Jan. 15, 2019

What does it take to win the stock trading game? It is not just a rhetorical question, but nonetheless, it does encapsulate a whole gambit of related questions from what is the game about to how to assure yourself you will, in fact, win the game.

First, the trading game is very very simple. You repeat the same one thing over and over again under uncertainty.

The game itself is too simple not to understand it within a few minutes. You buy some shares (q) of a selected stock: q ∙ p(in) and resell them later at q ∙ p(out). Your profit or loss on the trade will be: q ∙ Δp = +/- x. Trading implies repeatedly getting in and out of positions. And that is where the problem starts.

In a way, it is like any other business where you buy something to resell it later at a profit, that it be some merchandise, financial instrument, real estate or whatever. On any one transaction, you want it to terminate with a profit: Δp > 0 or x > 0. If you opt to hold the shares, you want them to appreciate over time and again show: Δp > 0.

The end result of trading is simple too: you just add up the outcome of all the trades taken (profits and losses) over the investment period: Ʃ x_{i} where i = 1, …, n identifies the trades by a numbered sequence as they occur.

A simple running total (your trading account liquidating balance) can keep track of where you are. It might not matter that much how you trade since in the end it will that sum: Ʃ x_{i} that will prevail, whatever that ending number may be. Therefore, why not plan for that outcome? Not by designing a trading strategy in the hope you will reach your goal **E**[Ʃ x_{i}], but by designing one that will.

You can keep the shares you buy for as long as you want or more appropriately for as long as you can. For whatever reason, you can dispose of them at any time of your choosing, either at a profit or a loss. You can even hold until a stock goes bankrupt should you want to.

It is all your choice: which stocks you buy or sell, when you do, and in what quantity. Evidently, within the limits of your trading account. You can do all the trade decision-making yourself or let it be done by someone else: another trader, some firm, a computer program, even your own software program residing on some machine somewhere.

The trader has a few problems to solve, and they come with the job to be done. Meaning that it is because he trades that these problems will surface. In essence, the trader by his very actions is generating the problems that need to be solved.

One that is of importance is in the nature of the game played. The trader cannot just do one trade, which could last a few days, then go away and retire on his winnings. He will have to do many many trades especially if his bets are a small fraction of his ongoing equity and are of relatively short durations. Because they will be of short duration, they will bring with them other problems to be solved. If the trader wants to finish ahead, meaning win the game, then it will be required and essential that: Ʃ x_{i} > 0. A win here and there is not enough.

The tactical problem is that the game is played with real money. It is not a simple Monopoly game. It really involves our future and can have quite an impact that we do the job ourselves or delegate it to whatever other decision processes. What we will find out is that no matter what we choose as trading decision surrogate, it will always be our money that will be on the line. And we do not want to hear: do not pass GO, do not collect.

That you like it or not, there is some math in the game. All the trades you might do might not be the same, nonetheless, adding their respective outcomes is just an addition: Ʃ x_{i}, no matter how many trades there are or whatever their outcomes. And this is where you get into trouble. It is with the word: many.

The problem is that traders do not win all their trades. The words: certainty, assuredly, and for sure, are not part of the vocabulary. However, the words: might, could, hopefully, are sprinkled all over the place as in a probabilistic way, even when traders cannot give the odds on winning the next trade or in fact any of their trades.

The math is: Ʃ x_{i} = (n - λ)x_{+} + λx_{-} where λ is the number of losing trades, and x_{+} the average profit per winning trade, while x_{-} is the average loss per losing trade. As (n - λ) approaches λ we can observe that the win rate is approaching 50% which in a way is not that good for a trading system especially if x_{+} is also approaching |x_{-}|. Since in such a case the total profit might tend to zero: Ʃ x_{i} → 0. And that is not a good way to build a long-term portfolio.

If you design your trading strategy to have an average profit on winning trades to be about equal to the average loss on your losing trades: x_{+} → |x_{-}|, then you will only have your win rate to provide you with an edge: (n - λ) > λ, as in: (n - λ) / λ > 1.

The average profit x_{+} is acting like the average profit target while x_{-}, the average loss per trade, is behaving like the average stop loss for the trading strategy.

Whenever you run a software simulation of your trading strategy you will get these numbers as a consequence of all the trades taken as part of the aftergame statistical compilation, a snapshot of what your trading strategy did. Whereas, you should have programmed your strategy to work on those essential numbers to generate what you wanted. Since in the end, all those strategies will show that those are the numbers that will matter, shouldn't we, therefore, concentrate on them, first and foremost. You want to win, then design your automated trading strategy to do just that.

Created... January 15, 2019, © Guy R. Fleury. All rights reserved