Most traders focus on cutting off strings of losses. But, if you apply proper risk management techniques, then strings of losses won’t take you out of the game. A much bigger problem, which many traders overlook, is that missing out on winners can hurt you far worse than losses. Your overall positive expectancy is based on your winners outpacing your losers, but for this to work out, you actually need to have the winners. And, you can’t have winners if you aren’t trading.

Based on that old saying “you can’t hit the ball if you don’t swing the bat,” I call this article “Keep Swinging!”

Important Caveats!

Many traders are not ready to take this advice, yet. The best thing for their accounts really is to walk away, for one or both of these two reasons:

• … because they let the losses affect their judgement. My article on how to recover from a loss points out that recovery is an aspect of your mindset, rather than your account balance. If you are not mentally recovering from your losses, walk away (and try to get better at recovering quickly).
• … because they do not have a system that works for them, and that they believe in. I don’t mean you need a mechanical system; even a completely discretionary system is fine. But, you have to know, either from testing, or your track record, or whatever, that it works and has a positive expectancy. If you are testing the waters and trying things out, please only make tiny bets if you trade at all.

So, if either of these two issues applies to you, by all means walk away from losses and regroup. But, it’s once you’ve addressed these two issues that your profits and confidence can really soar.

Excuses, Excuses…

In the past, when I had a string of losses, I would often quit for the day, or even take a couple days off. I would tell myself things like:

1. I must be off today… I better get away and get re-centered
2. The market’s mood is changing… I better stay away until it starts acting better
3. I am just unlucky today… better to save my capital and come back strong tomorrow

But those are just excuses, when you get down to it. I’d make those excuses because, when I was losing, I wanted to walk away. It’s hard on the ego to lose. But, I’ve come to realize that walking away is the last thing I should do.

Why not Walk Away?

I am going to assume here that one of your main goals as a trader is to be consistently profitable. That’s not to say you should be focused on making up your losses, or on the amount of money you have made, when trading. But, since we all know we’re trading in order to make money, it’s good to analyze how best to actually do that!

If you recall, in my article about how to be consistently profitable, I point out that there are two main factors affecting profitability. They are:

• the profit factor of your trading performance
• the number of trades you take

The profit factor is explained in the linked article, and is a somewhat fixed aspect of your trading system. The number of trades you take is up to you, though! The article shows that the more trades you find and take, the better the chances that you will be profitable that day (or week, or month… whatever your time frame is).

So, a trader that has a “three strikes and you take the rest of the day off” rule is actually crippling their chances of being profitable. By stopping in the red, they’ve dropped their chance of profitability that day to 0%, by default. But, even worse, the time off also means less trades will be taken that week. This lowers the chances that they will be profitable that week, and so on.

Another way to look at it: If you have a 60% win rate, then you can expect four out of ten trades to be losers. But, you don’t know which four they will be, and you shouldn’t care. If those four happen to be the first four of the day, then why would you stop, rather than go on to have your expected six wins? It’s not rational. Recall the caveats from earlier. We are assuming here that your losses don’t affect your judgement or performance. If so, then the outcome of the next trade has nothing to do with the previous trades. Your chances are still governed by your statistical win rate.

Of course, due to the nature of probability, there is always a chance you might keep trading and go on to have 10 losses. But, that’s what good risk management and money management are for. And, the fastest way to get back into the green is to keep trading.

You don’t make money by not trading.

Some traders, rather than quitting for the day, start placing smaller bets. This also cripples their chances of profitability. Say you cut your bets in half. Now you need twice as many wins as you needed before to get back in the green. I am a firm believer in risking a percentage of equity, so I do think you should trade smaller when your account is in a drawdown. But, that’s an adjustment to make each month or so. Not after every trade! I’ll go back to those caveats: if your judgement is not impacted, and you have a solid system, there is no good reason to cut your risk because of a few losses.

My Excuses Were Bogus, Anyway

Let’s look at the excuses I mentioned earlier, one by one. These were just three examples from my trading… Perhaps you can think of more, from yours.

First: “I must be off today.” Seriously? If I get all introspective, I can tell if I am truly off or not. I remember, one day last month, I kept pulling the trigger maybe a half-second too late, on three trades in a row. It was seriously cutting into my profits. I was pretty sure the markets hadn’t sped up, so I realized that I must have had slow reflexes that day. Maybe I was distracted, or whatever… doesn’t matter. That’s the time to walk away. Most days, though, I am just fine, and the “I must be off” theory is just a bogus ego band-aid.

