The relativistic change in the market is derived from the classical method of measuring change in value.

The classic formula for measuring change is as follows; where A is some original earlier value and B is some current value.

 

 

We remove the percentage to get the proportional expression.

 

 

Now distribute the ‘A’ denominator between the two numerator variables and write as a difference between to fractions.

 

This can be reduced a bit by changing    to 1, making the expression as follows.

 

The  part can be set equal to a variable, , to represent a value that is the proportion of  to .

 

 

The expression then becomes the following.

 

 

The expression tells us the difference in proportion of the current value to the original value and a fixed point of the proportion of the original value to the original value. Going forward we need to examine the  value and see how this changes by itself. Since it’s a direct proportion of our current value to our original value, anything greater than 1 is a gain and anything less than 1 is a loss. We can graph  by setting it equal to  and see how this looks by plotting the equation, .

 

As we can see in figure 1 above, it’s basically a slanted straight line. Regardless what values  and  are, as long as they are non-zero values, they will follow this line. To get the classical percent change, we can just subtract 1 and multiply by 100%.

In figure 2, we can see that different points on the line tell if there is a gain, no change, or a loss in market value. Point i indicates a loss, point j shows no change and point k means a gain in value.

 

 

In the past this worked well, however, there is a problem with this measurement. As we can see, the gain is any value greater than 1; all the way out to infinity. Yet, the loss is just the tiny range from less than 1 to 0. It seems to us there is a vastly different perception between gain and loss using these dissimilar ranges. On the gain side of the equation, there really is no need to be concerned other than, hey, protect your investment. On the loss side of the equation, there’s a problem. How do you gauge the loss that becomes a sense of urgency? Looking at the current plot in figure 2, there’s very little room for making an error in judgment when it comes to losing your investment. Point i seems to be at about 0.75 or 75% of the original value; that’s a 25% loss, seems urgent. What if it’s just a 10% loss? Does the level of urgency at 10% loss seem less than a 25% loss, maybe?

Using the old method of market change doesn’t really work well in sensing that level of urgency in loss. We need to rework the method so we can clearly see the level urgency in change on the loss side of the equation. For this, we need to go back and use some mathematical sleight of hand to rework this 20^th Century static methodology into a 21^st Century relativistic methodology. There’s a point in our reforming the expression  to the expression  that we need to examine a little bit and make a change before we continue with deriving the new expression.

Below is the point where we separated the expression into the difference of two fractions.

 

 

In the expression, the right side fraction is a static point that relates only to itself,  . It’s the moment of initial investment and is a past point relative to itself. This is where the problem of measurement can give a false sense of change. To overcome this, we need to change the static faction to a dynamic one. If we have the forward looking fraction,  , then we need to alter the static fraction,  , to be a backward looking fraction. We do this by changing  to  ; this now gives a proper relationship in both directions of time. The new equation then becomes the following.

 

 

If we apply the  proportion to the expression, we find that,

 

 

and taking the reciprocal of both sides it becomes,

 

 

plugging in to the new expression it becomes:

 

 

We can reform this into a fraction as follows.

 

 

We can plot this new expression by setting it equal to y and compare to the classic p value.

 

 

In figure 3 we can see how values for p less than 1 show a dramatic change in y the closer to 0 the p value gets. In the plot we can also see p values greater than 1 are positive, indicating a gain, and p values less than 1 are negative, indicating a loss. However, in this plot, it becomes much more apparent of the urgency in loss by the large drop in the curve. It also shows the classic p line and the y-axis are actually asymptotes of the  curve. Looking at the plot and using the new expression we can see a 0.90 value in p is just a -0.10 loss in the classical method, but in the relativistic method it becomes -0.21; a much more urgent value.

 

 

We can setup a table showing side by side the differences between the two methods. In table 1, we can see the classic method shows no level of urgency as it moves into negative values, however, the relativistic values show urgency almost immediately.

 

 

The reason this new relativistic market change works so well is because of the two difference fractions in the new equation,  and  . The two different fractions have difference meanings, but are dynamically tided to each other. The  fraction means in terms of a loss, “What have we lost?”, and the  fraction means, “What will we lose?” These are balanced magnitudes of change that become dynamically tided to each other through a subtractive comparison.

This leads into another subject of market change we like to call the Relativistic Market Speed. It’s a means of measuring market climb and market fall that strips out the economy of scale in an exponential growth system. We apply the relativistic market change to any market value by using the previous close, A, and the current close, B. We’ll post this a little later so you can have time to absorb this a bit.