Traders often look for ways to measure the price momentum. The rate of change (ROC) is one of the most commonly used indicators for that. Let’s take a look at the indicator.

**Often referred to as the momentum indicator, the rate of change (ROC) is a momentum-based technical indicator that compares the current price of a security to the price “n” period ago. It is plotted as an oscillator that moves above or below a zero-line as the momentum changes from positive to negative. Like other oscillators, the Rate of Change also has oversold/overbought levels that are adjusted according to the current market situation. At the end of the article we look at several ROC trading strategies.**

## What is the rate of change (ROC)?

The Rate of Change, which is also known as *momentum*, is a technical technical trading indicator that measures the momentum of price movements. It compares the current price of a security to the price “n” period ago. The indicator is plotted as an oscillator that moves above or below a zero-line as the momentum changes from positive to negative.

Like other oscillators, the Rate of Change also has oversold/overbought levels that are adjusted according to the current market situation. However, note that the market can remain at the oversold/overbought level for a prolonged period.

Here’s an example of how ROC looks on a chart:

The chart above shows the 15-day ROC, and as you can see, it oscillates pretty heavily, perhaps expected in volatile financial markets.

Nonetheless, the rate of change is an important concept in finance as it allows the market to be seen through the lens of momentum and other forms of trend.

For instance, a security with a positive rate of change or high momentum is likely to outperform the broader market in the short term (1-6 months), while one with lower momentum is likely to underperform the broader market in the short term and is seen as a bearish signal to investors. By comparing the momentum of various stocks with one another or with the broad market index, such as the S&P 500, we get the idea of relative momentum, which has been used to create profitable trading strategies over the years.

The rate of change is widely used to measure the average change in the price of a security over time. This is called the price rate of change which is derived by subtracting the price of a security at time A time from the price of a security at time B and then dividing that by the price at time A.

The rate of change can be particularly useful for options traders since they observe the relationship between the price rate of change of an option to a fractional change in the price of the underlying security (known as the options delta).

## What is the formula? ROC indicator formula

Before calculating the rate of change, you have to pick the “**n**” value. Long-term traders would normally pick a longer period like 100 or 200 days, while short-term traders may opt for a closer period like 5, 10 or 20. The “**n**” value is the number of periods in the past you are comparing with the current price. As usual, smaller “**n**” values will result in a more volatile reading of the indicator which may also lead to too many signals, while larger values are less volatile and produced fewer signals to trade with.

The ROC formula is as follows:

**Where:**

= closing price

= closing price n periods ago

**ROC **= Rate of change

## Who invented the rate of change?

The rate of change was developed by Tom Demark to measure the momentum of a security.

## What does the rate of change tell you?

The rate of change is plotted in a separate window below the price chart. It has a centerline (zero line) which is used to differentiate between positive and negative momentum. The indicator usually oscillates about the zero line, moving between the positive and negative territory.

A positive momentum usually indicates an increased buying pressure or rate of change, which tells you that the strength of the trend is accelerating. But a decreasing rate of change with an increase in price tells you that the uptrend will not be sustained. On the other hand, negative momentum below the zero line indicates downward momentum or selling pressure in a bearish market.

Most technical analysts consider centerline crossovers as an indication of a trend change. However, the centerline crossovers are prone to whipsaw, especially short-term. The “**n**” value has a great impact on how often the indicator crosses the centerline. Smaller values often result in more frequent crossovers or signal an early trend change. Larger values delay the crossover and give late signals.

The rate of change can also show extreme conditions in the market. Some analysts consider the market overbought when the ROC is far above the zero line (say +10) and oversold when the ROC is far below the zero line (say -10). However, these extremes are not bound to any value in particular as each security behaves differently from one another. To use this method, you have to study the indicator for each security to know the levels where the market had reversed in the past. This will give an idea of the overbought/oversold levels for that security. so

Furthermore, the rate of change can show divergence from the price action, which could signal a potential trend change. Divergence occurs when the price is moving in one direction while the indicator is moving opposite. A bearish divergence is when the price of a security is increasing while the rate of change is decelerating, which could indicate a trend reversal.

The same principle applies if the price of a security is declining with an increasing rate of change. This could indicate a trend reversal to the upside. However, divergence is not a reliable trading strategy as it could last for a prolonged time without any reversal taking place.

To wrap it up, if you want to use this indicator to create a trading system, make sure you combine it with other tools. Always backtest your system and optimize for robustness before putting your money on the line.

## Using ROC in Trading

There are many ways to trade ROC in trading. We can mention:

- Breakouts
- Overbought and oversold situations
- Zero line crosses
- Divergences

This is the theory, at least. Below we’ll make some ROC backtests to see if these ROC methods work.

## ROC indicator trading strategy (Rate of Change strategy)

Below you find a few ROC trading strategies (all backtested on S&P 500 (SPY)):

### ROC trading strategy no 1: oversold – oscillating

Let’s start with the easiest backtest: oversold – a mean reversion strategy.

We like to start with a strategy optimization to see if there are any “sweet spots” and how robust the trading indicator is. The table below shows the following:

- We calculate the RSI of the ROC indicator.
- We use ROC intervals of 2 to 14 days with 2-day intervals.
- When the the RSI of the ROC crosses below 35, we enter at the close.
- We sell at the close when the close is higher than yesterday’s high.

The strategy performance metrics are pretty good. The best ROC indicator settings are 4 and 6 days (column 1 shows the number of days).

The equity curve of the best strategy (4 days) looks like this:

The strategy looks decent, but it suffers from some pretty sharp setbacks along the way.

### ROC trading strategy no 2: breakouts

Let’s backtest a ROC indicator breakout strategy. We backtest the following rules and settings:

- We use a 4-day ROC based on the previous backtest done above (4-day ROC).
- When the ROC breaks above the N-day high of ROC (from 10 to 30 days), we go long at the close.
- We sell 20 days later at the close.

The strategy optimization looks like this:

The first column shows the lookback period for the breakout. The column called profit factor indicates that this is a poor trading strategy.

### ROC trading strategy no 3: zero line crosses

Let’s go on to backtest a ROC strategy based on “zero line crossings”. We backtest the following rules and settings:

- We go long when the N-day ROC crosses BELOW zero.
- We sell at the close when the N-day ROC crosses ABOVE zero.

Our strategy optimization gave us the following backtesting results:

The first column shows the different days in the lookback period (2-14 days), but the column called profit factor shows that the results are far from good.

When we backtested the opposite rules we got a lousy result (perhaps as expected).

### ROC trading strategy no 4: divergences

We decided not to backtest any ROC divergence strategies because it’s difficult to quantify and to set the proper rules and settings.

## Rate of Change Indicator trading strategies – Amibroker code

We have compiled Amibroker code for all the three strategies in this article. This code, plus code for at least 125 other different ideas and strategies, can be purchased here:

## ROC vs RSI

ROC might seem similar to the RSI indicator both in the name and how they look on the charts, but the calculations are completely different. To start with, RSI has both upward and downward price change (ROC only one direction). However, both indicators measure the velocity of the moves.

## ROC indicator trading strategy – ending remarks

Among the plenty trading indicators that exist, the Rate of Change indicator (ROC) is not among the best. Our backtested ROC trading strategies show that all of them fall short compared to the RSI, stochastic indicator, and Williams %R, to name the most obvious better trading indicators (please read our article called which is the best oscillating indicator). Thus, any **ROC indicator trading strategy** is most likely inferior to many others.