What exactly is Trading Edge ?

Any trader in the markets, for any length of time understand that in order to suceed as a trader they need to have:

1) Trading system with an edge

2) Money management

3) Good trader psychology and emotional quotient

Trading edge is a necessary condition, but not a sufficient condition. Even a system with a positive expentancy can end up in ruin with bad money management (position sizing). It's called the "Gambler's ruin". I will talk more about that in a different post. Even with a good trading edge and money management, you could fail if you do not have the right psychology to execute the trade and persist in the face of losses. That's another subject for another post. 1), 2) and 3) are necessary conditions, but not sufficient conditions in themselves. I have heard people say flippantly that even a coin toss with good money managment can make money in the long run. Absolutely untrue ! If you do not have a trading edge, money management and psychology are not going to help you. Trading edge is at the top of the chain and the most important one. Without an edge, you might just close you trading account and go fishing !

So what exactly is this trading edge ? It's not about how much money you made in the last few trades. It not about your high win rate. It's not about how big your wins are. It's not about picking tops and bottoms precisely. It's not about catching some dramatic crashes.

In mathematical terms,

Trade Expectancy (Trading Edge) = % of winning trades * Average Win Size - % of losing trades * Average Loss size

As you can see, Trading edge is not a function of Win rate alone. Yet there is this huge obsession about high winning rate, which is sheer ignorance. It's the combination of these 4 variables which makes the intuition of trading edge so tricky.

Now to understand better, let's look at various types of trading systems and associated edge.

High win rate, poor risk/reward trading systems

These are typically day trading systems, which scalps for small profits intraday. Their risk/reward ratio is typically 1:1 or 2:1. It's very easy to design these high win rate system. If i play the e-mini  S&P futures with a 2 point stop and aim for 1 point profit, my win rate would be very high, quite naturally.

Let's say i have 5 trades with a 80% win rate:

Trade #1: Win 1 point

Trade #2: Loss 2 points

Trade #3: Win 1 point

Trade #4: Win 1 point

Trade #5: Win 1 point

Trade expectancy = 80% * 1 - 20% * 2 = 0.8 - 0.4 = 0.4

So the trade expectancy is positive and hence the system can make money when traded. The trade expectancy of .4 here is the average return you expect from the system per trade. So if i made 5 trades, my total return would be .4 *5 = 2 points. If i made 100 trades, my total return would be .4 * 100 = 40 points.

So the trader who has backtested the system thinks it's fantastic. So if he makes 5 trades everyday, he would make 100 trades in a month and pocket 40 points E-mini points i.e $2000 every month per contract. By trading 2 contracts, he can now think of quitting his day job. When he trades 5 or 10 contracts, the sheer adrenaline of the outcome gets uncontrollable.

The system looks great on paper and backtesting. So what could go wrong ? You add the commisions and slippages and you could start seeing a totally different picture. Let's just assume a slippage of .25 points each side or .5 points per round trip. If you account for slippages, your trading profits/losses would look like:

Trade #1: Win .5 point

Trade #2: Loss 2.5 points

Trade #3: Win .5 point

Trade #4: Win .5 point

Trade #5: Win .5 point

Trade expectancy = 80% * 0.5  - 20% * 2.5 = 0.4 - 0.5 = -0.1

Now the trade expectancy is negative -0.1, which means you would lose money trading this system over a long run. If you add the commisions, the trading edge would become even more negative. As you can see, how sensitive the trading system here is to minor change in profit/loss expectations. Just a .25 point slippage ended up in turning a profitable system into a loss making one. No wonder you end with a negative ledger when you trade this with real money.

This is the problem with high winning rate systems. They are very sensitive to minor changes in profit/loss expectations, as they have very poor risk/reward profiles.

It's this kind of day trading systems they peddle all over the internet, with high winning rates and low risk/reward profile, which looks great on paper, but ends up with big losses for the subscribers. You can't argue with the vendor as he shows paper trading historical results, not accounting for real-life trading expenses. The novices who trade these systems think that it is their poor execution which is the cause of bad results, rather than the system itself. It will take a while for them to wrap their head around what's happening, before they know they are being fleeced. The vendors don't care as a sucker is born every minute ! Worse they peddle these kind of systems to people with day jobs, who can't possibly execute all the trades. Then the vendors have a convenient excuse that the traders did not execute all the trades.

Now let's say we design a trading system with a better risk/reward of 1:1, with a 80% win rate.

Trade #1: Win 1 point

Trade #2: Loss 1 point

Trade #3: Win 1 point

Trade #4: Win 1 point

Trade #5: Win 1 point

Trade expectancy = 80% * 1  - 20% * 1 = 0.8 - 0.2 = 0.6

That's great. We are back to positive expectancy. Now, let's add the 0.5 point slippage.

