Have you ever heard the cliché “I’m only as good as my last trade”? In other words, if I’m losing money, I must be a bad trader. I think just about everyone would say that of course that’s not true. But, I know I still have to fight that feeling when I have a few losses. The next trade I try to make, I start second-guessing myself, since I don’t feel like I know what I’m doing anymore. Reading a lot of trading blogs during the painful August and September time, I know others are falling into this trap sometimes.

In my article on loss recovery, I point out that the way to recover from a loss is to get back into the same mindset you were in before the loss. That’s good information to have, and I suggested getting away from your trading platform until you recover, but I didn’t talk much about how the heck you’re supposed to get your head back on straight. It’s hard! Here are a couple things I like to keep in mind, and repeat to myself until I fully believe them again:

• I wouldn’t beat myself up if a coin came up tails, would I? Trading is a probability game, just like tossing a coin. Just as I should not be surprised or upset when a coin flip goes against me, I should not be surprised or upset when a trade goes against me.
• 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.
• Judging myself based on criteria outside of my control is counterproductive and depressing. I can’t control the markets, so it doesn’t do me any good to value myself as a trader based on what the markets do.

All of that’s just longhand for you are NOT your trades. You are also not your expectancy, or your win rate, or your dispersion of losses. Rather, you are the trader, at the helm of it all. Should the captain of a ship blame himself when storms make for rough going? Or should he blame himself when he lets the ship fall off course through neglect? I think, the second, don’t you?

With that in mind, here’s a picture of how I think these things fit together:

• Your Trades Are Good If: they were executed according to your plan. (Covered fully in this article). In fact, this means that your trades can be good even if they all lose money because your plan is bad!
• Your Trading Plan Is Good If: the statistical measures for expectancy and consistency and risk of ruin are within your comfort zone. (I have written articles on consistency and several more on expectancy/risk of ruin)
• You Are A Good Trader If: you are monitoring and improving upon the other two items in this list. (That’s the point the present article is making)

Only that last one has anything to do with you, the trader. Let’s expand on what that last bullet means a bit further. To measure your progress as a trader, I suggest the following two criteria:

1. How well am I tracking and improving the way I trade to my plan? This is like the aggregate data version of the way I suggest you evaluate the quality of each trade. I suggested that you grade each trade against your trading plan in your trading journal. That way, you can periodically look over your scores. Try to make whatever changes are needed to get closer to perfect execution of your plan. This is completely under your control. For example, if you tend to pull your stops, you can start honoring them, somehow.
2. How well am I tracking and improving my aggregate trading performance? In other words, am I keeping track of my expectancy, win rate, dispersion of losses, profit factor, etc? And, once I have enough data to review, am I making adjustments to my plan to keep my overall trading within bounds that I am comfortable with? For example, if you are risking too much per trade, you will find that you are uncomfortable with your risk of ruin, and should adjust your risk management plan. I have an article in the pipeline about aggregate trading performance, which should help explain what all of this means, if you are not yet in the know.

This is easy to see as an expansion from the “trader as ship captain” viewpoint. As with anything you do, you will have successes and failures at this. I don’t suggest beating yourself up too hard in any case. It won’t get you any closer to perfection, I promise! But, at least this is a fair yardstick based on criteria that are rational, and under your control. Even after a string of really bad luck, when your account has taken a real dent, you can still feel good about yourself as a trader if you are doing those two things well. Because you are monitoring your per-trade and aggregate performance, you will be confident that bad luck was all it was, rather than a problem either with your system or your execution. That’s the kind of knowledge that can keep you sane during the bad drawdowns.

There’s a hypothetical scam that I’ve seen outlined in two trading books now, and I think it’s clever so I want to share it. A book I’m reading right now kind of turns its idea inside-out, with scary implications.

