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