Picking months and strikes are big decisions for options traders. Do probabilities matter? We think so.

By Ticker Tape Editors
April 1, 2014

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We’re visual creatures. We like pictures and colors. So, it’s understandable that charts are pretty attractive to investors and traders. What’s not to like? Bars and candlesticks. Trendlines and fibonacci. Momentum and moving averages. You can load up a chart with so much information hopefully it will give you a general idea about the direction of a given stock or index.

The reality is, to create a smarter strategy overall, it’s not just about the pictures. It’s about the math. While charts can be helpful, I’ve yet to have a chart master show me with absolute certainty the probability a stock or index will reach some dreamy target price. Nope, that’s math, my friend. And once you have the math right, you can pick an optimal strategy on both trend as well as probabilities.

Like powerful charts, probabilities are conveniently calculated on the thinkorswim^{®} platform.

The goal here isn’t to talk you out of your charts. In fact, it’s to help you turn a chart’s directional bias—bullish or bearish—into a strategy based on the probability of making a profit. Quantifying the probability of a profitable strategy, or even of a stock reaching a certain price, helps you longer term make smarter decisions. And you do that by looking at the probability of a stock’s option expiring in the money or touching its strike price. [However, “touching” probability, is not a certainty, the market can be inconsistent, and can move quickly and drastically.]

The probability calculation uses the option’s strike price, the current stock price, time to expiration, as well as the option’s implied volatility. Crucially, the implied vol is derived from the option’s market price, so a single probability number contains the market’s “implied” estimate of how much the stock price might move.

In fact, no chart can tell you that. But why should you rely on probability numbers? Because they contain current market information via the option prices themselves, making probability numbers more responsive to changes in volatility and time. Remember, the more volatile the stock, or the more time to expiration, the more likely a large price change. Market makers make out-of-the-money option prices more expensive to reflect this. All else equal, higher option prices mean higher implied vol, which feed directly into the probability formula.

In this way, it’s not just your opinion of a stock’s chart that should go into a strategy. It’s the market’s collective wisdom.

Visualize this with the “Probability of Expiring Cone” on the Analyze tab, under the Probability Analysis subtab (see Figure 1). This feature points to future dates, revealing the range encompassing one standard deviation of potential stock prices. That’s geek-speak for a 68% likelihood of price action staying within that range before expiration.

You can edit the “Probability of Expiring Cone” study to show a different probability range, say 68%, 95%, and 99%. The prices where the cone intersects with future expiration dates are the upper and lower boundaries of the stock price’s theoretical range for that probability number. The further out you look, the wider the stock’s potential price range.

Despite formal textbook definitions, traders tend to see strike prices differently. Strike prices above and below a current stock price are like boundaries—levels the stock price may or may not reach in the future. Looking at the probability numbers on the Trade page at different strike prices and for different expirations, you can see what the market thinks of a probability that a stock price will either stay inside, or move beyond, a particular strike price. And knowing the probability can help you develop a more confident strategy relative to your directional bias. At the end of the day, it’s easier to make sense of options with a few handy guidelines, to wit:

1. Pick the expiration

2. Pick the strike price

3. Pick the strategy

**Step One: Pick the expiration. **On the Trade page, scan the days to expiration on the left-hand side for each month. For opening trades, a trader may consider using options that have between 30 and 60 days to expiration, or whichever expiration is closer to 45 days, give or take a few days. The logic? For credit strategies that partly rely on positive time decay, the number of days to expiration has a balance of a growing rate of time decay, and a higher absolute level of option extrinsic value. Sure, you can place a credit strategy in an expiration with six months out that might have a large credit. But the rate of time decay is lower. And you can place a credit strategy in an expiration with only a couple of days left that has a high rate of time decay, but no premium. 45 days may be a good place to start.

For debit strategies that rely on a favorable movement in the stock look for a balance duration of 30-to-60-days to expiration. This might give the stock time to move enough so the strategy might become profitable. More time than 60 days gives you more duration, but your trade might not change in price much when the stock price changes. Less time to expiration can give you a more responsive debit strategy, but there isn’t as much time for the stock price to make a favorable move.

**Step Two: Pick the strike price **After narrowing down expirations, narrow down the strike prices. You may consider looking for out-of-the-money (OTM) calls and puts that have about a 68% probability of expiring worthless. That number is available on the Trade page as the “Probability OTM” field in the Customize choice in the Layout menu (Figure 2). “About” 68% might be 64% on the low side and 72% on the high side, for example. A 68% probability OTM means theoretically the option will expire worthless 68% of the time. This means, if you had shorted that option, theoretically 68% of the time you would keep the option’s premium, less transaction costs, as profit by expiration. Of course, 32% of the time the short option could lose money, so it’s not a trading strategy in and of itself and nothing is guaranteed.

Just looking at the “Probability of Expiring” numbers for strikes at levels important to you from your chart analysis, you can get a sense of market sentiment regarding the likelihood a stock might be above or below a price at expiration. If you add the “Probability of Touching” column on the Trade page, that further shows market sentiment of the likelihood a stock price trades at the strike price at any time between a given moment and expiration.

**Step Three: Choose a strategy. **Finally, create a trading strategy the combines your directional bias from both charts and probability numbers on the trade page. You can do this by comparing other options to the option at the strike that has about a 68% probability of expiring worthless and between 30-and-60 days to expiration.

If you have a bullish bias, maybe you’d look at a short OTM put vertical, a bullish option strategy that loses money when the stock drops a lot, but can make money if the stock goes up, stays the same, or even drops by a small amount.

Let’s say you see a short one-point put vertical whose short option is at that reference strike trading for a $0.40 credit. Look at the put vertical at the same strike in a further expiration. Is the credit much higher or lower? What’s the probability of the short option strike expiring worthless in that further expiration? What’s your potential credit if you move the short strike to the strike with a 68% probability of expiring worthless in that month? This lets you compare the credit you may get—higher or lower—for a bullish short-put vertical strategy when you move away from that reference strike. You might choose a lower credit for a higher probability of expiring, worthless, or a higher credit for a lower probability of expiring worthless. The point is, you’re quantifying the potential profit, max loss, and probability of a trade that originated from a chart so you can make a more informed choice.

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