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September 2, 2010

Math Club Talks Options

One of the hallmarks of option trading is its extreme flexibility in both the initial construction of positions and in the ability to mutate forms to accommodate the evolution of a trader’s thesis regarding the impending behavior of the underlying. The trader who limits his world to that of simply trading equities and ETF’s can only deal in terms of short or long and the change of a thesis often requires starting anew in the position. The option trader can usually accommodate the newly developed thesis much more fluidly, often with minor surgery on the position in order to achieve the right fit with the new world view.

One concept with which the trader needs to be familiar in order to orchestrate the necessary transmogrifications is that of the synthetic relationships. This concept arises from the fact that appropriately structured option positions are virtually indistinguishable in function from the corresponding long or short equity/ETF position. One approach to remembering the relationships is rote memorization of the relationships. I find remembering the mathematical formula and modifying as needed to be much more useful.

For those who remember high school algebra, the fundamental equation expressing this relationship is S=C-P. The variables are defined as S=stock, C=call, and P=put. This equation states that stock is equivalent to a long call and a short put.

Using tenth grade algebraic rearrangements of this equation, the various equivalency relationships can easily be determined. Remember that we can maintain the validity of the equation by performing the same action to each of the two sides. This fundamental algebraic manipulation allows us, for example, to derive the structure of a short stock position by multiplying each side by -1 and maintain the equality relationship. In this case (S)*-1 =(C-P)*-1 or –S=P-C; short stock equals long put and short call.

Such synthetic positions are frequently used to establish positions either ab initio or to modify existing positions either in whole or part. And you thought Math Club was only to meet girls.

Bill Burton

Writer, MTM