If you are trading with a goal of maximizing your long term
profits, you should be concerned with maximizing your expectancy.
But, if you are like me, and you want to keep your electricity on
via trading stocks, expectancy isn’t the right measurement to use.
In this article, I’ll explain how to gauge your consistency. In
other words, what percentage of your days/weeks/months can you
expect to be profitable? This is useful if you are designing a
system, and also useful if you want to know more about the system
you already use.
Note: Many of the ideas in this article are largely derived
from the first 6 pages of
this elitetrader thread, started by user Acrary. I’ve tried to
expand on that material with more detail and graphs, to make it
easier to understand. Plus, it’s a lot more fun to read without all
the elitetrader noise…
Expectancy: the Premier Profitability Measure
If you want to know if your trading system is profitable over
the long haul, you want to know about your expectancy. You can find
lots of articles on the web about expectancy, so I won’t spend long
explaining it here. Briefly, it is computed as:
Expectancy = win_rate * avg_win - loss_rate * avg_loss
For the purposes of this article, I am going to ignore exact
breakeven trades. This means that the loss_rate is directly related
to the win_rate, and expectancy becomes:
Expectancy = win_rate * avg_win - (1 - win_rate) * avg_loss
A positive expectancy means that if you took an infinite number
of trades, you would have more money than you started with when you
finished (assuming, of course, that you didn’t bust your account
during a bad drawdown–see
this article for more about the risk of ruin, and
this article for more about comparing the risk at different account
sizes). Similarly, a negative expectancy means you’d have less
money after an infinite number of trades, and a 0 expectancy means
you’d break even.
That’s great, but when’s the last time you made an infinite
number of trades? :-) What I’d really like to know is, am I going
to make money most weeks? months? years? Profitablility and
consistency are not the same thing!
Consistency Graphs
So, to get started, let’s look an example consistency graph for
a system with positive expectancy. There’s going to be a lot of
graphs like this one in this article, so let me explain what they
mean.
The horizontal axis describes a number of trades taken during a
given time period. The vertical axis tells what percentage of those
time periods will be profitable, given that you took that number of
trades. This was computed via a monte-carlo type analysis, with
2000 trials per dot on that chart.
So, let’s say you trade the depicted system, and you tend to
trade 20 times a month. This graph tells you that you will be
profitable around 95% of months you trade. If you trade 30 times a
day, then this graph tells you that you will be profitable about
97% of your trading days. If you trade 10 times an hour, then you
will be profitable around 85% of the hours that you trade. So it
works on any timeframe… you get the idea by now.
See how the graph starts out in the 70% range, and converges on
100% consistency as the number of trades goes up? In general,
all graphs of positive expectancy systems look like this,
in that they start out near the win rate % consistency, and
converge on 100% consistency. The width of the path, and the speed
of the convergence will vary.
Now, let’s look at a graph for a system with negative
expectancy:
Pretty much the inverse of the positive expectancy chart. It
basically says, the more you trade, the less chance you have of
being profitable. As an aside, this is exactly why your
best bet at a roulette table is to bet everything on one round.
Roulette has a negative expectancy for the player, so the more you
play, the less consistent your profits will be.
Finally, if your system has an expectancy of 0, the graphs all
look like this:
… as the number of trades increases, the consistency % forms a
band around 50%. Makes sense.
Effect of Expectancy Size on Consistency
So, by now, you should know that a positive expectancy is
necessary both for long term profits, and consistent
profits. You might wonder if a larger expectancy system will be
more consistent than a smaller expectancy system. The answer, which
surprises a lot of people, is: no.
Here are consistency graphs for a range of expectancies from
$40/trade to $440/trade. They are only marginally different:
If you think about the meaning of expectancy, you will realize
that the $440/trade system will make a lot more money than the
$40/trade system. But, for any given set of trades, expectancy is
clearly not the aspect of the system that governs the consistency
of the profits. We’ll just have to keep looking….
Effect of Win Rate on Consistency
Well, surely, if my system wins more often, I will have more
consistent profits? It turns out, winning more often increases
expectancy, but does not necessarily do much for consistency of
profits. Here are several consistency graphs for systems with
increasing win rates. You can see that, after you get above 10 to
15 trades per day/week/month/whatever, the graphs all look about
the same.
