A Randomly Generated Stock Market

An important aspect of the Elliott wave/socionomic theory is the Fibonacci relationships governed by the number phi (0.618034..., which satisfies the relation 1+phi = 1/phi), and the idea that fear, which governs bear markets, is more powerful but less persistent an emotion than greed, which governs bull markets.  Also important is the fractal nature of the markets, so that it doesn't matter whether we're dealing with decades, years, weeks, minutes, or milliseconds (other than for things like inflation).

So I had an idea.  Suppose we simulate a stock market by letting each time stamp (we'll call it a "day", for simplicity) have a 61.8% (phi) chance of being "up", and the rest of the time it's "down".  We start the market at zero points, and when the market is up, it goes up by 1 point.  When it is down, it goes down by 1.618 (1+phi, 1/phi) points.

Our expected return on investment is thus zero ((+1*0.618)+(-1.618*0.382)), so we should expect, on average, the "market" to be flat over a long period of time.

I generated three sets of 2000 random numbers, and ran them through this formula.  The results actually resemble stock markets rather well.

They all start at zero, and go up and down according to the individual random numbers.  For the "buy and hold" investor meeting with his or her broker on Day 0, Red Stock would have been the top choice, as it rose to 75 by Day 930 and has been within a "trading range" of 30 to 80 ever since.  BTFDers would find Day 1590 or thereabouts a great time to buy the red stock.

The green and blue stocks on the other hand, might not be the best long-term investments, though green might have seemed so at first and blue would have been a good play if you bought around day 70 and sold around day 275.

But the point is, these look quite similar to stocks.

Outsourcing Fictional History

Heck, you could use these to simulate fictional histories, taking into account the social mood variations:

"In the 1040s, this kingdom entered a golden age which lasted for about half a century, which ended in the devastating plague of the late 1090s.  The kingdom chugged along for the next couple of centuries - major war in the 1150s and again in the 1260s.  Though it tried to recover after the 1260s, it never regained its former glory, and competing countries started to invade it in the 1300s, ultimately ceasing to exist entirely in the 1400s.  But there was a glimmer of revolution around 1490, when the kingdom regained its independence..."

You get the idea.