Anyway, the scam goes like this: Say you want to grow your investment advisory business. One way to do it would be to mail out 10,000 newsletters predicting next month’s market direction. In 5,000 of the letters, predict up. In the other 5,000, predict down. At the end of the month, 5,000 people will think you understood something about the markets. So, next month, mail those 5,000 people another prediction (2,500 up, 2,500 down). Repeat, and after five months, about 300 people will think you have been right about the markets every month. Of course they will want to subscribe to your service to get your stock picks.

Cute, right? The book I was reading today, though, turned that scam inside out, and presented it like this: Say 10,000 traders commit their money via coin toss, either bullish or bearish on the markets. After 5 months, one would expect that as many as 300 of them will have made money every single month. Two or three will make money every month for a year. You can see by extension, with a large enough population of traders, some will be multi-year market superstars. Articles will get written about them, explaining how their superior methods led to their great success. Others will start following their trades, and seek their advice. Then one day, their luck will run out, but people will forget about that pretty quickly, replacing them with the next two or three lucky traders.

This book I’m reading, Fooled By Randomness, is slowly making me sick. I’m a fast reader, but I’ve had inordinate trouble finishing it–it’s taking a lot of willpower to pick it up. I think it’s because I don’t want to hear what it has to say. He’s making a pretty good case for a lot of so-called success in the markets being plain luck. And it’s not the run-of-the-mill efficient market crap, either. Being long in the market these last couple weeks hasn’t done a lot for my dispositon, as well! :-) I’d rather not read about luck when I have two positions hovering near their stops!

On the bright side, the author is a trader by profession, so he must not think it’s all hopeless. But, I’m 2/3 of the way through, and I’m still waiting for the part of the book that explains why there is some hope for us. It’s demoralizing!

We are all, theoretically, at risk of total financial ruin. Imagine you find a system with a 99.9% success rate, an average per-trade gain of 50% equity, and an average loss of only 0.01% of equity. You would use it, right? So would I! After all, the expectancy would be: .999 * 50 - (0.001 * 0.01) = 49.95% average equity gain on every trade!

BUT, it is not impossible for you to pick this system, and empty your account without making a penny. Think about it… you don’t expect to flip a coin and get tails 100 times in a row, but you know that it’s theoretically possible, right? Consider, too, that the average loss of 0.01% of equity is the AVERAGE loss. In theory, you could use the above system and blow your whole account on one trade. How likely this is depends on the variance associated with that average.

What can we learn from this line of thinking? Well, let’s start by getting it straight in our heads that, almost all the common statistical measures of trading success are only accurate under two conditions:

• You make an Infinite number of trades
• You can trade with a negative account balance

Obviously, neither of these conditions match reality. So, they can easily mislead you. The above example’s amazing expectancy is only guaranteed to materialize as the number of trades I make approaches infinity, and if I could somehow still trade with a $10 account.

Does this mean expectancy, and other such measures, are useless? No, but it does mean we need to take extra steps help ensure that our trading account doesn’t vanish. A small account doesn’t have the padding to weather long strings of losses. So early on, it can even make sense to choose a worse-performing system that has better-bounded worst case behavior. Right now, I’m thinking of three specific steps:

• Always risk a % of current equity
• Prefer systems with higher win rates and lower avg losses
• Prefer systems with less variance in the average loss data

1. Always risk a % of current equity

Clearly, if you want to stay in this game, you have to make money in the long run. But, you also need to never go broke in the short run. I’m going to define broke as $25k, since at that point your pattern day-trading account will be frozen. The conclusions are the same if you define broke to be $0.

Let’s say you start with $100k, and you risk a fixed 2%, or $2k, per trade. Your account will be frozen if you lose 38R. In the worst case (assuming away slippage), this means losing 1R 38 times in a row. (100k - 38*2k) = 24k = busted

Now assume you start with $100k, and you risk 2% of current equity per trade. This way, you would have to lose 69 times in a row before your account is frozen. (100K * (0.98)^69) = 24.8k = busted

Obviously, it is more likely you will go bust with a fixed risk. In the coin toss analogy, 38 consecutive tails is much more likely than 69 consecutive tails. (Again, never forget that 100 million consecutive tails is still possible, no matter how unlikely).