Second, “the market mood must be changing.” Really? If so, then why are my setups still setting up? I have not compiled statistics to prove this (and I doubt statistics would prove it, actually), but it seems like the first setup I skip always ends up being a big winner. Surely most traders have experienced this. And of course then you try the following setup, lose again, and feel just terrible. Losses suck, but missed gains followed by more losses really sucks. Moral of the story: take all your setups, when they appear.

Two weeks ago, on a Monday, my first three trades were all small losses. This did not feel good at all. I literally thought to myself “the markets aren’t acting right.” When I realized what I was saying, I got up, walked around a bit, and had a snack. When I felt normal again, I kept trading (I was extra careful to only consider “perfect” setups, to be sure). I made two more trades, for two wins, and ended the day at break-even. I’m sure you know the emotional difference between ending the day oh-for-three, and ending the day break-even. It’s a huge freakin’ difference.

At this point, you might be objecting: “but, sometimes the markets really aren’t conducive to my trading style.” My response is: whatever criteria you are talking about should be a precondition of your trading setups. In other words, if you are correct, then on those days you shouldn’t be able to find any trades to take. If you have loosely-defined setups which give false positives when the market mood shifts, then improve your setups and keep taking every good one you find. But, please wait until you have a lot of data to back you up! Remember that it’s a common misconception that you can judge what works quickly!

Third, “I am just unlucky today.” Yes, many times we feel like we are down on our luck. But, what does that really mean? I’m not sure I can say. It’s not like we literally have a luck jar that can be running low on luck juice. This is such a flimsy excuse for quitting! In my article on how to tell if you are a good trader, I pointed out:

“If a trader has a win rate of 40%, then there is a 7.8% chance that any string of five consecutive trades are all losses. Even at a 60% win rate, the chance is 1%. So, after hundreds of trades, I should actually be surprised if there are not a few strings of 5 or more losses! It’s to be expected, and not a reflection on my ability to trade in any way.”

Earlier this week, I scratched three attempts to scalp HD. Three times, in quick succession! It kept stalling, and I kept bailing. Then, it would retreat a few cents, and set right back up at the number I was watching. After the third scratch, I said “Enough! I am just not having any luck with HD” and I passed on the fourth setup. You can guess that the fourth one ran far enough to make a profit even after covering the commissions on the other three tries! That pissed me off, because it was clearly a mistake on my part to ignore a good setup because of previous failures. Once I got calm again, I went on to trade MNT and SLAB for wins, ending the day in the green.

It Goes for Winning Streaks, Too

I am personally still guilty of this mistake: If I have a string of winners during the day, I tend to take the rest of the day off. I am back to worrying that my “luck jar” will run out of “luck juice,” I guess. This is just as bad as stopping due to losses (though it doesn’t feel nearly as bad). More trades is always statistically better. Say I had 5 wins in a row, so I quit. The next day I have 10 losses. I think I would probably wish I had stuck around for a potential 5 more wins on my good day. So, this is something I’m working on.

As with strings of losses, the key here is to not let the strings of wins affect your judgement. If you start feeling like a trading god who can do no wrong, and get overenthusiastic, then by all means walk away (and work on improving in this area). I don’t get the god complex, but I have a kind of post-win lethargy. I lose all will to trade for a while. I think it’s just fear of losing my gains in disguise, and I’m working on just forgetting my previous trades, whether they are wins or losses.

So Keep Swinging

I view ideas like cutting down risk or stopping trading after a string of losses kind of like training wheels on a bicycle. They keep you from hurting yourself when you are still learning, and uncoordinated. Once you know what you’re doing, and have the proper confidence, take the training wheels off! Leave those crutches behind.

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:

1. Maximize the profit factor.
2. Double-check your win rate to make sure your risk of ruin is acceptable
3. Trade as many times as you can, within the parameters of the system.
4. Get the variability of your returns under control (using something like the modified sharpe ratio, for example)
5. Tune the expectancy (or add additional systems) in order to make enough money.

If you are designing a system for maximum profit:

1. Maximize the expectancy.
2. Double-check your win rate to make sure your risk of ruin is acceptable
3. Trade as many times as you can, within the parameters of the system
4. 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:

1. 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.