Even if both are played using the same stocks. It is as if anyone could design their own game within the game to suit their own perceptions and objectives, that they be short-term or long-term. All could call it their investment strategies, and technically they are right. Furthermore, they could all win.

However, most often than not, the majority does not even outperform market averages over the long-term, no matter the game they played, almost.

Here is a very basic question:

If you cannot predict tomorrow's price or next week's for that matter, why play as if you could?

And, it raises another question for the trader: what is the nature of what you intend to play with?

**Profit or Loss**

The profit or loss from a single stock trade is simple math: \( q \cdot (p_{out} – p_{in}) = \pm x \). It could also be expressed in many ways, for example, integrals: \( \int_0^t q \cdot dp = q \cdot p_t |*0^t = q \cdot (p*{t} – p_{0}) = \pm x. \, \) If you wanted only the \( + x \) side of the outcome, you would need to make a prediction and be right about it. You would need: \( p_t – p_0 > 0 \), or more succinctly: \( \Delta p > 0 \). Evidently, if \( \Delta p < 0 \), you have a loss.

We could also describe a price series as a stochastic price function having the form: \( p(t) = \mu dt + \sigma dW \) having the trend or regression line \( \mu dt \), and a Wiener process \(\sigma dW \).

Subtracting the trend would leave only the random-like part of the price movement often referred to as the residual or error term gives: \( p(t) = \mu dt + \sigma dW - \mu dt = \sigma dW \). The residual is the error term in a linear regression: \( f(t) = a \cdot x + \Sigma \epsilon \). The sum of the error terms tend to zero: \( \Sigma \epsilon \to 0 \).

The following chart shows the first 40 bars of a 30,000-bar of a randomly generated price function: \(p(t) = \sigma dW \).

Fig. 1 \( \; \) **Price Series, First 40 Bars**

The particularities of the above chart are: it was all randomly generated (open, high, low and close), making the chart's price movement totally unpredictable from one bar to the next. But where, nonetheless, you could make guesses or bets as to what the price might be for the next bar. And as such, we would all understand such plays as simply gambling.

**Random Price Series**

The following two charts use the same base price open to which was added randomly changing price variations to the high, low, and close. As if making each chart a what might also have been series. We could make millions of these charts. They would all look somewhat alike, but in neither of them could you successfully find a reliable method of predicting what would be the next bar.

Having done these charts in Excel, pressing F9 repeatedly would generate totally new price series which again would be totally unpredictable. That I make thousands and thousands of these charts, it would not make them more predictable. Even if I add all the statistical data that could be obtained from such an experiment. You know the answer even before doing any tests. There is nothing there to be had as predictive data.

Fig. 2 \( \; \) **Price Series, First 40 Bars**

Fig. 3 \( \; \) **Price Series, First 40 Bars**

**The What Was**

Looking back at stock prices is like looking at chart 1. There was one occurrence that came out. It would have been 1 in the gazillions of other possibilities. It is only that that was the one that happened first. And therefore, we never saw what could have been any other chart, no matter how many there could have been.

All 3 charts above might be based on the same opening price, but trading decisions would be made based on the previous closing prices which were also unpredictable. Any trading software would not be able to make real sense out of such a chart. To be politically correct, using past data, they could make a lot of assumptions and put all sorts of lines on these charts, but on future data, they could never outguess randomly generated price series such as these except by luck, almost by definition.

**Not Enough Data**

You could try to predict in other ways. From a 40-bar chart, there is not much you can do. One could say: with so little data, making predictions is not revealing in such cases. We could easily understand why. Not enough data to make anything statistically significant. Especially in a game which is intended to be played for years on end.

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