November 25th, 2016

My last series of articles started with setting up the mathematical backdrop to a stock trading methodology made to last. Putting a stock portfolio payoff matrix at the center of it all as the bean counter for any trading strategy: A(t) = A(0) + Σ(**H**.*Δ**P**). This time function was then reduced to: A(t) = A(0) + n * u * PT.

Three numbers of interest: the number of trades done, the trading unit used, and average profit percent for trade. Three portfolio metrics that are given by any simulated or live stock trading strategy whatever its portfolio composition. One could view n * u * PT as a trading strategy's signature.

Arguments were put forward that a trading strategy designer's job was to find ways to increase the output: n * u * PT since that is where trading profits came from. They were the only metrics that affected the total outcome of a trading strategy. There was time involved in the process, but at bean counting time, what mattered was: A(t) = A(0) + n * u * PT. On the right-hand side of the equal sign you only had numbers, and for unit, a dollar sign.

Were brought forward enhancer functions which were resumed in: A(t) = A(0) + (1+g(t)) * n * u * PT. Evidently, with g(t) > 0, portfolio profits will get larger. But, if we went a little further, and put on the table: A(t) = A(0) + (1+g(t))^{t} * n * u * PT, you would go much faster by introducing a time compounding function. It is a major distinction, in fact, a game-changer. It is like putting your existing trading strategy on steroids.

Since n, the number of trades could make such a difference in a portfolio's performance, it was suggested to find ways to increase it as much as one could, this on the premise that a trading strategy already had PT > 0, meaning it had a profitable edge.

In the **Prediction Dilemma** article, it was said that prediction is not that easy to achieve over the short term where a trader intends to play. Short term, randomness in stock price variations is rather high, so high in fact that most have a hard time escaping the randomness of the draw.

There was also this dilemma: whatever predictive tool you might have developed over past data might not be that predictive going forward. As if whatever you did as predictive simulation would be almost irrelevant since the future might not adhere to, or acknowledge, your view of the statistical world you built in your trading model. Or, if you could predict some price variations, the average spread might be insufficient to cover frictional costs.

It is not because you have some statistics on past data that they necessarily become probabilities on the future. And, if your statistics show close to randomness, then you might be just making quasi-random bets, gambling your way out, thinking you have a predictive system.

The stock market is complex, not simple. Sure, prices have only two ways to go: up or down. So, you can say: the probability of going up is close to 50%, but is it really? The closer you get to the 50/50 state, the more winning a bet will be due entirely to chance, and your game will just have been converted to a gambling proposition. Not investing, not trading, but simply gambling with all that it implies. And in such circumstances, maybe a fancy theory on how the market works and your declared ability to predict short-term price movements might be, may we say in need of a reality check.

The first consequence of putting the market in a 50/50 proposition is not knowing if you will end up winning the game at all, and that one is a bummer. You will have reduced your future to the equivalent of a single flip of a coin. Has anyone noticed that there are no individual short-term traders that have lasted for decades?

It was then proposed to extract tradable information from all the available data with an eye on n since it counted so much in the final output of a trading strategy.

All this was pretty basic, and with this foundation, it was time to start building a trading plan where n, u and PT would be the center of attraction. Everything you could program your trading strategy to do would be reflected in those 3 numbers. It didn't say which method to use, as if saying anything you want, it only said that the only 3 portfolio metrics of importance were: n, u and PT.

In **Controlling a Stock Trading Strategy**, it was shown how these principles could be applied to a trading strategy. I used DEVX8 for illustrative purposes, but it could have been done with other trading strategies as well. For instance, another example is **A Simple Stock Trading Strategy**. You will find a dozen more on my website showing different ways to slice and dice n, u and PT.

In the presented scenarios, an emphasis was put on controllability. As if saying you want more, then go out there and get more. Turn on the volume.

It was shown that small additions to enhancer functions would generate higher portfolio returns from the same trading strategy. Not a line of code changed, and yet, performance would increase due to these portfolio metrics being asked to do more. It was more like ordered to do more.

This is a major departure from a trading philosophy adopting a kind of Markowitz view of the market always rebalancing portfolio weights from period to period.

Here is proposed that one should look at his/her trading strategy not just from period to period, but as a whole over the entire duration, or the life of a portfolio. Not counting on tomorrow I rebalance, but, on a long-term vision of where you want to go, as if a trade was just part of a much larger long-term plan.

This point of view would be of interest only if it could provide a higher performance level than under a Markowitz trading environment.

In my last post: **A Buy & Weak Hold**, was shown that you can push on your machine with no real or significant detrimental side effects. In a way showing you could easily exceed traditional trading methods.

Enhancer functions were applied to a trading strategy. Changing the value of 4 numbers that had everything to do with the demands you made on a trading system. They were not wishes or better predictive methods, or better trading setups, or a better use of indicators, or changes in lookback periods. They were explicit demands to do more, to increase trading activity and accumulate more shares over the long run.

Simple bean-counting measures, administrative procedures directing and funneling the outcome of a trading strategy to its goal of building a long-term portfolio.

And yet, apparently, almost no one shows any interest in what could be quite a different approach from traditional trading methods. This is not a crackpot's perspective, but trading rules that can be implemented by anyone, even without the help of a machine.

These simulations only serving to say that there is something there worth more than just a glance. Especially, if it is based on such an elaborate mathematical backdrop. As said elsewhere: an equal sign is a powerful statement. Also, a simple observation, if there was nothing there, then the simulations would have shown it. They usually are without mercy on such things.

To make the point even more compelling, the program used was a year old, operated as if randomly trading with random-like entries and random-like exits using market order for the next day at the open. Those are really adverse conditions to make a buck.

No matter how we look at the market game, it remains a CAGR game and it is our job to design the best trading strategies we can. But that does not mean that we will be able to escape the math of the game.

In the article: **A Buy & Weak Hold**, you can see how just by changing 4 numbers, (4 constants by the way), starting with a $ 5 million stock portfolio, the strategy ended with $ 1.6 billion, managing a 32.33% average CAGR over its 20.7 year testing interval, doing 99,058 trades, and still managing to end with 60% of its equity in cash.

The same trading strategy was used for all 3 tests. No code logic changed, not a single line, no optimized or fitted data in any way. Each of the 3 tests was executed once with their respective settings to show the progression it could make. Using intermediate values would have generated intermediate results. Pushing for more would have resulted in still more.

This was taking what I view as a generic trading strategy and making it do more, trading the same way as it did before, but requesting an increase in trading activity. This was not done by increasing the bet size since it remained the same in all 3 tests. It was done by requesting an increase in the number of trades and an increase in the profit margin.

The outcome was to change the portfolio equation from: A(t) = A(0) + n * u * PT into a more elaborate self-engineered alpha generator: A(t) = A(0) + (1+g(t))^{t} * n * u * PT.

If your trading strategy already does better than what was presented in **A Buy & Weak Hold**, then, congratulation. Nonetheless, you might find that you could do even more using some of the proposed techniques. If your trading strategy does not do better, well, maybe looking at the presented principles might help you boost your performance level too.

Good trading/investing.

Created... November 25th, 2016, © Guy R. Fleury. All rights reserved