2. Prefer systems with higher win rates and lower avg losses

When talking about expectancy, it’s common for people to point out that you can win less than half the time, and still make money. They should really add the qualifiers “in the long run, if you don’t go broke first.” We’ll start with an absurd example, and then get more realistic:

• winRate = 3%
• avgGain = 200%
• avgLoss = 4%

… expectancy of 2.12 % equity gain per trade. Better than many systems! But, not usable in practice. At 4% avg loss, it would take 34 consecutive losing trades to bust a $100k stake. With a 3% win rate, there is (1 - 0.03)^34 = 35% chance that this will occur. WAY too risky. In general, the probability of busting an account without any wins is: (1 - winRate)^( (ln (25000/initialStake)) / (ln (1 - avgLoss)) ). Incidentally, that exponent will be the number of consecutive losing trades needed to bring down the account.

So, when comparing any two systems (or versions of the same system, if you are building one), it can be helpful to compare their probability of immediate ruin as well as their expectancy. In general (due to the equation above) higher win rates and lower average losses will perform better on the immediate ruin test.

Certainly, if two systems have the same expectancy, then you should prefer the one with the smaller probability of immediate ruin. That goes without saying. But, what about these two systems:

• winRate = 40%
• avgGain = 2%
• avgLoss = 1%

… expectancy of 0.20% equity gain per trade.

• winRate = 60%
• avgGain = 0.6%
• avgLoss = 0.5%

… expectancy of 0.16% equity gain per trade.

After 500 trades with a $100k stake, the first system is expected to make about $50k more than the second. But, it is also 2.8 x 10^79 times more likely to burn an account straight down to the $25k freeze point without winning once.

Now, at this point, you may do the math and point out that the probability of immediate ruin on the first system is only 2.5 x 10^-29 % in the first place. Isn’t that good enough that you wouldn’t want to give up $50k expected gains for more protection? I actually don’t know yet. It seems to me like the only way to answer would be to work out all 2^500 strings of trades and get a probability distribution of the outcomes. I can only say that minimizing that straight drop path’s probability should also reduce the probability of the other account busting paths, since all losing paths will have at least as many losses as the straight drop.

3. Prefer systems with less variance in the avg loss data

With the analysis we just did, on the probability of the account going straight down, we assumed we always experienced the average loss. This is another one of those statistical generalities that can mess you up. If the variance in the loss samples is large, then the average loss across a small number of trades could be way out of line with the overall average loss. Not only would that somewhat invalidate our supposed “worst case” analysis, but it could decimate our trading account!

For example, an average loss of 3% equity could have come about from either of these two strings of losses, for instance:

• string1 = 10% 5% 1% 1% 0.7% 0.25%
• string2 = 3% 4% 2% 3% 4% 2%

Across the first 2 losses, though, string1 averaged 7.5%, while string2 was still pretty much in line with 3.5%. And that’s just the difference between using 2 samples and 6! If 100’s of losses went into the expectancy calculation, then any string of 5 losses could could hurt your account far worse than the average would indicate.

As it happens, one way to remove some of the variation from the losses is to prefer systems that incorporate stops (lots of systems don’t!). This puts a cap on the loss amount, which has a side effect of making losses much more predictable. Further, in any worst-case analysis, you can assume all losing trades hit the stop, rather than assuming the average loss. That’s a very safe and conservative path to follow.

Why don’t all systems have stops, if they have so many desirable properties? Well, it would appear that lots of winning systems require you to ride out substantial paper losses on some of their trades, prior to exiting at a profit. Note that this is also why you can’t just add stops to a system that doesn’t have them… they wouldn’t be nearly as successful if they were stopped out in those cases.

But, for the small ($100k or less) account, I’m starting to think that systems without stops should be deemed too risky to use, no matter what the expectancy is. Small accounts just can’t take enough oversized losses to make it. My backtesting seems to bear this assumption out.