280 Chapter 6 Investments
(a) $6,740/$3,754.50 1.7952 179.52%. Since this is a loss, it should be expressed
with a negative number, so the answer is 179.52%.(b) I = PRT
$6,740 = $3,754.50(R)(52/365)
R 12.6008 1,260.08%His rate of return was thus an astonishing 1,260.08%.Just as a leveraged investment can produce astonishingly high percentage profits, it can
produce astonishingly high percentage losses. This example also reveals something espe-
cially worrisome about futures speculation: notice that if we consider Jimmy’s investment
to have been his initial margin, he actually lost more than the amount of that investment!
Once the loss on his investment became larger than his margin, Jimmy most likely would
have had to put up additional money for a margin call. While Example 6.3.3 suggested that
it was Jimmy’s choice to close his contract, it may have actually happened that Jimmy was
forced to do this as a result of an unwillingness or inability to meet a margin call.Options
Options are similar to futures contracts in that they are based on the idea of selling some-
thing for a specified price at specified future date. They differ from futures in one very
important respect, though. With a futures contract, both parties are obligated to buy and
sell at the specified date at the specified price. With an option, one party owns the contract,
and the owner has the choice of whether or not she wants to buy/sell the thing in question.
With futures, both parties are obligated to complete the deal; with options, only one party is
obligated. The owner of the contract has the option (hence the name) of completing the sale
or not, and so logically will only do so if the doing so works to her benefit. Options also
differ in that the contract’s owner can choose to complete the transaction (called exercising
the option) on the contract’s expiration date or at any time prior to the expiration date.^6
With futures, neither party really needs to pay the other anything for the contract, since
it is a mutual agreement that offers the same opportunities and risks to both sides of the
deal. Options are a bit more one-sided. Since the option’s owner has the right to exercise
the option when it benefits her and no obligation to do so when it doesn’t, the owner will
have to pay the other party (called the option’s writer) something for agreeing to the con-
tract. This payment is called the option’s premium.
There are two types of options. A call entitles its owner to buy something at a specified
price. A put gives its owner the right to sell something at a specified price. Options are widely
available for the stocks of large companies. Suppose that the price of the stock of Yoyodyne
Corp. is currently $48.00 per share. You buy a call option expiring at the end of this year,
which allows you to buy the stock for $60 per share. If the stock price never rises above $60,
you will never have occasion to exercise this option, and so it will expire worthless. If, how-
ever, the stock prices rises to $75 per share you can exercise your option and buy it for $60.
If you believe that the stock is going to rise in price, why not just buy the stock? Either
way, you would turn a profit if you are right. One of the advantages of options is that, like
futures, they offer the potential for a great deal of leverage, offering an exaggeration of the
rate of return of the underlying security. The following example will illustrate this:Example 6.3.6 You believe that Yoyodyne’s stock will rise in value between now and
the end of the year. The stock price is now $48 and you buy a $60 call option for 100
shares. The option premium is $1.50 per share. How much will you make if the stock
price rises to (a) $75 per share, (b) $64.50 per share, or (c) $55 per share?Whatever the stock price does, this option costs you ($1.50 per share)(100 shares) $150.(^6) This is true of American-style options. Another type, European-style options, can be exercised only on a specifi c
date. Since the overwhelming majority of options in the United States are American-style, we will assume this in this
section are as well.