The Mathematical Probabilities of Option Trades

I take no credit in the information contained here. This just happened to be on my list of suggested topics to discuss. McMillan takes the top ten strategies that have the highest mathematical chances of success and documents them in his book titled "Options as a Strategic Investment." Keep in mind the strategies discussed here totally discount the investor out of the equation- financially and psychologically. Keeping all things equal, these are just a list of strategies that have the best chances of profit. Notice how the strategies taking in large amounts of time value are the one's located near the top of the list!

Keep in mind, some of these strategies you may not have heard of, but it will give us opportunity to talk about them in greater detail down the road. Some of the strategies involve naked options and are considered high risk.

1. Ratio Writing- An options strategy in which an investor simultaneously holds an unequal number of long and short positions. An example would be having more short positions than long positions.

2. Ratio Spreading- An options strategy in which an investor simultaneously holds an unequal number of long and short positions. An example would be having more long positions than short positions.

3. Straddle Writing- An options strategy carried out by holding a short position in both a call and a put that have the same strike price and expiration date. The maximum profit is the amount of premium collected by writing the options.

4. Naked Writing- An option position held by a writer who does not hold a long position in the stock on which the option has been written.

5. Calendar Spreads- An options or futures spread established by simultaneously entering a long and short position on the same underlying asset but with different delivery months. Sometimes referred to as an inter-delivery, time or horizontal spread.

6. Covered Calls- An options strategy whereby an investor holds a long position in an asset and writes (sells) call options on that same asset in an attempt to generate increased income from the asset. This is often employed when an investor has a short-term neutral view on the asset and for this reason hold the asset long and simultaneously have a short position via the option to generate income from the option premium.

7. Debit Spreads- Two options with different market prices that an investor trades on the same underlying security. The higher priced option is purchased and the lower premium option is sold - both at the same time. The higher the debit spread, the greater the initial cash outflow the investor will incur on the transaction.

8. Butterfly Spreads- An option strategy combining a bull and bear spread. It uses three strike prices. The lower two strike prices are used in the bull spread, and the higher strike price in the bear spread. Both puts and calls can be used.

9. Buying ITM Options- The purchase of an option contract with intrinsic value.

10. Buying OTM Options- The purchase of an option contrat with no intrinsic value.

Just an interesting piece on the probabilities of an option trade. Remember that this is only looking at the mathematical and statistical equations rather than systems or individuals. The question now becomes, do you go for the probable win...which includes a small reward...or do you go for the lower probability trade, with a huge gain potential?

Be back in a flash!

Thanks for posting this Jeff. I was always curious to see this information.

Interestingly "Credit Spreads" werent specifically mentioned in the this list.
However I guess if one views a credit spread as :
(1) A covered naked position OR
(2) A subset of a ratio spread ,
then one could assume that credit spreads would be in the top 5 of this list.
Am I making the correct assumption here?

I must get my hands on that book I think as it seems to have a wealth of information.

John O'Shea

Interesting post Jeff. If I had a car valued at 20k and put it up for sale for 5k the probability of me selling that car is very high, but there is no reward for it.

Trading, (or any business) is a balance between reward, risk and probabilities. Effective traders and business people know this. Some of the most profitable traders in history are lower probability traders (Dennis, Eckhart, Livermore, Taleb).

Some of the worst are high probability traders (long term cap management).

Brilliant blog Jeff, thanks for digging up this information.



Point well taken. While I am surprised someone bought the car for $5k, the tragedy lies in the book value for having quoting it at $20k. Get a new quoting service.

I was anxiously awaiting this comment in hopes it would lead to a risk/reward post...which happens to be in the oven.

By the way, I hope your new irons have arrived. Hopefully there is a good reward behind the risk you've taken.


Jeff didn't you try to sell me a car for 20k that was worth 5K?


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  • From Saratoga Springs, Utah, United States
  • I am a professional trader and an instructor for Investools. I've had relations with the markets for 9 years. Born in Concord, CA, but reside in Saratoga Springs, Utah. Father of THREE, Husband of one.
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