Fundamental Equation of Trading (Part 2)

Let’s analyse the implications of the Fundamental Equation and see what it tells us about trading successfully.

The equation reads;

r x S + R x F = P

Probably, the more meaningful way to write it for someone focused on profit is:

P = r x S + R x F

Our primary goal is always to trade correctly. That is what BEING a trader means. Our intention and expectation is that this will lead to significant profits, the ultimate goal of any business.

How does this equation help us with that?

It tells us that total profit, P, is a function of 4 factors – r, S, R and F.

That’s it. There is nothing else. They are all the factors that need to be considered. The only way to change P is to change one or more of those factors.

So let’s look at each factor and study how each one might be improved to allow for the potential of more profit.

The simplest is N = S + F. This is the total number of trades. We can increase total profit by trading more trades.

How? By opening more trades which will lead to having more open trades at any given time. The problem here, which limits our opportunity to increase profits this way, is our ability to actively and correctly manage many open trades. Realistically, trading a daily time frame over short to medium horizons, limits our practical ability to about 5 or 6 open trades. An alternative way to increase the number of trades in a given period is to trade shorter time frames. Rather than daily bars, we use hourly bars, or 5 minute bars or even less. This is very common and can achieve the goal. It requires much more time involvement and a requirement for intense concentration. But it is a valid way of increasing profit over time.

Of course, a simple way, philosophically and theoretically, to increase profit, is to be “right” more often. That is the factor S. In other words, we need a system based on a set of Initial Conditions that gives a greater degree of reliability of yielding a profit. All other factors remaining the same, that will yield an increase in average profit, and therefore an increase in P. In pursuit of this approach, many, many sophisticated methods of analysis have been developed with the intention of being “right” most of the time. There are some methods that reportedly are “right” 85-90% of the time. These require a great deal of experience, education and skill, not to mention a lot of work to come up with a setup. But it apparently can be done. Whether a trader pursues this approach is dependent on their interests, capabilities and preferences. Generally speaking, there is a limit to the improvement yielded by this approach which might be judged as not commensurate with the reward. It ends up being a personal thing. An arithmetical analysis of varying this factor will lead to the conclusion that, by itself, the increased return is only significant enough to justify the additional work per trade if we use the increased reliability of the forecast to increase the percentage risk per trade. Then the returns become impressive. However, the trader must have developed a high degree of confidence in his methodology as well as a great degree of skill for this approach to be successful. If all these are true, then the probability component of R is reduced, and therefore the size of R can be commensurately increased to yield the same overall total risk over time. But increasing the size of R together with a higher success rate, leads potentially to spectacular results. There are historic examples of this being the case. W D Gann is one example. Another is Paul Tudor Jones, a modern day prodigy.

The factor F of course is simply the flip side of S, so we do not need to look at it separately.

Next are R and r. These are interlinked in that r is always measured and expressed in terms of R. 

Further, we find that, for a given set of Initial Conditions, the only way to reduce the likelihood of failure is to reduce the potential return. An initial set of conditions is based on observing sufficient evidence on our chart that there is an acceptable probability, based on our tested system, that a return may be expected. We can increase this probability by letting the price unfold and begin its journey in the direction of the trade before initiating an entry. Each bar in the direction of our anticipated trend adds confirmation that the trend is unfolding. However, each bar also brings us closer to the end of that trend. That means that, as each bar unfolds, the reliability is increased but the potential return is decreased. Also, each bar takes us further away from the stop loss thereby increasing the size of the potential loss while the likelihood of that loss decreases due to the additional confirmation. This is best observed directly on a chart to understand what these words are describing but the principle is that as the probability of success increases, the potential return of that success is decreased, and while the probability of failure decreases, the size of the risk increases. This is where careful and thorough testing of a proposed system of Initial Conditions, Filters and Trade Management is extremely important. We must test all these various possibilities to see what is the best balance, not just for profitability but also for our own psychological mind set, or our ability and desire to tolerate risk.

Next, we observe that r is always a multiple of R. So another approach to increasing total and average profit is to manipulate the correlation of these 2 factors. By that is meant that we look to increase n where r = n x R.

We can do this two ways, either together or using either of them. We can seek to reduce R ie. the SIZE of the risk, and to increase r, or the SIZE of the return. 

