Market Talk with Piranha is currently moving to its new home at The new site is up and running but many of the posts need editing as the images and stock charts did not transfer successfully (thanks blogger). I will post all new entries to both blogs – Thank you for your patience while I make this change!

Tuesday, May 16, 2006

What is Expectancy?

To Start: Here is the link to the Expectancy Calculator in Excel
Feel free to save it to your computer!

Use the expectancy calculator with my Position Sizing Calculator

I have been watching as a several people on a forum discuss, argue and lend their ideas about entry techniques. They are going crazy over what the proper entry should be and why one chart pattern is better than the other. One person has even said how they purchased massive amounts of software to help them enter the market. Now don’t get me wrong, I always use techniques to get me in the market but I understand that this is the least important factor weighing on an investor’s overall success. I use technical analysis every day and I study patterns that allow me to enter with the ideal buy point (what I believe to be the ideal entry) but I know that strong up-trending stocks give me just as good a chance to make money as stocks breaking out of a cup with handle pattern. I am one that makes my living buying stocks making new highs so I can basically prove that the random entry strategy does work as long as strong money management and exit strategies exists.

By reviewing my personal trades and the coverage of dozens of stocks on the MSW Index over the past two years, I can tell you that my system with the highest expectancy is buying fundamentally sound stocks that are making new highs on above average volume. Where do I find these fundamentally sound stocks? I use multiple computerized screeners that filter out stocks with increasing earnings, high EPS ratings and increasing relative strength ratings. Once I find these stocks, I narrow them down using my own eyes by performing technical analysis. The process is simple as I am basically looking for stocks making new highs with decent to strong fundamental numbers. The process is almost random. To tell you the truth, I could probably narrow down my buy candidates each week to a list of 20 and throw darts at ten stocks to buy the following week and still have a profitable year because I do use position sizing and strict sell rules. Think I am crazy: think again as I explain what expectancy is.

I responded on the forum by saying: Entering at the right time is important and it can lower your risk and increase your overall expectancy but money management and exits are much more important than entry.

Studies have been done between random entry systems and specific systems that use entries based off of chart patterns with amazing results. The random entry system typically outperforms the structured entry system when it uses money management (position sizing techniques) and a strong exit strategy (assuming that the structured system doesn’t employ money management tools).

I love CANSLIM and O’Neil but the entry is not the most important aspect you should be focusing on, it is money management and exits. Most people don’t want to hear this and that is why so many “entry based systems” sell so well over the years. How many of those systems actually make their users money? CANSLIM does use a 7%-10% sell stop rule but it ignores position sizing and never explains the probabilities of the system when implemented in certain ways.

As I said, I make money using a system based from CANSLIM (an entry system) but it is heavily balanced with strong money management techniques and a strong exit strategy.

So what is expectancy?

Expectancy tells you what you can expect to make (win or lose) for every dollar risked. Casinos make money because the expectancy of every one of their games is in their favor. Play long enough and you are expected to lose and they are expected to win because the “odds” are in their favor. Most games at a casino are completed in a short period of time so they can increase their odds of winning. The same holds true for investing. If your expectancy is positive; you can make more money with multiple trades in shorter periods of time. If you told me this ten years ago, I would strongly disagree based solely on beliefs. Now with experience, I continue to move down the path to more frequent trading and a structured system that is run like a business. I now have massive amounts of data based on real trading that I have performed over the past several years.

Expectancy is your profit percentage per win multiplied by your win rate minus your loss percentage per loss multiplied by your loss rate. I will use examples from Trader Mike’s: Trading 101: Expectancy and Van Tharp's Book: Trade your way to Financial Freedom:

Expectancy = (Probability of Win * Average Win) - (Probability of Loss * Average Loss)

Expectancy = (PW*AW) less (PL*AL)
PW is the probability of winning and PL is the probability of losing.
AW is the average gain (win) and AL is the average loss

So let’s do an example (assume $12,500 per position, a $100,000 portfolio using 1% equity risk):
If my trades are successful 40% of the time and I realize an average profit of 20% but I lose an average of 5%, my expectancy is $625 per trade.

