Markets as Wave Functions

Chart 1: SP500 1997 – 2018 Exponential Price Transform.

The above chart shows the application of and exponential price function with the directional variance between the two shown in the first indicator panel. This is then passed to the signal function in the second panel.

With the transform output in the lowest panel expressed in terms of a single contract, with an average delta of apx two over the last twenty years. So in the time a single buy and hold would have returned apx 1800 points the function returns 3725 points.

How it Works.

The function in the chart above is an exponential transform that converts from the price time domains to the price profit domain.

It is based on a combination of both the Fourier and Laplace transforms, coded to produce a long term trading signal on a weekly basis for the purposes of large scale portfolio optimizations.

I specifically coded this over the last ten years to create and early warning signal for the mathematically inevitable part two of the GFC, the Global Fraud Crisis.

Calculus and The Market.

There is an overwhelming meme in modern financial theory that you cannot curve fit markets and therefore you cannot apply calculus to discover anything useful in the data history. Nothing could be further from the truth, there is a simple conflict in what is being taught in university and how the real world actually works. 

The current thinking is that is all random walk, yet in the next breath you are taught that there is a boom bust cycle. Well it can’t be both something cannot be both random and cyclic at the same time, well not in this universe.

The single greatest misconception is that there is no relationship between past price action and future price action, this is simply wrong.  At any given instant every open position that is in the market  will be closed out in the future as a profit or a loss.

In other words the sum total of all the profit targets and mostly the stops in the market at any given instant, this is especially true in a leveraged market.

So not the past is not only inextricably connected to the future but is the causal factor of all future price moves, which is a long winded way of saying what goes up must come down. 

Another way of putting it more succinctly is that is to say that the sum total of all the market forces at any given instant in time are the same as the sum total of the profits and losses of all the open positions in the market at the point of time in question.  This can be expressed as an exponential contour as the average log returns of a market with respect to time, regardless of why people buy or sell financial instruments they are all looking for the same out come, the highest possible log returns.

To measure all this is not as difficult as it sounds all it gets down to is measuring the rate of change of the market with respect to a know rate of log return. As it turns out the SP500 has a very consistent rate of return when measured in these terms on both the long and short side.

Chart 2: SP500 1997 – 2018 Weekly Multiple Exponential Price Transforms.

To find this number is simply the sun of the log returns from the major or lows in the past to the present instant.

Which return a vector matrix  solution as the first second and third derivatives, in other words the first derivative tells you if the major trend is up and down, the second derivative tells you if it is speeding up or slowing down and the third the concavity of the change. 

The End of the Post GFC Boom.

In this next chart it is easy to see that the boom of the last ten years is well and truly over, and there is no reason to think that history won’t repeat itself over the next year or so, what goes up must come down.

The long term cyclic pattern in this chart is pretty straight forward, and most importantly Donald Trump is working from Reagan’s play book and everyone has forgotten that things went south in 1981 – 82 into the worst recession in 60 years reviving the song Moneys To Tight to Mention.

Ten years later in the early 1990’s 1991-1992 were again the worst recession since the great depression, in the last  hundred years the market has just about always peaked in the seventh to the ninth year of the decade and made lows in the first two years of the decade

1922 , 1932, 1942,  1952, 1962, 1972, 1982, 1992, 2002,

Were all recession years of of varying degrees the only reason 2012 doesn’t make the list is because the Fed printed their way out of it putting off the inevitable for ten years or so.

Chart 3: SP500 1997 – 2018 Weekly Parabolic Price Transform.


Chart 4: SP500 10 2006 – 2018  Weekly and Parabolic Price Transform.

In the next  chart you can see a more detailed breakdown  for the post GFC period using the same exponential function that generates a tracking curve using a more convex curve for greater resolution.


In the twenty years time the market has risen 1800 points, the signal has returned 3725 points, and has a average delta of apx 2 over the market. This method is best suited to weekly data as you need to look at least 20 years of data points and the run times get ugly very quickly.

In essence markets can be curve fitted you just have to have understand the curve in question, which to all intents and purpose is the average everyone else’s stops calculated as an imaginary number.

This can be found by the use of an exponential transform function such as the laplace transform, where you transform the data from the time price domains to the time profit domains in much the same way Fourier transform translates a signal from the time domain to the frequency domain.

To cut a long story short modern financial markets are nothing more than telecommunications networks, and money is nothing more than light, that’s how you know something is money because you can see it.

It will therefore have knowable differential equations and constants, you just need the correct transform to discover them.

The Simple fact is that financial markets are not a “random walk” at all they are nothing more than complex harmonic interference patterns with with respect to time and price.

This can be discovered using well understood calculus techniques and transforms that modern computers do so well.

Next In This Series The 100 Year History of The All Ordinaries.