33 lines
2.3 KiB
Plaintext
33 lines
2.3 KiB
Plaintext
Chapter 27: Arbitrage 431
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In an actuarial sense, the carrying cost could be expressed in a slightly more complex
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manner. The simple formula (strike x r x t) ignores two things: the compounding
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effect of interest rates and the "present value" concept ( the present value of a future
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amount). The absolutely correct formula to include both present value and the com
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pounding effect would necessitate replacing the factor strike (1- rt) in the profit for
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mula by the factor
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Strike
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(1 + r)f
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Is this effect large? No, not when rand tare small, as they would be for most option
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calculations. The interest rate per month would normally be less than 1 %, and the
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time would be less than 9 months. Thus, it is generally acceptable, and is the com
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mon practice among many arbitrageurs, to use the simple formula for carrying costs.
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In fact, this is often a matter of convenience for the arbitrageur if he is computing
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the carrying costs on a hand calculator that does not perform exponentiation.
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However, in periods of high interest rates when longer-term options are being ana
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lyzed, the arbitrageur who is using the simple formula should double-check his cal
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culations with the correct formula to assure that his error is not too large.
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For purposes of simplicity, the remaining examples use the simple formula for
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carrying-cost computations. The reader should remember, however, that it is only a
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convenient approximation that works best when the interest rate and the holding
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period are small. This discussion of the compounding effect of interest rates also rais
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es another interesting point: Any investor using margin should, in theory, calculate
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his potential interest charge using the compounding formula. However, as a matter
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of practicality, extremely few investors do. An example of this compounding effect on
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a covered call write is presented in Chapter 2.
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BACK TO CONVERSIONS AND REVERSALS
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Profit calculation similar to the conversion profit formula is necessary for the rever
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sal arbitrage. Since the reversal necessitates sho1ting stock, the trader must pay out
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any dividends on the stock during the time in which the position is held. However,
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he is now bringing in a credit when the position is established, and this money can
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be put to work to earn interest. In a reversal, then, the dividend is a cost and the
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interest earned is a profit. |