It makes sense that the win rate would have sway over the
answers when there are fewer than 10 trades per trial. So few
inputs go into the profitability calculation, that a little luck in
either direction changes the answer. Also, at the extreme end, any
1-trade-per-trial run will have a consistency % equal to the win
rate (since the single trade is profitable at exactly its win
rate).
Effects of Profit Factor on Consistency
Now, if you are an astute reader, you’ve noticed that in the
preceding two sections, each graph had a constant “Pf” label at the
top. And, since each set of graphs had fairly constant conistency,
you might conclude that this “Pf” is what really gauges the
consistency of a trading system. You’d be right.
“Pf” stands for “Profit Factor.” The equation for it has the
same terms as the expectancy equation, arranged differently:
Profit Factor = (win_rate * avg_win) / (loss_rate *
avg_loss)
Since the equation is so similar, you can see by simple
transformation that the profit factor will be 1 whenever the
expectancy is 0:
- (win_rate * avg_win) / (loss_rate * avg_loss) = 1
- win_rate * avg_win = loss_rate * avg_loss
- win_rate * avg _win - loss_rate * avg_loss = 0
Similarly, the profit factor will be greater than 1 whenever
expectancy is greater than 0, and less than 1 whenever expectancy
is less than 0.
Here are some charts of systems with increasing profit factors.
They are randomly-generated systems with respect to win_rate,
avg_gain, and avg_loss… the only thing I’m controlling is that the
profit factor of each is rising. It’s easy to see that the profit
factor is highly correlated with speed of consistency convergence
of a system, and that higher profit factors require fewer trades
per period to give a good guarantee of consistency.
If you think the graphs from 1.5 to 3.5 look very similar, check
the y-axis! The convergence is getting much faster! (On some of
these graphs, Mathematica cut off the early numbers, because it
converges on the 99% range so fast that it decided to blow up the
99-to-100% range. Recall that the point for 1 trade-per-period will
always be very close to whatever the win rate happens to be, no
matter how fast it converges after that.)
Reading that last chart, you can see that if you find a system
with a profit factor of 6, and you can trade 15 times a day with
it, you will make money 99.95% of days you trade. That means you
will have a losing day once every 10 years, if you trade 200 days a
year. Oddly enough, I bet you feel pretty bad that day… so try not
to let it throw you off! :-)
These trials confirm the advice given in the elitetrader thread,
which gives the following guidelines for trading frequency versus
profit factor:
| Profit Factor |
# Trades Needed
for 95% Consistency |
| 1.5 |
60 |
| 1.75 |
40 |
| 2.0 |
30 |
| 2.5 |
20 |
| 4.0 |
10 |
By looking at my graphs, you can see what the guidelines are for
any level you want to target, for profit factors from 1.5 up to
6.
Simplifications
I already mentioned that I ignored breakeven trades. This has
only a marginal effect on the outcome, while simplifying my job a
bunch. If you make 10 trades a day, and 9 of them are
exactly breakeven, then maybe you should do some mental
translation when using graphs like these. If your truly breakeven
trades are relatively rare (like they are for most people), then
you will be fine.
I also assumed during the random trials that a win is always the
avg_win, and a loss is always the avg_loss. I could have been more
exact by making a probability distribution of wins and losses, via
a standard deviation from the averages. Assuming the variance in
the wins and losses is not very large, doing this wouldn’t affect
the message of this article, and would just make the graphs a bit
more noisy. And, I could eliminate that noise by ramping up the
number of trials per dot up from 2000 to more like 1,000,000
anyway. So, I didn’t bother. However, if your trading is all over
the place, then you could have much wider swings in your
profitability than depicted here (especially if you don’t trade
often). Do try to keep the variance in your gains and losses as
small as possible, if only because it makes it easier to reason
about and predict your own performance.
Conclusions
So, here are some guidelines you can take away from all
this.
If you are designing a system for consistency:
- Maximize the profit factor.
- Double-check your win rate to make sure your risk of ruin is
acceptable
- Trade as many times as you can, within the parameters of the
system.
- Get the variability of your returns under control (using
something like the modified sharpe ratio, for example)
- Tune the expectancy (or add additional systems) in order to
make enough money.
If you are designing a system for maximum profit:
- Maximize the expectancy.
- Double-check your win rate to make sure your risk of ruin is
acceptable
- Trade as many times as you can, within the parameters of the
system
- Use the profit factor to frame your month-to-month
profitability expectations. No reason to be down on yourself for a
losing month, if your system should only win 60% of all
months!
