# Stock and Options

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```							                                      Stock and Options
Prof. Mike Sproul
3/5/2000

1.   Long and short positions: Someone who owns a share of stock is in a long position. Someone who
has promised to deliver a share of stock for a set price is in a short position. Figure s1.1 shows two
ways to create a short position in GM stock: (a) Borrow a share of GM and sell it, or (b) Sell an IOU
promising to deliver a share of GM.

A person who owns the stock obviously stands to gain if its price rises and to lose if its price falls. Thus the
long position is called bullish. A short seller will gain if the stock drops and lose if it rises. This position is
bearish. For example, GM is worth 60 and a short seller promises to deliver 1 share in exchange for 60
today. If GM drops to 50, the short seller buys GM for 50, delivers it to the holder of his IOU, and gains 10.
Conversely, if GM rose to 70, the short seller would have to pay 70 for GM and then turn it over to the
holder of his IOU. Thus the short seller loses 10. The profits earned in long and short positions are shown
in figure s1.2.

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2.   Call options give their owners the right (not the obligation) to buy a share of stock at a specified time
for a specified price. For example

“Holder of this piece of paper has
the right to buy 1 share of GM stock
from me for \$50 today.”

--J.P. Morgan

If GM sells for 60, then this call gives the holder the right to buy 1 GM from the option writer (Morgan) for
50, and then sell it on the open market for 60, thus earning 10. Anyone would be willing to pay 10 for the
paper that enables them to do this. Table 1 shows what happens to the price of the call as the stock price
changes, and figure s1.3 plots the numbers from table 1.

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3.   Put options give their owners the right to sell a share of stock at a specified time for a specified price.
For example:

“Bearer has the right to sell
me 1 GM for \$70 today.”

If GM sells for 60, then this put enables the bearer to buy GM on the open market for 60, and then turn
around and sell it for 70 to Adam Smith. Anyone would be willing to pay 10 for the piece of paper that
allows them to do this. Table 2 shows the price of the put as the stock price changes, and figure s1.4 plots
the numbers.

3
4.   Combining securities: If an investor is short, he will lose if the stock price rises. He can hedge against
this by buying a call. Every time the stock rises by \$1, he’ll lose 1 on his short, but his call will rise by
1, so he is protected or “hedged”. In return, he makes less when the stock price falls. This is shown in
figure s1.5.

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Figure s1.6 shows the profit of a put bought and a call bought. Adding the heights of both sets of lines gives
a v-shaped profit pattern, so that the holder of this portfolio gains if the stock price rises OR falls. He loses
if the stock price stays the same.

Exercises:
Draw the profit patterns for the following combinations (answers below)
a)   long + put bought
b)   long + call written
c)   short + put written
d)   put written + call written

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6

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