# Probability of Profit

Hi Mark,

I would like to know how to correctly calculate (and use) the “probability of profit” tool…

Everywhere I look amongst the options sellers I read about it, and, behind the obvious, I think it may be an useful tool, but only if correctly understood (and used).

Do you calculate it by yourself? Do you trust any site in particular?

Thanks, as always
Roberto

***

Hi Roberto,

‘Probability of profit’ is not something I calculate.  Too many variables are involved (see below).

However, these items can be calculated

a) Probability that an option will finish in the money (i.e., be ITM) at expiration

b) Probability that any underlying asset will move to touch the strike price (i.e., the option becomes ATM or ITM) of any of your short options at any time during its lifetime, even when it does not ‘finish’ ITM

c) Probability that an underlying will move to touch any specific price (presumably your target exit price) at any time during the lifetime of the option.  And you can set the ‘expiration’ date of the option to coincide with your planned exit date – for traders who prefer not to hold through expiration.

We cannot determine probability of profit because certain events may occur and each of them affects the final outcome: profit or loss.  For example, you may make an adjustment or exit quickly with a small profit.

There is no way to determine WHEN the underlying may reach the point at which you plan to exit.  You can determine the probability of reaching that price, but the time elapsed before that occurs determines whether you earned a profit [If you exit when the option is still OTM for example, you could have a profit if enough time has elapsed]

There is no way to know the implied volatility of the options at whatever future time you would choose to exit.  If you close the position on at unknown date and when options are trading with an unknown implied volatility, there is no way to know if the position will be profitable.

No. I do NOT calculate this myself.  Some brokers offer the tool that calculates ‘the probability of touching.’  I prefer to use, and trust, the free software made available by Peter Hoadley.

To make it work, set the strike price (or any other stock price of interest) and expiration day (or any other date.  If you plan to exit early, there is no reason to use the option expiration date.  Use your planned exit).  Select a volatility for the calculations, with your best bet being the current IV of the specific option that concerns you.

The calculator output gives the probability of touching at some point.  It does not give probability of profit.  Note:  Even when option finishes ITM, it may be a profitable trade – if it is ITM by a small amount.

882

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### 11 Responses to Probability of Profit

1. Jeff 01/25/2011 at 7:00 AM #

Very interesting and thoughtful question posed by the reader.
As a covered calls investor, I like to determine the ‘Probability of Profit’ prior to making the trade. For example, yesterday I bought 700 MSFT at \$28.15 and sold 7 Feb2011 \$29.00 strike options at \$.40. At the point in time this transaction was made and using the Black-Scholes Options Pricing Model in the Schwab Hypothetical Options Pricing calculator, the resulting probability of making a profit (if held until Feb2011 options expiration) for this Microsoft covered calls position is 58.9%. This compares with a probability of profit of 50.3% for a buy-and-hold of Microsoft stock over the same timeframe. I invest exclusively via covered calls, but I suspect the probability of profit for other options strategies could also be determined from sophisticated statistical analysis with options pricing models.

2. Mark Wolfinger 01/25/2011 at 9:14 AM #

Jeff,
I’m interested in knowing how you calculate the probability of profit for your trades?
Do you ONLY consider that probability at expiration? Do you ignore the real-world possibility of making an adjustment?
According to your data,
MSFT will finish above \$27.75 that 58.9% of the time. Is that the calculation you made (ignoring commissions)?
Have you considered what happens when MSFT falls to \$27 and you choose to make an adjustment?
Thanks

3. Jeff 01/26/2011 at 3:01 PM #

Mark,
Thanks for your reply. As you well know, active position management is one of our investing ‘edges’ compared with the traditional buy-and-hold investor. I have developed a set of rolling rules that work for me — so that my decisions as to when to adjust (i.e roll) a position is made whenever these criteria are met. This works for me as it negates the emotions that sometimes effect us (and causes us to act impulsively) when our stock is moving quickly either up or down; and thus distracts us from our desired goal of objective decision-making.
Regarding the other question, I normally only calculate the Probability of Profit just prior to entering the trade. Of course, the probability changes continuosly and can be recalculated at any point in time while the position is held but I don’t choose to do that. Once I’m in the position, then I’m on autopilot since either my rolling rules will dictate if/when to adjust the position. If the rules aren’t triggered, then the position is simply held until options expiration Friday.
It has taken many years to develop my detailed, well-defined covered calls decision-making process, but having very specific rules that substantially reduce the emotional roller coaster that is the market has both made investing much more enjoyable and also improved my results.
Regards and Best Wishes,
Jeff

4. Mark Wolfinger 01/26/2011 at 3:04 PM #

Jeff,
Nice. It’s great to trade with confidence and have years of experience. You know your system is viable.
Congratulations

5. Tom 01/29/2011 at 4:43 PM #

Jeff,

You wouldn’t mind sharing some of your “rolling rules”, would you? I’m not looking to mimic anyone, as I have some rules of my own that have been working for me. But, understanding what others find useful and why is always helpful to me, even if I ultimately discard it as “not my style”.

Thanks,

Tom

• Mark D Wolfinger 01/29/2011 at 9:24 PM #

Tom,
Good question. Keep in mind that some people have proprietary strategies that they do not share.
Jeff, we’d love to hear from you.

6. Jeff 01/29/2011 at 10:02 PM #

Tom,
Sorry I missed your most recent comment on the Probability of Profit post on Mark’s blog. Please recall that I am strictly a covered calls investor, so my rules apply solely to CCs. An article from my blog that describes my rolling rules is here:
http://coveredcallsadvisor.blogspot.com/2009/11/covered-calls-position-management-when.html
Regarding the 3 specific rules listed there, my current thinking is that the 10% criteria might be somewhat high. I will be conducting some sensitivity analyses (as soon as I get the time) because my gut is telling me that 7% to 8% area might produce a very slightly better overall ROI result.

Thanks for your interest in this important topic.

Best wishes

• Mark D Wolfinger 01/29/2011 at 10:02 PM #

Jeff,

Thanks for sharing.

• Tom 01/29/2011 at 11:21 PM #

Jeff,

Thanks so much for sharing! I am a CC-only guy right now, also, and look forward to taking a look at your rules.

Take care,

Tom

7. Shannon 02/01/2011 at 8:28 AM #

Mark,
Please elaborate on my opinion regarding probability calculators: I believe they are too simplistic because they do not account for trends, news events, and other technical indicators (like support and resistance). While the market looks random, it is not. For example, when the market is in an up trend I do not believe it has the same probability of moving up as it does to move down…the probability is skewed to a higher likelihood of moving up. But I don’t know of any product out there that will take this into account.

Thanks.
Shannon.

8. Mark D Wolfinger 02/01/2011 at 9:45 AM #

Hello Shannon,

Good comment.

I don’t believe YOU can use probability calculators effectively. Those calculators, by definition, do not ‘believe in’ trends, technical analysis, support or resistance. They offer a purely statistical analysis.

These calculators assume random market movement. That in itself ought to provide information of value because the market is not always trending.

I don’t think there is a calculator to meet YOUR needs. For example, what does ‘uptrend’ mean to a computer? How could a computer distinguish between strong and weak uptrends? I suppose one could program it to consider bouncing off support and resistance. But what probability should it assign to bouncing, rather than piercing?

Calculators are not for traders who rely on the factors that you mention. At least, I’ve never heard of any.

Regards