Calculating Potential Profit and Loss on Options

Key Points

  • Visualize your maximum gain, maximum loss and breakeven prices on an option strategy.
  • Calculate the probability of a stock reaching a certain level by a certain date.
  • Understand the basic functionality of the Trade & Probability Calculator.   

The Trade & Probability Calculator is a graphical tool that displays theoretical profit and loss levels for option or stock strategies. It helps you determine the likelihood of a strategy reaching certain price levels by a set date, using a normal distribution curve.  

Trade and Probability Calculator

Source: StreetSmart Edge.1

Where do I find it?

The Trade & Probability Calculator is available in the All in One trade ticket on StreetSmart Edge®, as shown above. 

How does it work?

To get started, you'll want to select the Trade & Probability Calculator tab (shown in the red box below). Then, you'll want to verify the graphical default profit and loss (P&L) settings: 

  • The date of entry (orange line)
  • The half-way point (blue line)
  • Expiration (purple line) 

You can change these defaults by selecting a specific date for any of the three lines. 

You can also view the numerical probability of reaching a specific target, above and below the current price, by expiration. To do this, move the vertical slider bars with your mouse or enter prices for the lower and upper targets (shown in the yellow boxes below).

Vertical Slider Bars

Source: StreetSmart Edge.1

All option pricing inputs can be changed. This allows you to view the price levels and probabilities that are most important to you. For example, you can edit the default implied volatility, dividend yield and interest rate settings to see how this might affect the outcomes, both numerically and graphically.

An example using the Trade & Probability Calculator

Let's suppose you are considering the purchase of 1 IBM 7/20/2013 205 Call at a price of 5.65, when the price of IBM is $203.91 (as shown in the screenshot above). Just like with the StreetSmart Edge Trade Screen and Symbol Hub, the following numerical calculations (shown in the pink box above) are done automatically:

  • Maximum gain = unlimited
  • Maximum loss = premium paid (5.65 x 100) = $565
  • Breakeven (assuming held to expiration) = strike price + option premium (205 + 5.65) = $210.65

The maximum gain for long calls is theoretically unlimited regardless of the option premium paid, but the maximum loss and breakeven will change relative to the price you pay for the option. These values are automatically calculated for many other option strategies, too, although the formulas are different.

When you select the Trade & Probability Calculator tab, the following additional calculations are done automatically and displayed graphically (shown in the green boxes above):

  • Probability of the option expiring below the lower slider bar. For example, if you set the lower slider bar to 195, this would equal one minus the approximate Delta of a 195 strike call or (1 - .6850 = .315 or 31.5%).
  • Probability of the option expiring above the upper slider bar. For example, if you set the upper slider bar to 205, this would equal the approximate Delta of the 205 call (.4579) or 45.79%. Since 205 is the call you are considering for purchase, this is also the same as the probability of the option expiring in the money.
  • Probability of the option expiring between the upper and lower slider bar. Assuming the two settings above, this would equal one minus the sum of the two previous calculations or (1 – (.3150 + .4579) = .2271 or 22.71%).

These probability calculations will change if you alter the lower and upper targets by either moving the slider bars with your mouse, or by typing in specific values for the lower target and upper target.

The profit and loss calculations (shown in the blue box above) for the date of entry (orange line), the half-way point (blue line), and expiration (purple line) are estimated assuming the price of the underlying stock remains unchanged from its current level. In this example, the 205 calls are out of the money initially so notice how the loss increases as time elapses toward expiration; this is due to time value erosion

To update pricing inputs, click on the "Refresh" button at the bottom of the tool.

If you would like to forecast the probabilities of the underlying stock reaching a different price on the various dates displayed, place your cursor anywhere on the chart and hold down the left mouse button. As shown in the pink circle below, this will display the probability of the option reaching that price at any time between now and expiration ("Prob. Touching") as well as the probability of the option reaching a certain price level at expiration ("Prob. Expiring").

Probability Touching

Source: StreetSmart Edge.1

In addition, you can easily make the following calculations, which many option traders find useful:

  • Probability of the option expiring below the upper slider bar. For example, if you set the upper slider bar to 205, it would equal one minus the probability of the option expiring above the upper slider bar (or 1 - .4579 = .5421 or 54.21%). This is the same probability as of the option expiring worthless.
  • Probability of earning a profit at expiration, if you purchase the 205 call option at 5.65. If you set the upper slider bar to the breakeven level of 210.65, this would equal the approximate Delta of a theoretical 210.65 strike call (.3058) or 30.58% (shown in red circles below). Note that while the option was only 1.09 points out of the money when purchased, the stock must increase by 6.74 points for the option to be profitable by expiration. This calculation estimates the approximate probability of that occurring.
  • Probability of losing money at expiration, if you purchase the 205 call option at 5.65. Once you have set the upper slider bar to 210.65, this would equal one minus the probability of earning a profit at expiration or (1 - .3058 = .6942 or 69.42%). You'll note that as in the previous examples, this is essentially equal to the sum of the other two probability calculations (shown in blue circles below) or 33.31% + 36.12% = 69.43%. 

Probability Calculations

Source: StreetSmart Edge.1

As shown below, if you would like to zoom in on the distribution curve, you can choose a closer date for the "Probability" calculation (shown in the red box below). This is helpful because it separates the visual profit and loss lines for the various dates. This will also cause the probability calculations (shown in the pink box below) to be oriented to the new date you selected, rather than the expiration date of the option (default setting). 

Probability Normal Distribution Curve

Source: StreetSmart Edge.1

As shown below, you can even turn off any of the various visual displays (the normal distribution curve in this example) by simply clicking on the colored box next to the date. 

Probability Lines

Source: StreetSmart Edge.1

Keep in mind

  • While profit and loss calculations assume that option positions will be held until expiration, you can usually close long or short option positions prior to expiration by buying or selling them in the market.
  • All probability calculations are based on an assumption of stable implied volatility values. Changes in implied volatility could dramatically affect forecasts.
  • Delta is often used as an instantaneous forecast of the approximate probability of an option contract expiring in the money. Just keep in mind that Delta is calculated continuously, so it will generally increase or decrease as the underlying stock price changes.
  • The projections and forecasts generated by the Trade & Probability Calculator are hypothetical in nature and should not be regarded as indicative of actual investment results.
  • Trading and investment decisions should not be based solely upon values or calculations generated by the Trade & Probability Calculator.

Coming up next

In reviewing the basic functionality of the Trade & Probability Calculator, you may have noticed how it can be a powerful tool in analyzing trades before you place them. In my next article, I'll go into more depth and cover additional functionality in analyzing specific option strategies.

 

Next Steps

Schwab clients: Contact a Trading Specialist at 800-435-9050 for questions or log in to the Trading Services Learning Center.
Not yet a client? Learn more about Schwab Trading Services.

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