Trade #1: Win 0.5 point

Trade #2: Loss 1.5 point

Trade #3: Win 0.5 point

Trade #4: Win 0.5 point

Trade #5: Win 0.5 point

Trade expectancy = 80% * 0.5  - 20% * 1.5 = 0.4 - 0.3 = 0.1

Well, the trading expectancy is still mildly positive. Now let's add the commissions. Let's assume you pay $5 round trip for a e-mini trade. $5 is 0.1 e-mini point. Accounting for commisions:

Trade #1: Win 0.4 point

Trade #2: Loss 1.6 point

Trade #3: Win 0.4 point

Trade #4: Win 0.4 point

Trade #5: Win 0.4 point

Trade expectancy = 80% * 0.4  - 20% * 1.6 = 0.32 - 0.32 = 0

Now your trade expectancy is zero. You might as well close your account and go fishing !

Even without accounting for changing market conditions, your expectancy is zero. Imagine what would happen if the market conditions changes into a dull, low volatile uptrend. Your 80% win rate cannot be sustained in that kind of environment and the win rate can drop very quickly and so will your expectancy, which would go negative.

Low win rate, Good risk/reward trading systems

These are typically the trend following type systems which cuts their losses quickly and let their winners run. This is diametrically opposite to the sexy high win rate, low risk/reward day trading systems.

Let's assume the win rate is 40% and the risk/reward is 1:4

Trade #1: Win 20 points

Trade #2: Win 20 points

Trade #3: Loss 5 points

Trade #4: Loss 5 points

Trade #5: Loss 5 points

Trade expectancy = 40% * 20  - 60% * 5 = 0.4 * 20 - 0.6 * 5 = 8 - 3 = 5

That's positive expectancy. Now let's account for a slippage of 0.5 and commision of 0.1

Trade #1: Win 19.4 points

Trade #2: Win 19.4 points

Trade #3: Loss 5.6 points

Trade #4: Loss 5.6 points

Trade #5: Loss 5.6 points

Trade expectancy = 40% * 19.4  - 60% * 5.6 = 0.4 * 19.4 - 0.6 * 5.6 = 7.76 - 3.36 = 4.4

Well, the effect of slippages and commissions is very minimal. It's still has a good positive expectancy with only a 40% win rate after accounting for all expenses.

The win rate is only paltry 40%. How much worse can it get ? Let's say the market is not trending well and the win rate drops to 30%.

Trade expectancy = 30% * 19.4  - 70% * 5.6 = 0.4 * 19.4 - 0.6 * 5.6 = 5.82 - 3.92 = 1.9

The system still has a positive expectancy with just 30% win rate acounting for slippages and commisions. What this demonstrates is that the system is not very sensitive to changing market conditions and the consequent reduction in win rate. It also is not sensitive to slippages and commisions. Wonder why most professional traders fall into the category of trend traders ? Wonder why the wise folks coined the phrase "Cut your losses and let your winners run" ?

Now if the system's profitability goes to say 20% or below on a sustained basis for a few months, then obviously it's time to re-examine your trading system or tweak the technical parameters to the new market conditions. There are various types of tuning that can be done technically to continually improve the edge. But the biggest edge comes from the fact "Cut your losses and let your winners ride". 

It gives me a chuckle, when i hear people saying "You can't trade the market with small stops". It's precisely the small stops (relative to the return) that gives you an edge. When i say a small stop, it's relative to the size of the return, not an absolute number. If you use 5 points stop and aim for a 15-20 points reward, i would consider that as a small stop. If you use 5 points stop and aim for 5 points profits, that's a big stop. If you use a 20 point stop and aim for 80 points profits, that's again a small stop relative to the return. 

Of course the system also needs to have a sound technical edge. I cannot just flip the coin and expect profits just beacuse i have a small stop. The distribution of returns matter too, not just the probability of returns. In an uptrending market, if the coin flips return 50 tails in a row and then 50 heads in a row (heads = long, tails = short), those 50 consecutive tails are going to kill me. Having a sound trend trading system will skew the distribution of returns in my favor. In other words, my system would generate more long trades than short trades in an uptrending market (and vice-versa in a bear market), if it's designed on sound technicals based on trends.

Again this is not a Day trading vs Trend trading debate. This is a debate of high win rate (poor risk/reward) vs low win rate (good risk/reward) systems and why the latter is preferrable to former, given it's ability maintain the trading edge despite changing market conditions and also after accounting for expenses (slippage + commisions).

Can you design a Low win rate, Good risk/reward day trading system which makes money in the long run ? Absolutely yes !. You could use a 2 point stop and aim for 5-6 points profits in the e-mini. But do not expect 70-80% win rate from this system over the long run. 40-60% win rate would be a more reasonable expectation. But it sure makes money in the long run.