If you already trade a system, and you want to be more
consistently profitable:
- Find more trades to take within your system’s parameters. This
doesn’t mean you start taking questionable trades, just to get the
count up. Instead, you have to be more efficient about finding and
exploiting opportunities to trade.
(this is why you’ve seen me post every now and then about
needing to find more trades to take… it’s the only way I know of to
be more consistent, without changing my system!)
If you’d like to see the Mathematica notebook that I used for
this investigation, you can read
the html version of it.
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12 comments:
What you are describing would indeed be very different. I wonder how many people would never get involved in trading at all if they realized that the learning curve was so potentially long (and steep).
BW
I agree that this trader development proposal is truly visionary and would work to instill some real professionalization in the trading industry. However, there is something about trader development that has been on my mind for quite some time now that poses some challenges to parts of this proposal.
In short, right now there is no such developmental structure in the industry, and yet there ARE and have always been many world-class experts. The argument though is that they are only 1 in 1000 because the structure isn't there to ensure more than this small number truly thrive. However, is this number really any different than all the other performance fields? If you look at sports, far less than 1 in 1000 ever become world class performers, despite all of the structure and professionalism in development in those areas. Even in medicine, while most students that undergo the rigorous multi-year training end up quite competent, isn't it probably safe to say that probably only 1 in 1000 doctors is truly a world-class expert performer?
So I think that what truly makes these world-class experts is something above and beyond all of the developmental structure. Indeed all doctors get very similar training and development and yet only a small number can be considered world-class like I just mentioned. I think this goes back to what you stated in your book that the essential thing is having the desire for that motivational high and the subsequent extraordinary immersion that results to reach it. And this immersion due to finding one's true "calling" is probably what spurs the special learning. And so it is with traders. Assuming we were to see such structure in trader development, I don't think we'd see a higher number of WORLD-CLASS performers. We would probably see greater competency and lower failure rates for sure, but I think the end result would be an overall more competent trader population but with still a similar number of world-class experts as a select few would separate themselves from the now more competent pack to reach ever higher levels of expertise.
Following this line of thinking, the only difference I think there is in all of the structured and professionalized performance fields and trading is that perhaps those fields are far more evolved in their participants. This greater evolution however does not imply more world-class talent, because by definition the talent bar is much higher and only a few will reach that level.
So as my personal conclusion, I would have to say that while such an evolution in trader development would raise overall competency, it would not really raise the number of traders that consistently make millions, which is all the 1 in 1000 statistic really refers to. And while a lot more traders will be competent (i.e. able to at least break even) we must remember that this is a unique zero sum game. No matter how you slice it and dice it, for there to be traders consistently making money, there must be traders consistently losing money; and as the entire population improves, it will simply mean more equal division of the pie, and not more brilliant performers running around.
Thanks for your insightful counsel Brett! I have implemented many of your excellent suggestions to my succsess, as limited and early in the journey it is. I created something I call TAMTA'S Trading analyzer. It allows me to do the things you speak about. I tie it into my Daytradingsnippets production. It is a powerful tool for selfreflection, comparing strategys, etc etc. Thank you so much for your endless counsel. Here is the link within the site to the analyzer. There is an instructional video and an update link that tracks the snippets trades. http://www.daytradingfutures.org-a.googlepages.com/daytradinganalyzer Thank you agian for all you do. Steve ~SSK~
yup
Nicker
I wonder how the dynamics of the markets would change if the majority of traders reached the "Competent" level of trading.
I also wonder if it is possible to have a far reaching mentorship program amoung traders, when many traders believe that profitability is the result of taking advantage of less informed traders.
Both Dalton and Steidlmaayer/Koy have stated that being "Proficient" or "Expert" reqires a combination of Market Understanding, Strategy and Self-Understanding. Most of us spend most of our time struggling with Market Understanding and Strategy. But, I suspect very few of us are willing to spend much time with Self-Understanding. As Ziad has stated, even with a professionally structured training program, only 1 in a 1000 would reach the "Proficinet" level.
Quite simply, most of the trading universe would refuse to undergo a structured program of Self-Understanding, which would be required to reach the "Proficient" level of trading.
