# When to expect profitability of a call options buying strategy

When could we expect consistent profitability of a call options buying strategy given specific statistical assumptions about X% chance of a stock price moving up by Y% within 1-5 days (or Z number of days). And what call options buying trading strategy parameters would be recommended to utilize to achieve such expected profitability?

For example an average casino would have 50.5% - 55.9% odds on Blackjack and be consistently profitable. Not sure if similar expectations can be applied to stock trading (winning average x% y% of the time vs losing average z%) because of large swings in loss percentages unless using stop-loss which then limits the number of times we may win. However, as options can be used to limit losses, I’m assuming there may be a specific way to calculate expected break even point and profitability when trading stock options based on statistically predicting specific stock price increase.

Examples:

• Can I expect profitably when buying call options given statistical 50% chance of stock A moving up by 6% vs 50% chance of moving down by 3% within 2 days.
• Can I expect profitably when buying call options given statistical 60% chance of stock A moving up by 3% vs 40% chance of moving down by 3% within 5 days.
• Can I expect profitably when buying call options given statistical 60% chance of stock A moving up by 3% vs 40% chance of moving down by 5% within 5 days.
• Can I expect profitably when buying call options given statistical 75% chance of stock A moving up by 3% vs 25% chance of moving down by 10% within 5 days.

As an example of specific stock we can use FB, currently priced at $140.34, with the following options chain: https://finance.yahoo.com/quote/FB/options?p=FB&date=1490918400 Furthermore, because of short-term expectations, I’d like to consider multiple options strike selection approaches: • a) In-the-money, with intent to sell purchased calls within several days • b) In-the-money, with intent to exercise them • c) Near-the-money • d) Far out-of-the-money, with intent to sell them within several days, for example expecting a \$0.10 option to raise in price above \$0.20 (100%) when stock price approaches in-the-money level.

NOTE: I'm looking for layman-level answers in a way similar to casinos explaining their odds. I was thinking about posting this question in http://money.stackexchange.com, but as an answer may require some math and degree of quantitative experience, I decided to post it here with hope that I can still get an answer in the form of basic math vs advanced quant formulas, especially as the answer could be helpful to anyone starting trading options.

• There is a class offered free to Interactive Brokers customers called Probability Lab interactivebrokers.com/en/index.php?f=5910 that purports to explain Options without using much math. I am not necessarily endorsing it but it might be of interest to you. – noob2 Mar 27 '17 at 12:56
• You ask about a 'call buying option trading strategy'. The strategy would not just involve buying. The strategy also involves the exit of the position. You make no mention of that ergo you have no strategy. What will happen if your position is up 9.9% but you are expecting 10%? Does your strategy does not exit? You need to consider this. Your trade is not similar to a casino at all. A casino game does not expire. Yours does. The casino stays open and takes bets continuously. Yours does not. The casino does not have Theta to deal with. You do. – amdopt Mar 27 '17 at 17:21
• Thanks @noob2 . I use IB as my broker, but their class don't seem to address my question. I also couldn't find related answers on Google, in various articles, or even in books. They all teach about general probability distribution where a stock has specific probability of reaching specific price - used for pricing options. While my input would statistical chance where I predict specific stock movement based on factors unrelated to basic probability. Once I expect that specific stock has an X% chance of moving up by Y% within Z days, I'd like to figure out what to do with this information. .. – Kon Rad Mar 27 '17 at 20:36
• @amdopt , per my comment above I'd provide input as statistical X% chance of a stock moving up by Y% within Z days. Im looking for any strategies that would monetize such expectations. I assume I could exit after Z days (number of days I expect the stock to go up) regardless if I actually hit a profit at that time or not. This would work just like trading stocks but using options to limit losses. I don't put any restrictions on entry or exit strategy. Just seeking to improve profitability and limit losses over trading stocks. But need to know what chances do I need to trade options profitably. – Kon Rad Mar 27 '17 at 20:47
• @KonRad Exiting after Z days is a start--by that I mean you now have an exit plan! Indeed your losses (per trade) are limited to your initial debit, however, 2 extra constraints are on each trade--Not only do you have to be correct in the directional move of the stock, you need the move be large enough to offset your theta loss and happen within a certain amount of time. These extra constraints (as opposed to outright equity purchases) can be tough to overcome. I'm not trying to discourage you, just suggesting that options do not necessarily limit account losses or improve profits. :) – amdopt Mar 27 '17 at 21:21