Stock Options Math : Part 1

Greetings As an options trader I am often asked if options is gambling? So given the mystery and reputation of options it’s a question which should be answered. I think the answer is sometimes. But I should add that all ...

7 years ago, comments: 10, votes: 90, reward: $2.31

Greetings
As an options trader I am often asked if options is gambling? So given the mystery and reputation of options it’s a question which should be answered.
I think the answer is sometimes.

But I should add that all investments are a gamble. A calculated one, but still a gamble. Now while people feel safer in certain investments then others , the safe option isn’t always safe and the risky investment doesn’t always have a larger return. Popularity and safety don’t always go hand in hand and popularity and good returns don’t either. What you need to do is learn to calculate rough probabilities of success by yourself to screen investments and then dig deeper.

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Let’s look just at the math of investments.
In general, all investments have a mathematical probability of success based on the number of possible outcomes. Because in math all outcomes have an equal chance of occurring. This is a good investment screening tool. For simple investments the math and probabilities are simple and straightforward. For example, If you buy something with the intention of selling it if the price goes up, the mathematical probability is relatively simple to calculate because the number of outcomes is limited.

Outcomes:
The price can go up, you sell and make money.
The price goes down, you sell and lose money.
The price stays the same, you sell and break even. From a statistical view point all three have an equal probability of occurring.

For example, if you buy gold tomorrow, you are hoping that in the future the price of gold goes up. But what is the probability that the price of gold will go up and you will make money?

So let’s do the math, what are the possible outcome?

The outcomes are:

  1. The price of Gold goes up.
  2. The price of Gold goes down.
  3. The price of Gold stays the same.

In general each of these has an equal probability of occurring. So, if there are three possible outcomes, and the probability of each occurring is equal, then the probability of each occurring is one out of three.

The math looks like this:

  1. The probability of gold going up is one out of three, 1/3 or 33%
  2. The probability of Gold going down is one out of three, 1/3 or 33%
  3. The probability of gold staying the same is one out of three, 1/3 or 33%.

Now, let’s look at the other half of the math of this situation. You must understand that probabilities, like a coin has two sides.
If the probability that the price of Gold will go up is one out of three, 1/3 or 33%, then then probability that gold will not go up, is 2/3 or the other side of the coin, which is the sum of the other two probabilities; 1/3 or 33% probability of staying the same plus 1/3 or 33% probability that it will go down, added together they equal 2/3 or 66% probability that gold will not go up, because it stays the same or goes down.

Think about this because it is important.
1/3 chance of success is a mild deterrent.
2/3 chance of failure is a strong deterrent.

Let’s look at the math:

All three possible outcomes have an equal chance or 1/3.
While 1/3 is the probability that gold goes up.
So 2/3 is the probability that it stays the same or goes down.
So if there is a 33% chance Gold will go up, there’s a 66% chance it won’t.
So is investing in gold gambling? Yes, in truth all investments are gambles. Your job as an investor is to put the probabilities of success on your side.

How do you do that?
By doing the math. You try to break down investments into their possible outcomes and then gather information to see if there are external factors which would influence the outcomes in one way or another. One reason Option investors are so happy is because they start with the math and so they can purchase investments with specific probabilities of success that mirror their risk tolerance. In Option investments you can pick high probability lower yield investments or lower probability higher yield investments. The important thing is you know your probability of success going into the investment. It’s not a hope or a prayer. When we invest in options, we use Nobel Prize winning mathematical models which accurately predict probabilities. They are not guaranteed, but they are very good ways of improving our odds of success.

✍️ @shortsegments

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