April 30th, 2014

In my **previous note**, I presented a chart displaying the evolution of the stochastic differential equation SDE based on the length of the trading interval Δt (from Δt → 0 to Δt → T (long-term horizon). The SDE is an idealized and acceptable model to depict price action and has been widely documented in academic papers for over 60 years. It's a simple regression line over the considered data.

Nonetheless, here it is again: dP = μdt + σdw. It says that the price variation is composed of two terms: a drift term (the slope of the regression line, viewed as the rate of return μ) to which is added a scaled random term (σdw), which long-term, as (Δt → T), should tend to zero: (Ʃσdw → 0). Here is the chart again:

**SDE Trading Interval**

(click to enlarge)

You put a graphic like that on the table (in the trading strategy forum I participate in), and there was no reaction. Yet, the chart is very damaging to the short-term trader (as Δt → 0), since it would imply that as the trading interval is shortened, μΔt → 0; meaning that whatever was defined as the long-term trend has a value approaching zero as Δt → 0. This would mean that on short-term intervals, the random component of the SDE (σΔw) dominates supremely. If such is the case, and it is, then short-term trading would tend to be akin to randomly trading and the random walk view of price movements would prevail.

There is no way to outperform a game of heads or tails, whatever the method that may be used, as long as there is no memory (no bias). If, after a long series of trials, you win, it can only be attributed to luck. There is no kind of know-how that can give you an edge. Period. You most certainly can not predict that long term you will win with certainty.

Now the bad part. Because, in the short term, you are dealing with a quasi-random price series, any kind of trading decision trigger will do. It is totally unimportant, they would become coincidental at best; something like flipping a coin to play heads or tails. This would imply that whatever your short-term trading method, be it random, based on fundamentals, or technical analysis using whatever combination of indicators, as simple or complex as you want, they will work or not (50/50), but won't change the nature of the game itself. The price movement will still remain random-like as the trading interval is shortened: Δt → 0.

Therefore, your short-term trading method is absolutely worthless in the sense that it won't generate any long-term alpha except by chance alone. Now, I've said it.

The good part. Whatever short-term trading method you use, as long as it is suitable to your belief system, whatever it may be, meaning that whatever the sum of knowledge accumulated over the years to make you trade the way you do is perfectly fine.

This would have a foregone conclusion that any short-term trading strategy is as valid as the other. You could read tea leaves or like astrology as trade triggering methods and have the same expectancy as the other guy playing Fibonacci retracements, MACD, or whatever. It would still not generate long-term alpha. The beauty of it all is whatever method you use to trade short-term, the market will accommodate. It will give you what you are looking for: action. As long as you do not shoot yourself in the foot by designing flawed trading methods like super-martingales.

You can push your particular brand of short-term trading method, and I would have absolutely no complaints to make. All I could say is: it's a trading method! (note: with no qualifier like good or bad).

This is a crazy game. It can satisfy one and all. Whatever short-term trading advantage you may think you have, the market will comply time and time again. But it will also remind you time and time again that it did not work this time. What really matters is not to win a trade here and there, it is to generate long-term alpha which is the only reason one should have in playing this game, otherwise, let's just call it gambling.

Created... April 30, 2014, © Guy R. Fleury. All rights reserved.