of a price decline, the ability of the farmer to withstand price declines, and the need of the farmer for cash.