Option Investor
Educational Article

Probability Of Profit

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By Lee Lowell

Going into most option trades, the trader feels pretty good about his/her chances of walking away a winner. They've done the research. They've checked the fundamentals, the technical picture, and maybe even done some volatility analysis (my favorite part). But have you checked your actual chances of success of your desired position? This would be achieved by checking the "probability of profit." It's very easy to do. All you need is to have access to a probability calculator. If you've ever done studies on this subject, you'll find that most option buying strategies lie somewhere in the range of having a 2%-35% chance of success, while option selling strategies fall somewhere in the range of 70%-95% chance of success. The reason that most option buyers have such a small chance is due to the fact that most will buy overvalued, out-of-the-money options. Be that the case, I'm still going to show you how to check your chances of success for whatever strategy you choose.

Since I like to sell options to take advantage of daily time decay, I'm going to walk you through the steps I take to find the probability of the strategy yielding a winner. I never sell naked options so most of my trades are selling credit spreads on either the indices or some individual stocks. One of the keys to any selling-type strategy is to find an underlying security with above- average implied volatility. One of the easiest securities to do this with is the OEX. You can find its implied volatility by looking at it own volatility index called the VIX.

The graph above is a one year chart for the VIX. As of Friday, 2/16/01, the VIX was trading just around 25 which is a little under the average for the last year. The VIX tells us how expensive or cheap the options on the OEX currently are compared to its past. We need to know these numbers because it will come into play when using our probability calculator.

The OEX closed on Friday 02/16/01 around 675.

Since I believe that the OEX will not make a substantial rebound in the very near term, I want to sell some call spreads on the OEX for the nearest expiration month. I will concentrate on selling out-of-the-money(OTM) options since these are usually overpriced, and because they have a smaller chance of becoming profitable. If I am wrong on my prediction and the OEX starts to rebound, the OTM calls give me more room for error since they have no intrinsic value to begin with. I'm looking at selling the March OEX 705 calls and buying the March 710 calls for a credit of 1 point. My reward is limited to $100 per spread and my risk is limited to $400 per spread. Does that seem like a good deal? Risking $400 to make $100? We won't know until we check our odds. Let's take a look at the probability calculator.

On the top of the calculator you will see the inputs area. Here you enter the current price of the underlying security along with the days to expiration, volatility estimate, and your target price level. I have loaded the current price of the OEX of 668, 24 DTE, a volatility estimate of 25% and my target price of 706 which is my breakeven level.

If you look at the results, you will see the chances of the OEX going above the breakeven point of 706 that I set in the inputs section. It's only giving me a 19.40% chance of the OEX going above 706. So I have approximately an 80% chance of this trade working out in my favor. Going back to our question above: does this seem like a good deal to risk $400 to make $100? I think if you have any chance over 80%, then it's a pretty good deal. You can look at it on the flipside too as the option buyer. Would you rather risk $100 to make $400. On the surface this seems like the better bet. But if you only have a 20% chance of winning that $400, would you do it? It's a personal preference, but as the option seller, I like taking the odds of an 80% chance of winning over a 20% chance.

We need to discuss the inputs for a minute. Since the price of the underlying, DTE, and breakeven points are known numbers, the only one we need to be careful about is the volatility component. Since the volatility input is usually a guesstimate, we can achieve different probability numbers. I like to stick with the market's implied volatility forecast because that usually represents a wide consensus of most market participants. The OEX is easy to use because the VIX is a readily available number. When pricing individual stocks, you need to have a good handle on the volatility estimate. Look at historical volatility charts along with the implied volatility charts and come to some sort of average. If you're looking to sell options, choose the higher volatility number. This will give you more room for error because you'll be more cautious of the strikes you choose.

For those of you who like riskier trades and have the capability in your brokerage account to sell naked options, you can get some pretty good chances of success for the options to expire worthless. Take a look at selling the MARCH OEX 560 put/720 call strangle for 2 points. This makes our breakeven points 558 on the downside and 722 on the upside. (THIS IS BY NO MEANS A RECOMMENDATION OF ANY KIND TO SELL STRANGLES ON THE OEX!)

This gives us a greater than 99% chance of the OEX not reaching our downside parameter and an 88% chance of the OEX not reaching our upside parameter. Granted, there is unlimited risk in this trade, but the chances of that happening within 24 days are slim. If the OEX stays within our wide trading range, we get to keep our $200 premium. Think a stock like Brocade (BRCD) is due for a quick and large recovery? Why not buy some cheap OTM calls. How about the March $70 calls for 1 point? C'mon, it's only $100.

Taking into consideration that BRCD's implied volatility levels are at yearly high's, you'll only have about a 6% chance of making any money on that option. Good luck.

Now, these probability calculations are not the end-all be-all of options trading. Since the outputs are based on guesses of your volatility input, the outcomes can always surprise you. Your volatility estimate at the time of trade may be different a week later, or some earnings warning may come out and drastically move the price of the stock. Check your chances with the calculator during the course of the trade to see how the odds change. This is why I like to make my sell-side trades on the indices instead of individual stocks because they are prone to less dramatic moves.

The probability calculator is just another tool to add to your arsenal when trading options. Use it before you buy that next OTM option. Your chances of success might surprise you.

Until next time...


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