# How Algebra Helps in Options Trading

02/20/2013 7:00 am EST

**Focus:** OPTIONS

*Before your eyes glaze over after you see the word, algebra, remember
that applying some of the formulas can help an options trader exponentially,
notes Dan Passarelli of MarketTaker.com*.

One of the greatest advantages of options trading is its extreme flexibility in both the initial construction of positions and in the ability to adjust a position to match the new outlook of the underlying. The trader who limits his or her world to that of simply trading equities and ETFs can only deal in terms of short or long. A change in an outlook often requires starting a new position or exiting the old one. The options trader can usually accommodate the newly developed thesis much more fluidly, often with minor adjustments on the position in order to achieve the right fit with the new outlook.

One concept with which the trader needs to be familiar in order to construct the necessary adjustments is that of the synthetic relationships. Most options traders neglect to familiarize themselves with the concept when learning to trade options. 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 to memorize all of the relationships. I find remembering the mathematical formula and modifying as needed to be much more useful and easier.

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 high school algebra to formulate 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 adjustment 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 or to modify existing positions either in whole or part. You might have hated algebra when you were in school, but applying some of the formulas can help an options trader exponentially!

**By Dan Passarelli, Founder, MarketTaker.com**