High win rate, Good risk/reward = Snake oil

Let's say somebody shows you a system with High win rate (say 70% or more) and a good risk/reward (say 1:4 or more), would you beleive them ? Run for your life as fast as you can. This is the snake oil world of optimized systems. Most of these systems are black-box systems optimized for certain market conditions. If you ask the vendor, he would provide the back-tested results only for certain market conditions or time period. Why black-box ? Well, if the system was revealed, you would test it in other market conditions and reveal that the emperor has no clothes. This is another scourge in the trading systems world. If you take a certain time period and fit a curve to data series, you can find the most optimal returns scenario and model your system based on that. A simple polynomial fit can generate some magical returns. Stay away from these systems as they are not real and even if they are, they are not going to last long.

When you consider the optimal returns under various market conditions, the true optimum is not the global optimum, but it's the least common denominator of the local optimums. For those, to whom it sounds too mathematical,  when a system is tested against various market conditions, choose the one with the least optimum. That is the one which is going to surive in the long run with minimal modifications.

A high win rate, high risk/reward is nothing but a highly optimzied version of a trading system, which is not going to last for long. A slight change in the market condition will kill it. If durability is of concern to you, stay away from them. It's too good to be true. Human nature doesn't fit into a polynomial !

Moderate win rate, Moderate risk/reward

This belongs to VST (very short term) and/or day trading type trading systems. I am talking about a 50% win rate and a 1:2 risk/reward. The systems perform well in stable market conditions, but are susceptible to changing market conditions.

Trade #1: Win 4 points

Trade #2: Win 4 points

Trade #3: Win 4 points

Trade #4: Loss 2 points

Trade #5: Loss 2 points

Trade #6: Loss 2 points

Trade expectancy = 50% * 4  - 50% * 2 = 2 - 1 = 1 (positive expectancy)

If you account for a slippage of 0.5 and commision of 0.1, it still gives a positive expectancy

Trade expectancy = 50% * 3.4  - 50% * 2.6 = 1.7 - 1.3 = 0.4  (positive expectancy)

Let's say the win rate drops to 40%

Trade expectancy = 40% * 3.4  - 60% * 2.6 = 1.36 - 1.56 =  -.26 (negative expectancy)

As you can see, the system can quickly turn from a positive to negative expectancy with slight change in the win rate. This makes the system sensitive to changing market conditions and requires constant tuning.

Putting it all together

So essentially what it boils down to is that, you cannot have your cake and eat it too. Trading system optimization is a balance between high win rate vs high reward to risk. Having a high win rate and high reward to risk is mathematically impossible. You cannot fit a polynomial to human nature. Markets are inherently inefficient, irrational and constantly changing. One needs to design systems which adapt to changing market conditions, which implicity means a lower win rate. If you set the bar too high, the market will fail you. You cannot sustain a high win rate over a long period of time, just as you can't sprint like Usain Bolt for hours. Low Win rate systems are like Marathoners, which can keep on trucking even with changing market conditions. The low win rate has to be compensated by going for high reward i.e "Let your winners run".

So the bottomline is, it's preferrable to go for low win rate systems as they tend to be more durable and adapt to changing market conditions, but aim for high reward to risk, on individual trades. This is exactly opposite of what normal intuition will have you beleive. 

Yet why this obsession with high win rates? 

One is psychological, which is that folks with straight "A"s all their academic life, cannot digest 30-40% win rates. They think with their high IQs, they somehow can unlock that door which leads to holy grail of trading systems which gives them the high win rates which can be sustained infinitely. If human nature was predictable and could be mathematically defined, it would have been possible. Alas, if that was the case, everybody with straight "A"s would have no marital discord. 

Secondly, the trading expectancy is not a function of just win rate, rather a function of 4 variables. This is not very intuitive to a novice entering the trading world.

Thirdly, there's a cottage industry of trading systems and trading related service sellers, who advertize high win rate systems, which makes a strong impression on traders minds. You can't blame these system sellers. If anybody advertized a low win rate, high reward to risk system, even though it would make money, there would be absolutely no buyers of such a system. You cannot sell anything that does not appeal to human intution. So they cater to what is in demand.

Now that we have established that it's the trading expectancy that matters for the overall profitablility of a system, how do we improve it ? Well, one needs to first determine a good risk/reward that he expects out of the system and then start working backwards to design a system with the technical tools, to acheive the most optimal win rate for that given risk/reward. Not the other way around. Most people get it wrong. They start tuning their systems for high win rate and then start scratching their brains on how to achieve a high reward to risk, trying to mainting the high win rate that they have established. That results in an endless wild goose chase !