The Mathematics of Money

(Darren Dugan) #1

278 Chapter 6 Investments


Luis has purchased the right to sell 5,000 bushels for 612.5 cents per bushel, which we can
work with more conveniently as $6.125 per bushel. So the total price he can sell them for is:

(5,000 bushels)($6.125 per bushel)  $30,625

While it may have felt strange to write a dollar amount with three decimal places, the issue
disappears when we fi nd the total.

The market price for his soybeans at the delivery date is:

(5,000 bushels)($5.43 per bushel)  $27,150

Since he can sell his soybeans for more than the market price, Luis can be seen as making
a profi t of $30,625  $27,150  $3,475.

We don’t know here whether or not Luis is a soybean grower with actual beans to sell, or a
speculator simply hoping to profit from changes in soybean prices. If he is as speculator, won’t
he need to go out and buy soybeans on the spot market in order to be able to deliver what was
promised to the buyer? If the buyer was a speculator with no actual interest in actually pur-
chasing any actual soybeans, won’t the buyer then have to sell the beans on the market after he
buys them from Luis? It certainly seems that there could need to be an awful lot of buying and
selling going on to wrap up the deal in the end. Is all of this really necessary?
In fact, it isn’t. Luis had a contract that allowed him sell 5,000 bushels of soybeans
for $30,625, when the spot market price was $27,150. It seems that in order to realize his
profit, he would have to actually sell 5,000 bushels of soybeans for $30,625. He would
then have to actually have 5,000 bushels of soybeans. But there is an alternative. Instead of
actually buying the soybeans and selling them, Luis could equally well just agree to take
$3,475 in cash from the other party. If he is a grower with actual beans to sell, he can sell
them for $27,150, which together with $3,475 gives him $30,625. If he is a speculator, just
taking the $3,475 makes matters far simpler.
This works out equally well for the other party. If the buyer actually wants the soybeans,
he can then go buy them on the spot market for $27,150. The price, plus the $3,475 paid to
Luis, would mean a total cost of $30,625, which is what he agreed to in the first place. If
the buyer is a speculator, it is easier to just handle things with a cash payment. By settling
the contract in cash, we get to the same financial result for both parties with less buying
and selling required. Since this cash settlement approach is far simpler, it is the way in
which futures contracts are normally actually settled. In fact, many futures contracts are
specifically cash settlement contracts, meaning that right from the start both parties agree
that cash settlement will be used.
In this example, things worked out well for Luis. He was right about what would happen
to soybean prices, and he made a nice profit from this. Of course, no one gets it right every
time. What if someone takes a futures position and then decides before the delivery date
arrives that he was wrong? He cannot bail out of the contract early; that would not be fair to
the person on the other side. He can, however, enter into a new contract with someone else
to offset his obligation under the first contract. The following example will illustrate.

Example 6.3.3 Jimmy believes that petroleum prices will rise. In March, he went
long a September contract for 1,000 barrels of oil at $75.09 per barrel. By May,
though, the price of oil for September delivery had declined to $68.35 per barrel, and
Jimmy decided he was wrong. Fearing that the price would decline further before the
delivery date, he went short a 1,000-barrel contract. Calculate his loss.

The total dollar value of the initial (long) contract was:

(1,000 barrels)($75.09 per barrel)  $75,090.

The total dollar value of the later (short) contract was:

(1,000 barrels)($68.35 per barrel)  $68,350.

Jimmy’s long contract obliges him to buy 1,000 barrels for $75,090, but his short contract
allows him to sell those 1,000 barrels for $68,350. No matter what happens to the price of
oil in the interim, his buying and selling prices are now locked in. So he will lose $75,090 
$68,350  $6,740.
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