(0.4 * $3,125) - (0.6 * $625) = $625

$1,250-$375 = $625

I lose 60% of the time yet I show a profit of $625 per trade. If I have a system that produces 65 trades per year, I would realize an annual gain of $40,625 (hypothetical scenario). A 40% gain on the original $100,000 (minus all commissions, fees, taxes and compounding).

Trader Mike offers an example geared towards a day trader:
"As an example let's say that a trader has a system that produces winning trades 30% of the time. That trader's average winning trade nets 10% while losing trades lose 3%. So if he were trading $10,000 positions his expectancy would be:
(0.3 * $1,000) - (0.7 * $300) = $90

So even though that system produces losing trades 70% of the time the expectancy is still positive and thus the trader can make money over time. You can also see how you could have a system that produces winning trades the majority of the time but would have a negative expectancy if the average loss was larger than the average win:
(0.6 * $400) - (0.4 * $650) = -$20

In fact, you could come up with any number of scenarios that would give you a positive, or negative, expectancy. The interesting thing is that most of us would feel better with a system that produced more winning trades than losers. The vast majority of people would have a lot of trouble with the first system above because of our natural tendency to want to be right all of the time. Yet we can see just by those two examples that the percentage of winning trades is not the most important factor in building a system. " - Trader Mike

Most traders look for three major factors when developing a system:
The right odds or positive expectancy
Multiple trades (opportunity)
Shorter holding periods to compound the profits

Let’s look at the calculation one more time using only percentages:
PW: 48%
AW: 10%
PL: 52%
AL: 4%

(48% * 10%) - (52% * 4%) = 2.72%

Using a trade size of $12,500, each trade would return you $340 or 2.72% (profit). Let’s say this system gives you 200 trades per year; your result would be a $68,000 profit with only 1% of equity risked or $12,500 on $100,000. This doesn’t include compounding profits with each successful trade.

A positive expectancy can come from an unlimited amount of numbers or scenarios. You could have a system that produces winners 30%, 50% or 80% of the time and each system could be positive or negative based on PW, AW, PL & AL. An infinite number of trading systems and/or number combinations can be used to find a positive expectancy system.

The one thing I have realized over the past few years as my account grows is the fact that opportunity must exist to make money with a positive expectancy system. Think of the casino; the more you play, they more they win. The same is true for trading; the more you play with a positive expectancy system, the more your odds are for that system to return the expected number.

I have been tailoring my system to produce more trades and opportunity so I can take full advantage of the mathematical odds. As many of you know, I graduated as an architectural engineer and love numbers since my courses were based in advanced math and physics. Numbers don’t lie; I love to play poker because I understand the odds so I am typically successful over long stretches of time at the table because I have the emotional stability to only jam the pot when the odds are in my favor. Like stocks, I do my best to let go of losing hands and losing positions (sometimes I follow a committed hand in poker or a committed position with stocks but the odds are no longer in my favor and more times than not, I lose the hand or settle for my maximum stop). I am attracted to games with numbers and odds and the stock market is the best game in the world (in my opinion). Poker is a close second.

I want you to think about one more example (provided from ARB 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%." - ARB Trading



At 9:09 PM, Anonymous Terry Zink said...

I calculated my expectancy earlier this year. In April, when all my trades were going up, I was quite impressed with my expectancy. Since mid-April, when my gains started to retrace themselves (fairly rapidly) and some new breakouts I got into forced me out a couple of days later, my expectancy has dropped considerably (but still positive).

I calculate my expectancy on the short side and the long side separately. My strategies are different so I calculate my expectancy differently.

I have found that even though I try to keep my losses tight (8% or less) they seem to get away from me quickly (ie, big gap moves or massive selling that goes to 11 or 12%). I have never used limit orders on stop losses, only mental stops, but I may start using them now.

At 11:04 PM, Blogger Wilson said...

good article.

I also wrote about the art of expectancy here:

At 5:49 PM, Anonymous Anonymous said...

There's a minor math glitch in your example:

$1,250-$375 = $625 ??

Based on a $12,500 position and 20% profit, the average win in the sample calculation should be $2500, not $3125.

Thanks for the article - it really helps reinforce the importance of money management in trading.

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At 8:00 PM, Anonymous stefan said...

I do not understand why traders bother with above formula for expectancy. Expectancy = average trade (=net profit/number of trades). Both formulas are equivalent. Stefan

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