The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

exchange. Likewise, an electric utility looking to purchase coal can do so at an exchange

rather than make direct contacts with coal producers.

How is the price for a commodity determined? As with anything else in a free market, the

price is whatever willing buyers will pay and willing sellers will accept. If a farmer hopes to

sell his corn crop for $3.50 per bushel, but other farmers are willing to sell for $2.75, buyers

will naturally choose to buy at the lower price. Likewise, if a buyer hopes to buy corn for

$2.00 a bushel but other buyers are willing to pay $2.75, sellers will naturally choose to sell

to that other buyer. In this case, the market price for a bushel of corn would end up at $2.75,

since it is the highest price that buyers will pay and lowest price at which sellers will sell. If

demand increases and/or supply decreases, the market price will most likely rise; on the other

hand, if demand fades and/or supply swells, the market price will most likely drop.

To keep things simpler for all involved, the contracts made on commodity exchanges are

generally only certain standardized types and only for certain standardized sizes. Each contract

will provide for the sale of a certain set quantity of the commodity in question, and contracts

will be offered for sale only with certain specific dates on which the sale is supposed to actually

take place. Most exchanges specify the delivery date by month only; a “July contract” means

that delivery must be made in July, though the exact date in July is not usually mentioned.

The market prices of some commodities (especially petroleum and gold) are often reported

on daily TV and radio business news reports; daily farm reports in rural areas will usually

give updates on the prices for agricultural commodities. Quotes given in the news usually

only give the spot price, though, or price for a limited number of delivery dates. Price quotes

for other commodities are sometimes listed in newspapers, though this is becoming less com-

mon as people looking for these quotes rely more and more on the Internet as a source.

A futures quote will generally contain the information shown in the example below:

SOYBEANS DELAYED FUTURES FRIDAY AUGUST 23 1:35 PM

Contract Last Change Open High Low Previous

October ‘06 612-5 3-6 608-2 615-4 603-1 608-9

This quote gives the market price information for the October 2006 soybean contract as

of August 23. Interpreting this quote requires some background information. You would

first need to know the units. Each commodity trades in a set unit amount. While the units

involved are often familiar, some may not be to the average consumer; milk is commonly

sold by the “hundredweight,” for example. Soybeans commonly are traded in bushels.

Also, the prices for soybeans are usually given in cents, with the hyphen used in place of a

decimal point. So this quote tells us that at 1
35 PM the current market price of soybeans

for October delivery was 612.5 cents (or $6.125) per bushel. Quotes often will show the

open (the price of the first trade of the day), high, and low (as the name suggests, the

highest and lowest prices seen in trading during the day so far), and the previous close or

previous settlement (the price as of the close of trading on the prior day).

Because these quotes require some background knowledge, interpreting them can be frus-

trating at first. However, anyone with a professional or other serious interest in a commodity

will be aware of that information, and anyone trading commodities or futures will both fall

into that category and be working though a broker who has that knowledge as well.

Note also that while it is unlikely that anyone would be buying or selling a futures contract

for a single bushel of soybeans, the price is generally quoted per bushel, not the price for the

entire quantity of a contract. We will see in the following how the mathematics works.

Profits and Losses from Futures Trading

Example 6.3.2 Suppose that Luis believes that the price of soybeans will decline.

He takes a short position in October soybeans for 5,000 bushels, at 612.5 cents

per bushel. At the delivery date, the spot market price per bushel is 543.0 cents per

bushel. Calculate his profi t.

6.3 Commodities, Options, and Futures Contracts 277