Stock and Options



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.

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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.” |

| |

|--Adam Smith |

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.

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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.

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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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