## 19 July 2009

### Probability Is Only Part Of The Puzzle

Over the last couple of weeks I've been concentrating on option trading myths and nonsense, in particular the myth of 90% of options expiring worthless, but only alluding to the second part of the puzzle. That second part of the puzzle is mathematical expectancy.

As Dean from www.masteroptions.com pointed out in a comment on my previous post:

The debate over what percentage of options expires out of the money misses the point. Even if it were true that 90% of options expired worthless it would mean nothing. There's also the matter of how much you make on your winners vs how much you lose on your losers.

Never a truer word said. Probability of win is irrelevant on its own.

The expectancy equation has two parts, 1) probability of win and 2) win size vs loss size. One way of expressing this mathematically is with this equation:

Expectancy = ((1 + reward/risk ratio) * win/loss ratio)-1

One way to have a look at this principle in practice is to wander down to the casino and play a little roulette. It is a wonderful way to understand this principle, because at the roulette wheel, it does not matter one iota with what probability we play, the negative expectancy cannot be overcome. On a 00 wheel the negative expectancy is -5.26%.

We can create a ~90% probability, but that won't help us a jot. A chip placed on 34 numbers gives us a ~89.5% probability of winning paying 36/34, but it's still a losing strategy in the long run. Let's look at the maths:

Expectancy = ((1 + reward/risk ratio) * win/loss ratio)-1

= ((1 +2/34) *34/38)-1

= -0.0526

= -5.26%

Likewise, an option strategy with a theoretically 90% probability, whether an actual statistical probability, or an erroneous probability, doesn't make the trader profitable in the long run. We are all aware of the snatching pennies from in front of a steam roller analogy.

If you make \$1,000 90% of the time and lose \$10,000 10% of the time, you're down a hole. In fact, you lose \$1,000 every ten trades on average.

F### that!

High probability trades are nice in theory, but a trader still has to develop a positive mathematical edge. So our "90% of options expire worthless so sell options" pseudo-gurus actually make two major misrepresentations; that 90% options expire worthless and that this automatically confers profitability.

Mathematics outs in the end.

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