# Options Unlike Stocks Are All About Probabilities: IWM As A Case In Point

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Includes: IWM
by: Reel Ken

Options trading has gained popularity in the last few years. It seems that everywhere you turn someone is offering strategies to take advantage of this popularity. Even one of the major TV stations devotes some programming just to option trades.

The promoters of these strategies market them in many ways - protecting against downside risk, adding a little income, leveraging stock movements, and others. Any of these strategies can and does work some of the time, possibly even most of the time. It is not my purpose to single out any strategy as superior to any other strategy, but to provide a lesser known way to evaluate their merits. In essence, a methodology that can help you determine if you are on the winning or losing side of the option trade.
Let’s take a very simple strategy and analyze it from a probability perspective. That is, we will not question whether the trade will or will not work, just evaluate it in terms of expected outcome.
There are many popular strategies --- verticals, condors, butterfly, calendar spreads, etc. For purposes of this article I will use just one simple strategy, though the concept works for all strategies. A very popular strategy that is often promoted is an “Out of the money Bear Call Spread”. This strategy pays off if the underlying stock closes below the strike price, and loses if the price is somewhat above the strike price. Let’s look at an example using the iShares Russell 2000 Index ETF (NYSEARCA:IWM), which is currently trading around \$67.
A typical promotion suggests selling the October Call at, say, \$77 and buying the October call at \$79. Entering this trade would mean a net credit of \$.20 (receive .46 for selling the call and paying .26 for buying the higher call).
If you made this trade for, say 50 options (each option is 100 shares), you would receive \$ 1,000. Provided that IWM closes at or below \$77 at expiry, you get to keep the whole amount. If it closes above \$77 you start to “give back.” At \$77.20 you break even. At \$79 you hit your maximum loss of \$1.80 per option or \$9,000.
When I see these types of trades promoted they almost always come with hyperbole that IWM would have to climb 15% in a month for you to lose and is, therefore, a low risk trade.
But, let’s look at the trade from a probability view. Many of the most popular Option Houses provide software that calculates the probability of any strategy. So using one of the most popular and widespread, we find the following: There is actually a 83.22% chance that IWM closes at or below \$77 and you win. Sounds like a pretty good bet and one you may want to take. This seems to be in line with the “low risk” hyperbole.
Let’s look a little further. There is a 12.82% chance IWM hits \$79 and you suffer a maximum loss. The remaining 3.96% is the likelihood that it finishes between \$77 and \$79 and you lose some, but not the maximum.
Now, let’s just apply the math. The maximum potential gain is \$1,000. This has an 83.22% probability, so the statistically calculated expected gain is \$1,000 times 83.22% or \$ 832.20. Your maximum potential loss is \$9,000 and has a 12.82% probability of occurring. Therefore the expected loss is \$1,153 (\$9000 times 12.82%).
Calculating the partial loss is complicated, but it is around \$160, the total expected loss is \$1,313.
Now we can calculate the expected outcome --- expected gain minus expected loss (\$832-\$1,313) or a \$481 loss.
What this means is that for every time you place a trade (frequency), given enough trades, you can expect to lose \$481. Make this type of trade, say 10 times, and you will likely lose \$4,800.
If you want to make this trade just once, the odds (83%) make you a favorite to win. But that begs the question, if you win, will you walk away or try again. The more you try again, the greater your likelihood of becoming a loser. Make this type of trade once per month and you stand to be a big loser.
If all this sounds like casino betting - you are absolutely correct. Options, unlike stocks, are all about probabilities. The “House” sets the odds and takes its piece.
Well, if the Bear Call Spread at these levels is a loser, wouldn’t that mean the opposite strategy, a Bull Call Spread, would be a winner? Let’s bring the same analysis.
The probability of success is exactly opposite, but the expected outcome is not quite. The reason is simple - the Bid/Ask spread. The Bear Spread resulted in a net .20 credit, but the Bull Call Spread results in a net .24 debit. This difference of .04 times 50 contracts results in a \$200 differential. So, instead of gaining the “inverse” of \$481, you gain instead \$281.
Looking at the Bull and Bear Spread together, the Bear Spread expects a loss of \$481 and the Bull Spread a profit of \$281, so the “Tandem Trades” result in a loss of \$200. That is a loss to the option traders and not the market maker; the option “House” has its \$200 profit.
What I find most interesting in this trade example is that the Bear Call Spread with its high apparent probability of success seems intuitively to be the better choice. After all, wouldn’t you prefer an 80% chance of success over a 20% chance of success?
Of course this would be the odds on favorite if the amount to gain or lose were close in value. Not so, as it is a high probability win of a little money versus a low probability loss of a much larger sum. The odds are actually against you and like casino play, few individuals have the discipline to just walk away a winner. They come back, because the same elements that inspired them to make the first bet still remain. This “frequency” trading all but assures they will ultimately lose.
Now, don’t come to the conclusion that Bull Spreads are better than Bear Spreads or any similar “rule.” Given different strike prices, expiry dates and volatility could have different results.
What is worthwhile noting, however, is that in most cases one strategy (Bear Spread) and its “Counter Strategy) Bull Spread is not neutral. One side of the “Tandem Trade” is often a winner and the other side a loser. To make money over the long run you want to be on the winning side of the trade as often as possible.
On the other hand, if you were using options to hedge other positions, rather than make an independent bet, you could use this type of analysis to determine your long term expected cost of protection.
I would be remiss if I didn’t mention two other critical points.
First is the “skill” component. Skill can change the odds. For instance, the odds of winning at Blackjack favor the House. However, if you “card-count” the odds turn in your favor. Likewise, if you have special knowledge about the probable move in the underlying security, you can turn the odds in your favor. For instance, if your research indicates that IWM is much more likely to go down then up, and your research is correct, the dynamics of the trade change.
Second, you could try and to close the trade before expiry if it turns against you. Many people believe that this will increase their chances of winning or losing. Actually, this is not the case. Closing the strategy is just another trade and subject to its own separate analysis.
This means that if we analyzed closing the trade, we may find that it helps and we may find that it hurts. Furthermore, making an additional closing trade increases your frequency and brings you closer to the expected outcome.
In conclusion, Options pricing has at its core probability theory. This surfaces with terms such as delta, theta, volatility, etc. One can, with a little work, use the same principles to help them determine the probable outcome of any trade and whether the trade actually makes sense. It is the hope of this author that you have a better understanding of how this can be accomplished.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.