Sept. 24, 2018

My previous article concluded that it would be possible to design trading strategies that could “almost surely” win, in the aggregate, almost all the time, given time. It was also said that simply adding back the removed trend line to the presented stochastic equation would be sufficient. I would like to substantiate it so that it is not just a claim or an opinion but something that can be translated into facts.

We all know that randomly trading stocks is not destined to be that productive over the long term. It has been demonstrated again and again. However, by changing one's trading procedures, even in the face of uncertainty, one can have such trading strategies perform with a positive edge, provided that these series, on average, show some upside biases. All that is needed is to show that it can be done.

I have done such tests some years back. My intention here is to elaborate more and give a better understanding of the methodology. In my 2012 article: Changing the Game II, the case was made that a portfolio of randomly generated prices having an aggregate average upward drift was sufficient to generate profits even if using a randomly generated trading strategy to do so. This might have been written some 6 years ago, but nothing has changed. All of it still holds today.

You had this portfolio of random-like price series with fat tails and random drifts to which a randomly generated trading strategy was applied, and you won almost all the time. Each time you pressed F9 in this Excel spreadsheet, it would generate a totally new set of price series with jumps, and totally new trading strategies. The new price series and strategies had no memory of whatever prior occurrences. Yet, again and again, you would win. It would show a positive payoff matrix almost every time (>98%). The price generation formula used was: pi(t) = µidt +σidWi + Ʃiji. The mean returns were randomly set, and outliers were also random with random amplitudes.

You could not know how the price series would behave, what would be the next price variation added or subtracted, nor could you know when or if a trade would be taken or exited. You could not predict any of the outliers either.

The strategy would, at times, buy tops and sell bottoms, just as it could do the opposite. In fact, it would buy and sell anywhere on those curves due to the almost random properties of the trading strategies. And yet, the sum of all profits and losses from all the executed trades for each of these strategies would result in profits.

These tests were summarized in the following paper: A Changing Game.

One might not be able to predict where prices are going, but can still play the game and win. Overall, I say the same thing as Mr. Buffett has said numerous times and for a long time about the US stock markets: investing in stocks “is a bet on America”. And over the past 50+ years, he has been right.

There is much to learn from A Changing Game. It said that trading procedures could dominate the outcome of a trading strategy. For me, it demonstrated the trading mechanics by which alpha could be powered up. It led to the design of better trading strategies. So, I hope it can help you by presenting this “different” point of view.

The reason this randomly generated stock trading strategy wins is very simple. You could use the same principles and apply your skills to trade better than randomly.