35 lines
2.4 KiB
Plaintext
35 lines
2.4 KiB
Plaintext
Chapter 27: Arbitrage 441
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between 50 and 60 at expiration. In that case, the out-of-the-money, written options
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would expire worthless-the January 60 call and the January 50 put. This would leave
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a long, in-the-money combination consisting of a January 50 call and a January 60
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put. These two options must have a total value of 10 points at expiration with XYZ
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between 50 and 60. (For example, the arbitrageur could exercise his call to buy stock
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at 50 and exercise his put to sell stock at 60.) Finally, assume that XYZ is below 50 at
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expiration. The calls would expire worthless if that were true, but the remaining put
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spread- actually a bear spread in the puts -would be at its maximum potential of 10
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points. Again, the box spread could be liquidated for 10 points.
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The arbitrageur must pay a cost to carry the position, however. In the prior
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example, if interest rates were 6% and he had to hold the box for 3 months, it would
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cost him an additional 14 cents (.06 x 9½ x 3112). This still leaves room for a profit.
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In essence, a bull spread ( using calls) was purchased while a bear spread ( using
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puts) was bought. The box spread was described in these terms only to illustrate the
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fact that the arbitrageur is buying and selling equivalent positions. The arbitrageur
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who is utilizing the box spread should not think in terms of bull or bear spread, how
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ever. Rather, he should be concerned with "buying" the entire box spread at a cost of
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less than the differential between the two striking prices. By "buying" the box spread,
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it is meant that both the call spread portion and the put spread portion are debit
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spreads. Whenever the arbitrageur observes that a call spread and a put spread using
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the same strikes and that are both debit spreads can be bought for less than the dif
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ference in the strikes plus carrying costs, he should execute the arbitrage.
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Obviously, there is a companion strategy to the one just described. It might
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sometimes be possible for the arbitrageur to "sell" both spreads. That is, he would
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establish a credit call spread and a credit put spread, using the same strikes. If this
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credit were greater than the difference in the striking prices, a risk-free profit would
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be locked in.
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Example: Assume that a different set of prices exists:
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XYZ common, 75
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XYZ April 70 call, 8½
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XYZ April 70 put, 1
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XYZ April 80 call, 3
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XYZ April 80 put, 6
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By executing the following transactions, the box spread could be "sold": |