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Expectancy along with position sizingare probably the two most important factors in trading/investingsuccess. Sadly most people have never even heard of the concept. Out ofthe 30 or so trading books I've read only a few even touch on anyaspect of money management. Only one of those handful of booksdiscussed expectancy. In simple terms, expectancy is the average amountyou can expect to win (or lose) per dollar at risk. Here's the formulafor expectancy:
Expectancy = (Probability of Win * Average Win) - (Probability of Loss * Average Loss) As an example let's say that a trader has a system that produceswinning trades 30% of the time. That trader's average winning tradenets 10% while losing trades lose 3%. So if he were trading $10,000positions his expectancy would be:
(0.3 * $1,000) - (0.7 * $300) = $90
So even though that system produces losing trades 70% of the timethe expectancy is still positive and thus the trader can make moneyover time. You can also see how you could have a system that produceswinning trades the majority of the time but would have a negativeexpectancy 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 wouldgive you a positive, or negative, expectancy. The interesting thing isthat most of us would feel better with a system that produced morewinning trades than losers. The vast majority of people would have alot of trouble with the first system above because of our naturaltendency to want to be right all of the time. Yet we can see just bythose two examples that the percentage of winning trades is not themost important factor in building a system. As Dr. Van K. Tharp points out:
... your trading system should have a positive expectancy and youshould understand what that means. The natural bias that most peoplehave is to go for high probability systems with high reliability. Weall are given this bias that you need to be right. We're taught atschool that 94 percent or better is an A and 70 or below is failure.Nothing below 70 is acceptable. Everyone is looking for highreliability entry systems, but its expectancy that is the key. And thereal key to expectancy is how you get out of the markets not how youget in. How you take profits and how you get out of a bad position toprotect your assets. The expectancy is really the amount you'll make onthe average per dollar risked. If you have a methodology that makes you50 cents or better per dollar risked, that's superb. Most people don't.That means if you risk $1,000 that you'll make on the average $500 forevery trade - that's averaging winners and losers together. In 'Trade Your Way to Financial Freedom'Dr. Tharp defines the following four components of expectancy (In thesame section of the book Dr. Tharp also discusses how the size of youinvesting capital and your position-sizing model must be considered along with expectancy. I'll talk about position sizing in another post, but I highly recommend reading Tharp's book for a thorough understanding of these concepts.):
- Reliability, or what percentage of time you make money.
- The relative size of your profits compared with your losses.
- Your cost of making a trade. (commission & slippage)
- How often you get the opportunity to trade.
The fourth item in that list is a very important and oftenoverlooked aspect of trading. If you had two systems that both had thesame positive expectancy, let's say $100, the system that produced moretrades would make more money over time. For example, system A produces3 trades per week while system B produces 10 trades per week. Afterjust one week B would have made $1,000 while A would only have made$300. Gary B. Smith has discussed this before:
I think of my equity as inventory. In that respect, my goalis to maximize not profit per dollar, but profit per dollar per day. Inessence, I try to make a small percentage on my equity each day, butcompound that amount as rapidly as possible. And in another article Gary said:
Q: What aspect of trading took you the longest to learn?
GBS: I'd say the view that my equity is the same as a retailer'sinventory. Your profit per piece doesn't matter if you never turn yourinventory. And your turnover doesn't matter if you're losing money oneach sale. What matters is the turnover times profit per piece.
That's the same concept I try to apply to my trading. I start with$1 and want to figure out how to quickly turn that into $10. Mostpeople focus on buying a stock at $20 and selling it at $40, and theyrarely care how long it takes them to do that.
However, if during that time I can buy 10 $20 stocks and sell themeach at a 10% gain, I'm way ahead if I continue to compound my equity.
To touch on the importance of the size of your equity and positionsizing I'll use part of a snowball fight metaphor that Tharp uses inhis book:Imagine that you are hiding behind a large wall of snow.Someone is throwing snowballs at your wall, and your objective is tokeep your wall as large as possible for maximum protection.
Thus, the metaphor immediately indicates that the size of the wallis a very significant variable. If the wall is too small, you couldn'tavoid getting hit. But if the wall is massive, then you are probablynot going to get hit. The size of your initial equity is a little likethe size of the wall. In fact, you might consider your starting capitalto be a wall of money that protects you. The more money you have,assuming all the other variables (the components of expectancy listedabove) are the same, the more protection you will have.
Now imagine that the person throwing snowballs at you has twodifferent kinds of snowballs -- white snowballs and black snowballs.White snowballs are a little like winning trades. They simply stick tothe wall of snow and increase its size....
Imagine that black snowballs dissolve snow and make a hole in thewall equivalent to their size. You might think of black snowballs as"antisnow." Thus, if a lot of black snowballs were thrown at the wall,it would soon disappear or at least have a lot of holes in it. Blacksnowballs are a lot like losing trades -- they chip away at your wallof security...
Tharp continues walking the reader through different scenarios andpossibilities. Like considering the relative sizes of the snowballs ofeach color. What happens to your wall after being hit by some blackboulders of snow? Or considering how the rate at which snowballs arethrown affects the wall. You can see how important each aspect ofexpectancy is as well as the huge importance of both the amount ofequity (the size of your wall) and position-sizing (which willdetermine the size of the snowballs).
Expectancy, position-sizing and other aspects of money managementare far more important than discovering the holy grail entry system orindicator(s). Unfortunately entry techniques are where the vastmajority of books and talking heads focus their attention. You couldhave the greatest stock picking system in the world but unless you takethese money management issue into consideration you may not have anymoney left to trade the system. Having a system that gives you apositive expectancy should be in the forefront of your mind whenputting together a trading plan. |
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发表于 2010-1-18 05:22
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