Thursday, October 8, 2009

The Trade Off: Risk-Reward vs. Probability of Profit

When entering the realm of options spread trading, it is imperative that a trader understands probability of profit. Not only how to calculate it, but also the role it plays in the decision making process. I would hope most visitors to this blog are already cognizant of this concept, but there are no doubt newcomers to the options arena that might benefit from an overview. In my next two posts I'll review a simple method for calculating probability of profit and illustrate the relationship between increasing probability of profit and decreasing risk-reward. Be forewarned, there will be some math involved, so hold your head still so nothing spills out!

As a precursor to calculating probability of profit, a trader must first understand the greek delta. One of the characteristics of delta is it calculates the probability of an option expiring in-the-money. For example, suppose stock XYZ is trading at $100 and the 90 strike put option has a delta of .20. This means there is a 20% probability that the 90 strike put will be in-the-money at expiration. Put another way, there is a 20% probability the stock price will be below $90 at expiration. Now, we can use a little arithmetic to calculate the probability of an option expiring out-of-the-money. We can all agree that there is a 100% probability of the stock price residing somewhere. If there is a 20% chance the stock will be below $90, then it stands to reason that there is an 80% chance of the stock residing above $90 at expiration. Thus the formula for calculating the probability of an option expiring out-of-the-money is: 1 minus delta.

Although delta can be used to calculate probability of profit on most option spread trades, I'm going to focus on vertical spreads. Remember, the four verticals are the bull call, bull put, bear call, and bear put spreads. The two bullish spreads consist of buying a lower strike option and selling a higher strike option of the same type in the same expiration month. To realize the maximum profit we want the stock to be above the higher strike price at expiration. Alternatively, the two bearish spreads are constructed by buying a higher strike option and selling a lower strike option of the same type in the same expiration month. Capturing the maximum profit on these two spreads requires the stock to be below the lower strike price at expiration. To calculate the probability of profit on a bull spread, simply use delta to calculate the probability of the stock residing above the higher strike. Conversely, for a bear spread calculate the probability of the stock residing below the lower strike.

Suppose stock ABC is trading at $50 and we enter a bull put spread by simultaneously buying the 40 put and selling the 45 put. To realize our maximum profit we need the stock to be above $45 at expiration. Using delta we can calculate the probability of the stock residing above $45, thereby calculating our probability of profit. The current delta of the 45 put is .30, implying the stock has a 30% probability of residing below 45 at expiration. We can plug this delta (.30) into our formula: 1 - .30 = .70. In addition to knowing the risk-reward of the 45-40 spread, I now know the likelihood of realizing my profit is 70%.

For other posts on delta, check out:


Stay tuned for Part Two...

2 comments:

Tee Chess said...

When entering into trade we all wants to know the probability of profit against the risk involved. In this post you have provided a clear overview about it. I am thankful to you for throwing light on this important aspect.
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Ayesha Jaiswal said...

You have enlightened very useful points. You have provided a good overview of how the probability of profit is essential to know against the risk involved in the trading. A clear understanding of risk and profit percentage is good to avoid future loss.
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