Rate of Change & Acceleration

by Feb 22, 2017All Articles, Technical Analysis

This is a bit of a rant about some incorrect naming conventions. While writing the new thirteen week courses for CMT1 and CMT2 (CMT3 will be re-written later this year), I discovered that the way we’ve been calculating Rate of Change is incorrect. It turns out that nearly every other package in the world is also doing this wrong—we’ve all just accepted it.  Let me back up a bit and start with Momentum.

Momentum measures the difference between today’s price and the price a number of bars ago. The theory is that we want to capture earlier warning that the trend is changing. Detecting a change in the “distance” travelled is a good way to do that. The tool smooths the data for us and reacts faster than a Moving Average. See the following chart:

Momentum indicator on Gold Index

You can see that the Momentum indicator is reacting to the turning points in the market before the Moving Average. The other great thing is that Momentum drops in sideways markets, making it easier to stay out of them and look for better opportunities.

Where the problems start, for those of us fixated on physics and engineering, is that Momentum is not really measuring momentum (speed) but rather distance (price) travelled in a fixed amount of time (number of bars). That would be like saying “I don’t know how fast I was driving, but today I drove 16.7km in 10 minutes”. To be consistent, we define a time unit. For example, “I was travelling at 100 km/h”.

What is worse is that the true Physics definition of momentum is Mass x Speed.

Now that will be an interesting adaptation. Take the speed of a security and multiply it by its market cap….hmmm. I quickly added a script to see what this would show me in a Watchlist:

When you consider the percentage change in price (we have to use percentage change as all equities are valued differently) and multiple by market cap, Microsoft is the equity with the most positive momentum in my list of securities. But……I digress.

Analysts quickly saw the issue with Momentum, particularly when trying to compare the momentum from one security to another. What made a lot more sense was to calculate the percentage change. This is where history has taken another turn towards naming chaos.

Instead of calling it “Momentum Percentage” or some other appropriate name, it became knows as “Rate of Change”. Arrgghh…Rate of Change is supposed to measure how something changes in relation to units of time!

Momentum and Rate of Change are then basically the same thing, but Rate of Change is in terms of percentage change. Both have the same shape, but slightly different scales. Sigh. As an engineer and a bit of a perfectionist when it comes to naming and analysis, this really bothers me. True Rate of Change should be the average change that this security has per bar.

In Optuma, you will find that our Momentum has a “Type” property that can be changed to “Percentage”. This is the same as the traditional ROC calculation. I did look at changing ROC to be per bar, but I underestimated how many people were using it. Sorry to the Beta testers that were on the receiving end! Instead, what we are doing is adding a “True Rate of Change” indicator.

The shape is still the same, but the values reflect the average change in the price per bar (the real speed). What I think is more important is to look at the acceleration (rate of change of the rate of change).

By examining the acceleration, we are able to get early warning that the trend is slowing down and changing. Thinking of Physics again, if a vehicle is travelling down the highway, then it will still be moving forward while it is slowing down. The deceleration is the early indicator that something is about to change with the motion of the vehicle.

Here is a chart showing Acceleration on the bottom. The script I used for this is simply:

The green lines, when acceleration has turned positive, would be possible times to enter.

Of course, this would not be Optuma if we did not do some quant testing of the ideas. Here are those results:

Just looking at changes of acceleration yields way too many results (more than you could trade)—but it still has a moderate probability of gain and good one-month profit. I really like the “high and tight” profit distribution. It just needs to have some work to reduce the number of signals that we are dealing with.

What started as a rant about incorrectly named indicators (still an issue mind you!) has turned into a way to test a new idea of using Acceleration as an early warning of a change in trend.

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Mathew Verdouw, CMT, CFTe

Mathew Verdouw, CMT, CFTe

CEO / Founder Optuma

As a Computer Systems Engineer, Mathew started Market Analyst (now Optuma) within 18 months of completing his degree. From that point on, Mathew has made it his mission to build the very best software tools available.

Since 1996 Mathew has been learning about all aspects of financial analysis, and in 2014 earned the CMT designation (Chartered Market Technician). In 2015, he was also awarded the CFTe designation. In 2017, Mathew started to teach the required content for the CMT exams at learn.optuma.com. He is the only person in the world who teaches all three levels due to his broad exposure to all forms of financial analysis.

As someone who has dedicated his life to find better ways to analyse financial markets, Mathew is set to drive innovation in this sector for many years to come.


  1. teekid

    Thank you for your wonderful analyzing.

  2. Kalvert

    In our household we have had many robust discussions about this, great work.


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