# Great Expectations

The next step in building our casino so that we have the house odds in our favor is to look at the edge, or in system trading terms, expectancy. Let’s take a look at the house edge in a few casino games:

 Game House Edge Baccarat 1.2% Blackjack 0.8% Craps 1.6% Roulette 5.3%

So exactly what does this mean?  Let’s look at it from the bettor’s side—in the case of blackjack, he can expect to lose 0.8% of every bet he makes, so if he is making an average bet of \$10 per hand, he can expect to lose about \$0.08 on each hand. That number is called the grind, and in building a trading system, we most definitely don’t want to lose a little bit on every trade and try to make it up in volume!

Let’s look at how to calculate expectancy, and how to think about it in the context of building a trading system that not only is profitable, but also matches our individual personalities. Expectancy is a simple enough concept—it is the average winner times the winning percent less the average loser times the losing percent. Let’s look at a couple of examples:

How about a trading system with a 90:10 win/loss ratio—sounds good until we look at the average winner and loser.  Let’s assume that the average winner is \$250 and that the average loser is \$2500, so

Expectancy = (0.9 X \$250) – (0.1 X \$2500) = \$225 – \$250, or – \$25

Unfortunately the vast majority of traders would rather be right than make money—it is part of our psychological programming from the time we were young, and it really manifests itself in the world of trading. In this example, the trader could be right 90% of the time, and eventually lose all his money trading it. Reminds me of my first hedge fund where we sold option premium with a 96% win rate, and our average winner was about \$3000 and our average loser was \$50,000—seriously—that is not a misprint.  Do the arithmetic:

Expectancy = (0.96 X \$3000) – (0.04 X \$50,000) = \$2880 – \$2000, or \$880

It worked great when the VIX was in the stratosphere in 2001 through early 2003, but was completely unprofitable when the VIX fell below 20 or so.

How about a different example with a win/loss ratio of 40:60 and an average winner of \$1000 and average loser of \$500—this would be pretty typical of a trend following system.

Expectancy = (0.4 X \$1000) – (0.6 X \$500) = \$400 – \$300, or \$100

It won’t make you psychologically happy if you have the need to win, but if traded over and over, it can make you wealthy. And those are pretty much the numbers from our core trend following system today. They are psychologically difficult to watch—we trade it with a black box—but the profits just keep adding up, with drawdowns to be sure, but since we know the trading system has been vetted in all sorts of market environments, we can let it run, and not sweat too much.

You pick: can you force your innate need to be right into the background so can make money by building a trading system that may go completely against the grain of everything you hold dear? With a negative expectancy, eventually you have to lose all your money, but with a positive expectancy, you have the opportunity to win and win big.

A positive expectancy is just the first step—without it you cannot win, and eventually must lose all your money, so we’ll look at how to turn a positive expectancy into a winning trading system in our next few articles.

Rick Martin