Notebook

# No Alpha. No Game.Â¶

Recently, I have mostly talked about the above automated stock trading strategy that was described as gambling its way to the finish line over its 14.42-year journey.

Playing the stock market game has no rerun buttons. It also has no refunds. As a trader, you win, good, it is yours. You lose, well, you lost, next, please.

So, it would sound more than reasonable to make as sure as possible that over the long run you end up a winner. And, you can do this only with some alpha generation.

Otherwise, you will have played, traded a lot, and produced no added value. You would have been better off playing the averages by buying index funds. Without this assurance, you are simply gambling even if it all turns out to be to your advantage to have done so.

There is nothing wrong with gambling. We do it all the time, in every aspect of life. But here, you have a game where you can technically decide beforehand how it will end for you. Will you get positive or negative alpha?

You can gamble any which way you can, or you can opt to trade with a purpose knowing you will win. That is a matter of choice. It is in your hands.

When looking at the output of my simulations, we could see, from chart to chart, increasing alpha generation. Here, alpha represents the excess return above market average ($r_m$), as in: $A(t) = A_0∙(1 + r_m + α )^t$. It can be viewed as an expression for the portfolio manager's trading skills (discretionary style), or for the premium attached to a software program generating the said alpha (automated mode).

Alpha could also be expressed as $r_p - r_m = α$, where $r_p$ is the portfolio's return $r_p = r_m + α$. One should consider $r_m$ as what the market is giving away just for passively participating for a long time. For example, by buying low-cost index funds. If $r_p \rightarrow r_m$ then $α \rightarrow 0$, as should be expected.

If you do not outperform the market average $r_m$, then, what you get is: $r_p \leq r_m + \alpha$, it requires the alpha to be negative or zero: $\alpha \leq 0$. The alpha generation is what we can bring, as traders, to the mix. Therefore, our efforts should not only aim for long term positive alpha: $α > 0$, they should also strive to make sure we do get it.

Evidently, the higher the alpha, the higher the outperformance level. Since the above equation is compounding, both time and alpha can take major roles in the outcome.

Which should come first, discretionary or automated? Either. It is a matter of choice. The above equation: $A(t) = A_0∙(1 + r_m + \alpha )^t$, does not care. It only deals with starting and ending equity.

We come to the point: do you design an expert trading system that will mimic the individual's vision of the whole trading process, or will you let a machine find its own way out of the conundrum using machine learning, deep learning, and artificial intelligence? A portfolio manager can always elect to be assisted by a machine that will execute what it is programmed to do.

Personally, I go for using person learning and simply intelligence. I do not, as yet, see a need for it to be artificial, just plain intelligence still suffice.

This, de facto, makes me lean to an expert trading system model. It goes on the premise that before making it artificial intelligence, it should start with a better understanding of the game at hand, a better vision of the problem itself.

##### Even artificial intelligence would be hard press to decipher near randomness and predict the outcome of the next flip of a randomly biased coin with random jumps.Â¶

Opting for an expert system model does not mean you forego machine assistance. It is only that the machine will do what you want it to do; follow specific trading procedures designed to execute trading routines based on your vision of things. With artificial intelligence, I would be transferring to a machine the decision process when I want a trading program just to be a surrogate to my thinking. I do not want it to think on its own. I want to know why a trade was taken.

Even if I design an expert system, it will be constrained by the above equation as anything else, meaning that the alpha will have to be positive to generate any excess return ($\alpha > 0$).

It is the same problem whatever trading method we might want to use.

Alpha generation is not that easy to come by. Half of the market is in index (passive) funds of some kind where the alpha generation, almost by definition, tends to zero ($\alpha \rightarrow 0$), meaning that all they can do, on average, is the market average: $A(t) = A_0∙(1 + r_m )^t$.

This is pretty straightforward. The longer they last (t), the more they will asymptotically approach the long term average market return ($r_m$).

### It is not that they could not do better, it is only that they elected to do no more.Â¶

They have seen the past and realized that achieving market averages is a lot better than doing less than the averages.

They have accepted to be satisfied with that. In some ways it is understandable.

Is it that hard to generate excess return ($\alpha > 0$)? Yes. Look at academic portfolio management literature. That it be modern portfolio theory, prospect theory, no free lunch, efficient market hypothesis, or a portfolio's efficient frontier, they all converge to ($r_m$) as your most expected outcome over the long run. As if accepting: it is all that the market has to offer.

There are reasons for this. Most are related to the uncertainty in the whole portfolio management process. What will be the future five or ten years from now? What will it be tomorrow or next week...?

If they knew with any certainty, they would know immediately what to do, and determine what should be their best course of action. They would easily generate positive alpha ($\alpha > 0$). It would be almost given away for their ability to predict what is coming next.

Half of the stock market investment industry is saying: we can not do it. Since their alpha does tend to zero: $\alpha \rightarrow 0$.

It is the whole premise of index funds. They know that over the long term they will do about average with a higher degree of certainty. Just playing averages will give them these long term averages. And, if they are on the lucky side of things, they might even exceed the averages a little. Nonetheless, small fees will still have an impact on a long term portfolio: $A(t) = A_0∙(1 + r_m + \alpha \;– fc\%)^t$, where $fc\%$ represent frictional costs incurred due to trading expenses and fees.

Why put index funds on the table?

Simple: a trader has to find trading methods that will do better than market average with some certainty too. Why deliberately opt to do less than average? Index funds are the no effort scenario, you buy and you wait. If you want to trade which will require your continuous attention then you better do better than average, since if not, why do the added work?

It is not by throwing darts at the financial pages of a newspaper that you will beat the averages. The expectancy on that kind of procedures is to average out to the most expected outcome which is achieving the long term average market return $A(t) = A_0∙(1 + r_m – fc\%)^t$ and still pay frictional costs.

As a trader, we need to push for more: $A(t) = A_0∙(1 + r_m + \alpha \; – fc\%)^t$. It can only be given if we can generate some positive alpha $\alpha > 0$, and also have $\alpha > fc\%$ to cover the cost of trading. We also want this alpha generation to have some certainty too.

We should be ready to accept alpha generation, even if it is the result of some luck. After all, we are in it for the money. As long as someone can demonstrate where it is, we should consider the matter. Look at the data, make our own assessments, and determine for ourselves if this thing is suitable for us over the long term. This can have major consequences. As said before: it is a matter of choice. It is in our hands.