Saturday, September 16, 2017

Two Mice and a Maze

Today I came across an old analogy highlighting the dangers of curve fitting your approach too much: 

"Construct a maze that is relatively intricate and that requires a fair amount of twisting and turning to get to the centre. Train two mice to navigate the maze.

The first mouse learns that if it turns left twice, then takes five steps, then turns right three times, takes two steps, turns left once, and then turns right twice it will be at the centre of the maze.

The second mouse learns that at every junction it first turns left, and if it bumps into a partition it should turn around and go the opposite way.

The first mouse, once it has learned the pattern, negotiates the maze flawlessly every time. The second mouse is slower, although it eventually arrives at the proper destination.

Contrary to How it Appears, the First Mouse Does Not Have The Advantage

The first mouse seems to have an obvious advantage. It finds its way to the centre of the maze with ease, while the second mouse, handicapped by a much simpler navigation system, struggles and makes many wrong turns before finally reaching the goal. The second mouse clearly seems much less capable than the first mouse.

A Similar Maze but A Difference

Now let's build a new maze...make it similar to the first for a few turns, but different thereafter. The first mouse will proceed confidently for a while, but will soon be hopelessly lost and disoriented, much like some traders we have observed.

The second mouse won't notice the difference between the first maze and the second. The mouse that had previously seemed inferior plods along and treats every twist and turn in the new maze the same simple way. Slowly and inexorably the second mouse will find its way to the centre, no matter how the maze is configured.

Rewards Providing the Maze Doesn't Change

The first mouse either performs perfectly or terribly because it has been taught an overly curve-fitted system, while the second mouse has learned a crude system that enables it to get to the centre every time.

The first mouse will perform extremely well and will be rewarded as long as any maze the mouse encounters is substantially the same as the original maze that it memorized so capably. The second mouse will be slow but it will eventually be rewarded no matter what changes you make to the maze.

Trade Successfully With Crude Methods

The principles in our analogy hold true when trading systems are applied to the maze of futures prices. If we are going to navigate the markets successfully, we must create relatively crude systems that will work no matter what maze is created by tomorrow's prices."

What this analogy highlights is that the second mouse has a simple, robust method of getting to the centre, regardless of any changes to the design or complexity of the maze. 

The first mouse gets completely thrown off course when conditions outside its control (the construction of the maze) change. The second mouse just follows its 'crude' process and can continue to move forward.

For traders, the obvious comparison here would be changes  in any of the market states - trending, non-trending, stable or volatile.

To me, a good, simple, trend following method is like the second mouse - not curve fit, simple and robust that can deal with changes in market environment.

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