Charles
Charles - ziad actually said 1 in 1000 would be "world class" traders, not merely "proficient". In terms of your question about what would happen if everyone were to become competent, then the implication would be of a much more efficient market environment - one in which above average profits would become much harder to achieve.
ziad - While I agree with the bulk of what you've said, I would make one big point which contradicts some of your argument in the last paragraph. Not all markets are zero-sum. I actually posted something on that subject on my own blog a while back:
The Zero Sum Game
Brett ~
Your use of medical training as an analogy for building robust expertise seems particularly apt. In finance there are programs leading to broad-based knowledge, such as the Chartered Financial Analyst designation. These, though they do address market mechanics, do not include trading as part of the curriculum.
Brandon, above, makes an excellent point when saying, “… how many people would never get involved in trading at all if they realized that the learning curve was so potentially long (and steep).” Many people are drawn to the craft’s superficial luster. It must be admitted this was part of the initial appeal for me.
The first year of blundering led me to dive into “Market Understanding” and “Strategy.” It was during my second year trading that I realized markets are mirrors returning to us what we put in, and the need for “Self-Understanding” became apparent.
As Charles, above, rightly points out, “… very few of us are willing to spend much time with Self-Understanding.” You would probably agree that this is the longest, steepest part of the learning curve. It’s a nearly merciless focus on this to which I attribute any success I have had.
I think many of us are interested to learn how this last, key aspect would be built into your trading curriculum.
Wonderful posts. Thank you for sharing your ideas with us.
Adam.
John,
Thanks for your excellent comment. I'm a futures trader so I tend to think in terms of that market. But you're absolutely right, the stock market does not have the zero sum characteristic. However even given that, I don't think my argument changes much. Whether stocks on the whole are appreciating or depreciating, the more competent the trader population the more equally profits will be dispersed among the non buy-and-hold crowd. In fact, I think you put it perfectly by saying that markets would become more efficient and above average profits harder to come by.
Given all of this, it makes me (somewhat selfishly perhaps) question the benefit of professionalizing the industry. As a trader, I am GRATEFUL that there is inneficiency, and the more of it there is to exploit the happier I am. So maybe it is worth questioning... What would we be truly trying to do by professionalizing the industry? If we're not creating relatively more world class talent as we initially intended, could we be simply "socializing" the system by changing it from one in which the majority of the profits and wealth are in the hands of the few to one in which greater equality reigns supreme? And would that be the intended outcome? It seems somewhat absurd for me to be questioning such a noble undertaking as ensuring greater competence among the majority of traders, but in an industry where those traders are technically my competitors, it is human nature to wonder.
Ziad & John ~
Your combined posts sum to an interesting insight with which I fully agree.
In theory, more equal distribution of both skills and information would tend to increase market efficiency. Under such a regime returns would regress toward the market mean, making individual security selection less likely to return a risk premium. This remains, however, just a theory.
Has more equal distribution of market information changed the relative percentage of winning and losing traders from any previous regime of information distribution? I don't know.
The famous (infamous?) Turtle experiment demonstrated ~ despite some claims to the contrary ~ that traders cannot be bred like amphibians. They might thrive under the careful nurturing of a skilled breeder, but once released into the wild, one or less out of a dozen survives.
Given the wide variance of human nature, no matter the curriculum offered, I think it's reasonable to expect that the percentage of people who could reap long-term benefit from it would remain vanishingly small.
Adam.
Here is a summary of my trading training to date..
Thanks Brett
http://59-cedar-st.blogspot.com/2008/02/mumbo-jumbo.html
Thanks, all, for the excellent comments that really illuminated the post. Very good points about the learning curve for self-understanding, as well as the curves for learning markets.
Brett
This was an excellent post. I worked at Morgan Stanley in 2006 and 2007, and the training you've described is dramatically different than what is offered at the investment banks. While an archive of trading knowledge is available (online courses in market fundamentals, access to books, etc.), and if you're lucky enough to land in a group that believes in properly training new traders you can get hands on guidance and feedback (but that's rare), training at the firm is by dropping a new trader in and seeing how he/she does.
I think good training is a matter of cost. To a hospital, from a cost perspective, it's essential that new doctors are properly trained (to avoid lawsuits, ensure return patients, etc.). At an investment bank, if 1 in 1000 traders will have what it takes to be successful, wasting resources training 1000 when you could instead discover the 1 using a sink or swim approach makes more sense. Also, those experienced traders qualified to mentor new traders are better utilized making money for the firm, rather than training 999 probable loss generating new traders and the 1 winner.
Here's hoping for a change!
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