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Expectancy

At the heart of all trading is the simplest of all concepts�that the bottom-line results must show a positive mathematical expectation in order for the trading method to be profitable. ~Chuck Branscomb

What is expectancy in a nutshell?

A trading system can be characterized as a distribution of the R-multiples it generates.  Expectancy is simply the mean or average R-multiple generated. 

What does that mean?

By now you should know that in the game of trading it is much more efficient to think of the profits and losses of your trades as a ratio of the initial risk taken (R).

But let�s just go over it again briefly:

One of the real secrets of trading success is to think in terms of risk-to-reward ratios every time you take a trade.  Ask yourself, before you take a trade, �What�s the risk on this trade?  Is the potential reward worth the potential risk?� 

So how do you determine the potential risk on a trade?  Well, at the time you enter any trade, you should pre-determine some point at which you�d get out of the trade to preserve your capital.  That exit point is the risk you have in the trade or your expected loss.  For example, if you buy a $40 stock and you decide to get out if that stock falls to $30, then your risk is $10. 

The risk you have in a trade is called R.  That should be easy to remember because R is short for risk.  R can represent either your risk per unit, which in the example is $10 per share, or it can represent your total risk.  If you bought 100 shares of stock with a risk of $10 per share, then you would have a total risk of $1,000.

Remember to think in terms of risk-to-reward ratios.  If you know that your total initial risk on a position is $1,000, then you can express all of your profits and losses as a ratio of your initial risk.  For example, if you make a profit of $2,000 (2 x $1000 or $20/share), then you have a 2R profit.  If you have a profit of $10,000 (10 x $1000) then you have a profit of 10R.

The same thing works on the loss side.  If you have a loss of $500, then you have a 0.5R loss.  If you have a loss of $2,000, then you have a 2R loss. 

"But wai"t, you say, "how could you have a 2R loss if your total risk was $1,000?"  Well, perhaps you didn�t keep your word about taking a $1000 loss and you didn�t exit when you should have exited.  Perhaps the market gapped down against you.  Losses bigger than 1R happen all the time.  Your goal as a trader (or as an investor) is to keep your losses at 1R or less.  Warren Buffet, known to many as the world�s most successful investor, says the number one rule of investing is to not lose money.  However, contrary to popular belief, Warren Buffet does have losses.  Thus, a much better version of Buffet�s number one rule would be to keep your losses to 1R or less.

When you have a series of profits and losses expressed as risk-reward ratios, what you really have is what Van calls an R-multiple distribution.  As a result, any trading system can be characterized as being an R-multiple distribution.  In fact, you�ll find that thinking about trading system as R-multiple distributions really helps you understand your system and learn what you can expect from them in the future.

So what does all of this have to do with expectancy? 

When you have an R-multiple distribution from your trading system, you need to get the mean of that distribution. (The mean is the average value of a set of numbers).  And the mean R-multiple equals the system�s expectancy.  

Expectancy gives you the average R-value that you can expect from the system over many trades.  Put another way, expectancy tells you how much you can expect to make on the average, per dollar risked, over a number of trades. 

So when you have a distribution of trades to analyze, you can look at the profit and loss of each one of the trades that was executed in terms of R (how much was profit and loss based on your initial risk) and determine whether the system is a profitable system.

Let�s look at an example:

So this �system� has an expectancy of 2R,  which means you can �expect� to make two times what you risk over the long term using this system based on the data you have available.

Please note that you can only get a good idea of your system�s expectancy when you have a minimum of 30 trades to analyze, and the preference would be to have 100 to 200 trades to really get a clear picture of the system�s expectancy.

So in the real world of investing or trading, expectancy tells you the net profit or loss that you can expect over a large number of single unit trades.  If the total amount of money in the losing trades is greater than the total amount of money in the winning trades, then you are a net loser and have a negative expectancy.  If the total amount of money in the winning trades is greater than the total amount of money in the losing trades, then you are a net winner and have a positive expectancy.

Example, you could have 99 losing trades, each costing you a dollar.  Thus, you would be down $99.  However, if you had one winning trade of $500, then you would have a net payoff of $401 ($500 less $99)�despite the fact that only one of your trades was a winner and 99% of your trades were losers.

We�ll end our definition of expectancy here because it is a subject that can become much more complex.

Van Tharp has written extensively on this topic and it is one of the core concepts that he teaches. As you become more and more familiar with R-Multiples, position sizing and system development, expectancy will become much easier to understand.

To safely master the art of trading or investing, it is best to learn and understand all of this material. Although it may seem complex at times, we encourage you to persevere because like any worthwhile endeavor, as soon as you truly grasp it and then work towards mastering it, you will catapult your chances of real success in the markets. 

About Van Tharp: Trading coach, and author Dr. Van K Tharp, is widely recognized for his best-selling book Trade Your Way to Financial Fre-edom and his outstanding Peak Performance Home Study program - a highly regarded classic that is suitable for all levels of traders and investors.

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Trading Tip 

Trading Tip

A Review of Market Models: Fibonacci Numbers

by D. R. Barton, Jr.

This Leo was �titanic� long before DiCaprio hit the big screen.

Leonardo Fibonacci (or Leonardo de Pisa, as he was known in the �hood�) was a 12^th century Italian mathematician who is credited as the western developer of the number series that now is called by his name. 