We reduce R by entering the trade closer to the stop loss ie. earlier in the confluence of factors that we describe as our Initial Conditions. That usually means that we require fewer Initial Conditions to make a setup. This leads to an earlier entry into a trade, thereby reducing the size of the risk by being closer to the protective exit point. This allows us to take a larger position for the same total risk, thereby increasing the potential total profit, P. We can do this reliably by either choosing to pursue some of the more sophisticated and laborious analytical methodologies that increase the reliability of our forecast, or by simply accepting a higher failure rate that is compensated for by yielding more trading opportunities with the same r potential. Then, either way, n is increased. That is, when the trade is successful, the return, r, is a greater multiple of R, risk, yielding, long term, a greater potential total profit, P. This must be tested.

We can also increase n by pursuing a greater average r over the course of our trading horizon. This means that our trade management methodology must be designed to stay in the trade longer thereby squeezing out as much of the potential profit from a trade that the market is willing to offer. One approach is to test for Initial Conditions that are usually present when a long trend develops. We then employ this as our system for entry to ensure that we are always in the market when a long trend will come into being. An example of this is the methodology taught by Profitunity as developed by Bill Williams. However, this will also mean that we will be stopped out more often in whipsaw markets because, whereas those Initial Conditions may usually be present when a long trend develops, that does not mean that those conditions exist exclusively at the beginning of a long trend. Those conditions exist at other times as well which will lead to losses. This requires us to have decided on our trading philosophy. This approach is a specific, and valid, approach to trade entry, and can be our exclusive method or part of a portfolio of systems we use.

We can also increase r by simply staying in longer. This means playing with different approaches to signalling the time for exit. There are various ways that this can be done but it usually requires studying market behaviour, “chart whispering”, to identify what signals the market is giving about its intentions. These signals will include momentum, indicator divergence, moving average crossovers, bar lengths, higher or lower pivots, multiple bar pivots versus single bar pivots, approaching resistance, time cycles, trend lines etc including many sophisticated and even esoteric methodologies. All these will depend a lot on the personal preferences of the trader, their familiarity with various tools and gut feel once the trader is experienced. Also, each trading instrument will have its own personality and familiarity with that personality will influence the choice of tools as well as the choice of time to apply those tools. This is one reason specialisation often yields better results.

PERSONALITY is a characteristic that describes the behaviour of a trading instrument such as a specific stock or a specific futures contract or even a specific currency. The behaviour of that instrument is a reflection of the behaviour of the participants in that market. As particular groups of traders and investors tend to focus on specific instruments, the behaviour of those instruments tends to develop patterns reflective of those specialist groups. As one becomes familiar with both general market behaviour and the characteristics of a particular instrument, which comes solely through time and careful observation, one develops the ability to weigh the probabilities of movements in selected instruments based purely on the behaviour indicated by the charts. This is not just the outcome intuition but primarily of educated chart whispering. It is difficult, if not impossible, to set this down as a list of factors in a trading plan but should not be ignored. Traders who achieve remarkable trading results will usually do it as a result of their ability in this area of chart reading. This cannot be taught. It is a personal ability resulting from a trader’s innate skill with patterns, interpretation and objective observation. This skill can be learned, to some degree, through experience and conscious observation. Different traders have this ability to different degrees.

The conclusion we come to, after considering the factors in the Fundamental Equation, is that the best return on effort comes from working on the R and r. Consideration of the R factor leads to the conclusion that more trades with smaller size of R is an effective way to increase overall profit without an inordinate amount of skill and effort required. Consideration of the r factor leads to the conclusion that Trade Management is the MOST POWERFUL way to improve results as measured by the bottom line.

Hence, on consideration of all factors, we conclude that we should focus on developing a system that has a trade selection method yielding a good S/F ratio, but then focusing primarily on improving our Trade Management ability to maximise the return obtained from successful trades. This will often result in some trades yielding exceptional returns which dramatically increase the average return over time. We want to be there when that happens. If we can get an S/F ratio of 2:1 and an average r/R ratio of greater than 2:1 for successful trades while keeping R at 1 for unsuccessful trades, it is not hard to demonstrate arithmetically that this is a viable trading methodology.

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