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October 23, 2014

Math is Beneficial for Option Trading

One of the greatest advantages for an option trader is the initial flexibility of the position and the ability to adjust a position to match the new outlook of the underlying. The option trader who limits his or her world to that of simply trading equities also limits the position and outlook to either long (bullish) or short (bearish) positions. A change in an outlook regardless of the reason often requires starting a new position or closing out the old one. The options trader can usually change with  the newly developed outlook with much more ease, often with a minor option adjustment on the position in order to achieve the right fit for the new outlook.

Option Adjustments

One concept with which the option trader needs to be familiar in order to construct a necessary option adjustment is that of the synthetic relationship. Most options traders neglect to familiarize themselves with this 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 position. One approach to remembering the relationships is to memorize all of the relationships. It may be easier to do this by remembering the mathematical formula below and modifying as needed.

Synthetic Formula

For those who remember algebra probably that was taught back in high school, 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 option positions or to make an option adjustment either in whole or part. You might have not liked or did well with algebra when you were in school, but applying some of the formulas can help an option trader exponentially!

John Kmiecik

Senior Options Instructor

Market Taker Mentoring

May 15, 2014

Delta and Your Overall Position

Delta is probably the first greek an option trader learns and is focused on. In fact it can be a critical starting point when learning to trade options. Simply said, delta measures how much the theoretical value of an option will change if the stock moves up or down by $1. A positive delta means the position will rise in value if the stock rises and drop in value of the stock declines. A negative delta means the opposite. The value of the position will rise if the stock declines and drop in value if the stock rises in price. Some traders use delta as an estimate of the likelihood of an option expiring in-the-money (ITM). Though this is common practice, it is not a mathematically accurate representation.

The delta of a single call can range anywhere from 0 to 1.00 and the delta of a single put can range from 0 to -1.00. Generally at-the-money (ATM) options have a delta close to 0.50 for a long call and -0.50 for a long put. If a long call has a delta of 0.50 and the underlying stock moves higher by a dollar, the option premium should increase by $0.50. As you might have derived, long calls have a positive delta and long puts have a negative delta. Just the opposite is true with short options—a short call has a negative delta and a short put has a positive delta. The closer the option’s delta is to 1.00 or -1.00 the more it responds closer to the movement of the stock. Stock has a delta of 1.00 for a long position and -1.00 for a short position.

Taking the above paragraph into context one may be able to derive that the delta of an option depends a great deal on the price of the stock relative to the strike price of the option. All other factors being held constant, when the stock price changes, the delta changes too.

An important thing to understand is that delta is cumulative. A trader can add, subtract and multiply deltas to calculate the delta of the overall position including stock. The overall position delta is a great way to determine the risk/reward of the position. Let’s take a look at a couple of examples.

Let’s say a trader has a bullish outlook on Apple (AAPL) when the stock is trading at $590 and purchases 3 June 590 call options. Each call contract has a delta of +0.50. The total delta of the position would then be +1.50 (3 X 0.50) and not 0.50. For every dollar AAPL rises all factors being held constant again, the position should profit $150 (100 X 1 X 1.50). If AAPL falls $2, the position should lose $300 (100 X -2 X 1.50).

Using AAPL once again as the example, lets say a trader decides to purchase a 590/600 bull call spread instead of the long calls. The delta of the long $590 call is once again 0.50 and the delta of the short $600 call is -0.40. The overall delta of the position is 0.10 (0.50 – 0.40). If AAPL moves higher by $5, the position will now gain $50 (100 X 5 X 0.10). If AAPL falls a dollar, the position will suffer a $10 (100 X -1 X 0.10) loss.

Calculating the position delta is critical for understanding the potential risk/reward of a trader’s position and also of his or her total portfolio as well. If a trader’s portfolio delta is large (positive or negative), then the overall market performance will have a strong impact on the traders profit or loss.

John Kmiecik

Senior Options Instructor

Market Taker Mentoring