36 lines
2.2 KiB
Plaintext
36 lines
2.2 KiB
Plaintext
Options and the Fair Game
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There may be a statistical advantage to buying stock as opposed to shorting
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stock, because the market has historically had a positive annualized return
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over the long run. A statistical advantage to being either an option buyer or
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an option seller, however, should not exist in the long run, because the
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option market prices IV. Assuming an overall efficient market for pricing
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volatility into options, there should be no statistical advantage to
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systematically buying or selling options. 1
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Consider a game consisting of one six-sided die. Each time a one, two, or
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three is rolled, the house pays the player $1. Each time a four, five, or six is
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rolled, the house pays zero. What is the most a player would be willing to
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pay to play this game? If the player paid nothing, the house would be at a
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tremendous disadvantage, paying $1 50 percent of the time and nothing the
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other 50 percent of the time. This would not be a fair game from the house’s
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perspective, as it would collect no money. If the player paid $1, the player
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would get his dollar back when one, two, or three came up. Otherwise, he
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would lose his dollar. This is not a fair game from the player’s perspective.
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The chances of winning this game are 3 out of 6, or 50–50. If this game
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were played thousands of times, one would expect to receive $1 half the
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time and receive nothing the other half of the time. The average return per
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roll one would expect to receive would be $0.50, that’s ($1 × 50 percent +
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$0 × 50 percent). This becomes a fair game with an entrance fee of $0.50.
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Now imagine a similar game in which a six-sided die is rolled. This time
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if a one is rolled, the house pays $1. If any other number is rolled, the house
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pays nothing. What is a fair price to play this game? The same logic and the
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same math apply. There is a
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percent chance of a one coming up and the
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player receiving $1. And there is a
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percent chance of each of the other
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five numbers being rolled and the player receiving nothing. Mathematically,
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this translates to:
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percent
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percent). Fair value for a
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chance to play this game is about $0.1667 per roll.
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The fair game concept applies to option prices as well. The price of the
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game, or in this case the price of the option, is determined by the market in |