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Expectancy

Las Vegas. Great food, show girls, and a multi-billion dollar gambling business. The money made by the casinos is only matched by the profits on Wall Street. And the profits of both are based on mathematical probabilities.

 Casinos make money because “the odds” or a game’s expectancy are in the house‘s favor. This means that if you play long enough, the casino wins. Over the short term, the casino knows it may win or lose. But if you play long enough, the house always wins. The casinos increase their profits by offering games that are completed in a short period of time – a roll of dice, a spin of a wheel or a few cards turned over.

What does this have to do with trading systems?

  • We want the odds of a trade to favor us – expectancy
  • We want a lot of trades – opportunity
  • We want turn over so we can compound the profits – holding time.

What we as traders must do is become the house. The odds in our trading must favor us, we need a reasonable number of trades during the year and the trades must be completed in a reasonable amount of time for compounding to be effective.

 Expectancy is simply the product of your profit percentage per win and your win rate minus the product of your loss percentage per loss and your loss rate. For example:

  • Win percentage                       6%
  • Win rate                                 60%
  • Loss percentage                      4%
  • Loss rate                                40%.

The expectancy is 2.0% per trade, or (6% x 60%) - (4% x 40%).

That means, on an average trade, 2% of the money traded is yours to keep. That’s better odds than a casino gets on blackjack. Now, that may not sound like a lot of money. If your average trade is $10,000 – 2% is $200 profit per trade. If you have 300 trades per year, then you have a $60,000 profit per year with an average trade of only $10,000. This does not even include the profits if you compounded the average trade.

If you explore the expectancy formula, you will notice that there is no one set of numbers that could give a positive expectancy but an infinite number of sets and therefore an infinite number of trading systems that could be profitable.

Given that, it is possible to develop systems where the stop loss is larger than the profits. The stop loss is academic, as long as your profit expectancy is positive.

Here’s another example:  we could use a 20% stop loss and a 5% profit target and come out with the same exact 2% expectancy as long as my win rate is high enough! An 88% win rate in this example would yield 2.0%, the result of (5% x 88%) - (20% x 12%).

Or, you could arrive at a positive expectancy with a very low win rate. One of the more famous expectancy numbers comes from William O’Neil, advocate of the CANSLIM system and founder of Investors Business Daily. If we use his stop and target numbers of 8% and 20% and his published win rate of 30%, the expectancy can be calculated to be: (20% x 30%) - (8% x 70%)  or +0.4%.

The bottom line is:  expectancy must be positive if you want to make a profit over time. Never use a system with a zero or negative expectancy. You will not win. You can not beat the house over a long series of bets or trades. Be the “House”.

No matter what your expectancy is, you will not make a great deal of money unless you have a lot of opportunities to trade. Again, the casino analogy. The casino may only make 1-2% per hand of blackjack, but they turn over those hands very quickly – 30 to 40 hands per hour. Play blackjack long enough and you will lose over 40% of your money per hour! No wonder they can offer those wonderful comps.

We now know how to create a method, at least on paper, with a positive expectancy. Let’s say we develop a system with 8% expectancy, but if the system only yielded one trade per year, what good would it be? We might as well just put the money in a savings account. Or, if we had a method that yielded 0.2% per trade, you might pass on it? But what if that system generated 1,000 trades per year? 1,000 times 0.2% becomes serious money in a very short time.

The most overlooked area of trading is the "holding period." In order to make money, you must have a system that generates a positive expectancy and a lot of opportunities. But you must have access to your money. If your trade’s hold time is too long, you can't take advantage of all or even most of your opportunities. Your trading money or buying power is always tied up because you have to wait too long to close your trades.

Casino analogy time. If the house odds in Blackjack are 2.5%, that means for ever $2 bet, the casino makes, on average, 5 cents. If you only play 1 game per hour, the casino makes 5 cents per hour. If you play 60 games per hour, the casino has all of your $2 in 40 minutes. All things being equal, the game with the fastest turnover is the more profitable for the casino.

It's no different with trading. You will be more profitable with $100,000 that you could "turn" 250 times per year, than $500,000 that was tied up in one trade for 12 months. As an example, let's say we have one trade and that trade yielded a 50% return. You just had a great year - a $250,000 profit.

On the other hand, say you had $100,000 for stock purchases, and your expectancy was only 1.2% per trade but you turned over your stocks 250 times in the same year. This method ends up generating $300,000 for the year, and that assumes you never increase the position size as the equity grows. You just had a better year. And it is easier to get 1.2% per trade than 50%.

The bottom line for a great bottom line is:

  • A positive expectancy
  • A good number of trades
  • A short holding period
     

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