Regardless of your market and timeframe, profitable trading requires that the profit expectation is greater than zero. However, this is a requirement of profitable trading and **not** the secret as some book authors and academic types argue. The secret is finding a sequence of market entry and exit points, or trades, that will achieve a sufficiently large expectation throughout the trading period. This is the secret to profitability.

Trade profit expectation, a.k.a *expectancy*, is a very illusive concept. The profit expectation E[T] is calculated in the literature using the averages of winning and losing trades as follows:

E[T] = w × avgW – (1-w) × avgL (1)

where w is the win rate, avgW is the average winning trade and avgL is the average losing trade (in absolute value). This assumes a finite number of trades N.

However, this definition is problematic in many respects. As I have shown in this post, the right hand of equation (1) equals the average trade:

AvgT = (∑W – ∑L)/ N (2)

Where ∑W is the sum of winning trades, ∑L is the sum of losing trades and N is the number of trades.

The first problem is that the expectation E[T] is approximately equal to the average trade AvgT only for sufficiently large samples (Papoulis, p. 138). This is also common sense. But what is a sufficiently large sample? That depends on many factors.

The second even more important problem is that E[T] is not stationary in general but can vary as a function of trade count N. If E[T] varies, we want the value to stay positive, of course, throughout the course of trading activity but also remain large enough so that it results in a satisfactory return above what we get from “risk-free” interest rate. We also want the variance to be small so that the resulting equity curve is as smooth as possible and without large swings.

**Why most traders fail to maintain a sufficiently large trading expectation?**

(1) It is quite unlikely that **discretionary trading** can maintain sufficiently high expectation for extended periods of time. This is the second most important reason that most trades fail. (The first and most important is account undercapitalization.) The outcome of decisions based on discretion will approach a win rate of 50% over time due to the law of large numbers for the best of trades. Thus, the best trades will be able to win only if they can make more than they lose on the average. This is not easy to accomplish. A careful analysis of the markets shows that low risk/reward ratios are hard to realize and maintain. But some will succeed due to either luck or skill but remain a small percentage of the total.

(2) Traders using** technical analysis** have no chance to remain profitable over the longer-term because this type of analysis easily leads to compulsive actions triggered by subjectivity and wishful thinking. There are some that have developed an edge using this type of analysis but they have invested the amount of time and effort that is beyond the norm. In my opinion, 99% of technical analysis users cannot maintain a positive expectation.

(3) **System traders** have a chance because this approach to generating expected values does not involve emotions and/or illusions. However there are some problems with some approaches followed that can lead to performance similar to that of discretionary or technical trading. Specifically, the following approaches to developing a trading system can lead to negative expectations:

(a) Systems based on **technical analysis** indicators, chart patterns or naive candle stick analysis (out of context). There is basically no difference between a system trader using an automated technical analysis program to find double bottoms, for example, and someone who does it manually. They are both destined to fail unless they have managed to extract some kind of illusive edge from this type of analysis

(b) Systems developed automatically using **genetic optimization** or programming, neural networks, walk-forward optimizers that incorporate indicators or algorithms with adjustable parameters. These type of systems involve Type-I curve fitting. They looks good on paper but the expectation turns negative as soon as the underline market conditions change. Some of these programs do not worth the amount of memory they occupy on a computer, yet many traders use them because of the hype.

**Methods that seem to work under certain conditions**

(A) Very **high frequency tr**ading. This style of trading is beyond the reach of retail traders due to its complexity and high upfront cost. It is a proven high expectation generating process and this can be justified mathematically. It has nothing to do with front-running or other misconceptions of the public. The proof is beyond the scope of the post but intuitively, these traders profit from providing liquidity to the market.

(B) Other **proprietary methods** that are fairly unconventional but constitute an edge. I am working on two such methods and I cannot talk about them at this moment. One involves precognition. Do not try this at home!

(C) Parameter-less systems of Type-III curve fit. An example of a system that generates parameter-less systems based on **price action only** is Price Action Lab, the software I have developed. This program allows finding systems with a large enough sample of trades for high reward/risk. Some people are confused and think that each and every price action signal must have a large sample. This is not true in the case of such systems because price action is similar action and only differs in details. As a result, one looks at the sample size of a system that consists of many price action patterns/signals, for example. There are of course issues here, like determining the significance of out of sample tests.

(D) Trading price action based on **support & resistance**, swing high/low, etc. This is also a parameter-less method but unless some strict guidelines are used, it can result to compulsive actions and negative expectation. I am not aware of any concrete set of rules for this type of trading but I am sure some have developed then and use them to their benefit.

**References**

*Papoulis, A. Probability, Random Variables, and Stochastic Processes* by 1965. McGraw-Hill