Using statistics and probability in Options Trading

Professional gamblers prefer not to use the word "luck"
when evaluating their methods. Instead they choose
to say: "favorable return period" or "positive abberration".
That's because they see every game as a calculated
risk with all decisions based strictly on the best probability
of profit.

One must use the same "no nonsense" approach in evaluating options trades
An effective way to evaluate any options trade is to gather
the following statistical information: maximum risk and reward,
probability of profit, expected return, and profit zone (breakeven points).

Maximum risk and reward

The first question one must ask when looking at an options trade is:
"What's the most I can make or lose on this trade"
These numbers can easily be calculated on a PL vs Price graph.

Here we build a call debit spread position for MSFT on 12/14/00. Microsoft is trading at 57.688
The options are as follows:
buy 1 jan-01 47 call @ 12.125
sell 1 jan-01 50 call @ 9.750 From the table on the upper right corner, we see that them maximum reward for this spread is \$63 and the max risk is \$(238).
As we observe from the PL graph, this position is profitable at any point above 48.97 with the max profit at 50.

The next question one would ask is "what are the chances that this will be a profitable trade?"
We would review the probability of profit which shows 80.97%

Finally we would ask: "what is the projected return of this trade, taking in to consideration: max risk / reward and probability?"
We would review the expected return which shows \$5.
Expected return is calculated as: (max reward x probability of profit) + (max risk x probability of loss)

Finally we would want to see are are profit zone on this trade in relation to the price history of the stock: As we can see, this spread is profitable at any price above 48.97 (yellow line).
The 90 price history (blue line) of the stock has consistently been well above this point.

Now lets review the statistics and probabilty for a ratio call spread.
Here we build a ratio call spread position for MSFT on 12/14/00. Microsoft is trading at 57.688
The options are as follows:
buy 1 jan-01 57 call @ 4.875
sell 2 jan-01 60 call @ 3.500 Let's review the statisical information on the table in the upper right corner.
This ratio spread has a max reward at \$359 and an unlimited risk.
As we see from the PL graph, this spread is profitable if MSFT stays below 65.12.
The probability of profit is 74.20% and the expected return shows an unlimited risk.
From the net cost, we would receive \$213 when we open this spread.

Next, we would review the Profit zone vs 90 day historical price chart. We see from this position is profitable anywhere below 65.12 (yellow line).
The 90 historical prices have penetrated the profit zone from jul - sep and
during most of oct. It is currently well below it.

From these two spread examples we see how effective statistics and
probability can be in evaluating any spread.