Fibonacci was solving a biological word problem involving rabbits, but wrote extensively about the number series and the �golden ratio� that it uncovers.

The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765�

Any number divided by the next larger number in the series equals the �golden ratio� of 0.618 starting with 55 / 89 .  (The numbers before that pair get closer to the golden ratio as they get bigger.)

So why the math history lesson?

Fibonacci numbers are some of the most widely used and watched numbers in all of trading.

Fibonacci is less of a complete �market model� than some of the others that will be described in this series.  But it is so pervasive and so many people use it to make decisions that it is treated as a market model by lots of folks.

Fibonacci Retracements & Extensions:  Mesmerizing or Mysticism?

For clarity, I must interject that Fibonacci numbers are used within the Elliott Wave Theory that was discussed in last week�s article.  Today�s discussion, however, is about a specific and distinct use of Fibonacci�s numbers:  retracements and extensions.

When a stock, futures contract, currency, etc. has had a defined price move, Fibonacci proponents expect a retracement of the total move to test key levels, specifically 0.382 times the price move, 0.5 times the price move and 0.618 times the price move. The resultant levels are expected to be key testing points where price will be repulsed or will break through.

For strong price movement, adherents also look for extensions of a move to go 1.618, 2.618, etc. beyond the previous high or low.

Now, let�s look at our standard list of questions for market models:

Is it theoretically credible?  The levels are mathematically sound and they make sense from a market psychology perspective.  Many useful market theories are based on predicting (or simply observing) moves followed by retracement followed by extension.

Who�s it most useful for?  Fibonacci levels are useful for most traders and investors looking to understand the �three steps forward, two steps back� nature of the markets.  Countertrend players can use retracement levels and breakout players can watch extension levels.  There�s really a little something for everyone.

How fanatic are the fans?  Rabid.  Whether or not they are part of the Elliott wave crowd, Fibonacci followers believe that these numbers contain the underlying order of the universe.  And they have plenty of occurrences in nature to back them up.

Is it being used by real-life traders?  You betcha.  Fib retracement levels are followed far and wide (extension levels are less widely followed).  Most of the traders that I know use some form of Fibonacci retracement levels in the their analysis, even if it�s just to see the numbers that numerous other traders are looking at.

Next week we�ll continue our series with another market model.  Until then�

Great Trading!

D. R.

D. R. Barton, Jr. is the Chief Operating Officer and Risk Manager for the Directional Research and Trading hedge fund group. D. R. has been actively involved in trading, researching, and teaching in the markets since 1986.  D. R. has taught extensively in many investment areas including intra-day trading, swing trading, and cutting edge risk management techniques. 

His writing credits include co-authoring Safe Strategies for Fin-ancial Fre-edom and co-creator and contributing author on Fin-ancial Fre-edom Through  Electronic Day Trading.

D.R. presents the IITM Swing Trading Workshop and Professional Tactics for Day Traders Workshop. Each workshop is only held once each year. 

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Market Mastery Newsletter from IITM 
Author: ryutaroh
Date: 05-25-06 09:55

Hello,

I am a long-term subscriber of the Market Mastery (MM), a newsletter published by IITM. I have received its final issue recently.

MM has been very useful for my growth as a trader. I was a losing trader, but MM and other educational materials from IITM (especially the PP home study course) helped me to transform myself and I could increase my capital from 4,000,000 JPY to 50,000,000 JPY in two years by Japanese stock and commodity futures markets, which have been very bullish in recent years.

I am a totally discretionary and intuitive trader, and adjusting my own psychology is indispensable with this type of trading. MM and the back issues of Course Updates helped me to work on myself very much.

The last issue said that the number of subscribers was not so many, which surprised me a little bit. Because I guessed that users (not owners) of the PP course found MM useful for them. It was also surprising that the back issues of Course Update and MM were regarded as obsolete and useless for today's trading. I want to emphasize that they are still useful today, at least for discretionary traders.

Regards,

Ryutaroh

Reply To This Message 

Re: Market Mastery newsletter from IITM 
Author: Terry 
Date: 05-25-06 21:13

Hello Ryutaroh,

Adjusting and growing one's personal psychology seems to me to be a necessity for personal development, whether it applies to trading or life in general. I am also a discretionary trader and find in general most traders don't view the psychological side of their trading with enough emphasis. You can tell by the type of questions they ask.

I had an interesting experience recently. About a month ago, my wife and I went deep-sea fishing off St. Lucia and met an Italian businessman who builds yachts for a living. He was in his mid to late thirties, and because of his age, I thought he either got involved in the business through his family or he bought something that pre-existed. In fact, he started the business from scratch. At some point in his life, he determined for himself that he could do anything he wanted, his belief structure was so firm that he could create anything his imagination was capable of. I asked him where he got his motivation from and he said much of it came from Tony Robbins motivational CD's.

He was an incredible personality and full of the most positive energy I have seen in a long time. It shows you the power "beliefs" have and how they can be applied to everything.

If traders spent as much time with their personal psychology as they do with looking for the "holy grail" of systems, they might find their "methodology" fall in place considerably easier.

Thanks for your interesting post!

Regards, Terry 

(Buy the Back Catalog of Market Mastery)

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