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# Rate of Change

Updated on July 23, 2024
Article byKhalid Ahmed
Edited byAaron Crowe
Reviewed byDheeraj Vaidya, CFA, FRM

## Rate of Change Definition

Rate of change (ROC) defines the percentage change of a variable like securities over a certain time with respect to its original value. It determines the velocity or momentum of a particle through a defined period. In investing, it is a technical analysis tool that helps investors ascertain a security’s price or volume change.

For eg:
Source: Rate of Change (wallstreetmojo.com)

Typically, the rate of change indicates the momentum of a certain security or mutual fund traded in the stock market. Momentum reveals the ability of security prices to continue their trend. Thus, traders use ROC to determine price trends to time the market correctly. Therefore, it is an established strategy of trading. The value of ROC can be positive, negative, or zero.

### Key Takeaways

• Rate of change measures the variation in the value of a variable like a security over a specific period of time.
• It is calculated by subtracting the old value from the current value of the variable and dividing it by the old value. It is expressed as a percentage.
• It is used to assess the momentum of a security’s price or volume in finance.
• Momentum means the tendency for rising prices to sustain the uptrend and declining prices to continue the downtrend.
• Rate of change helps in identifying bull and bear market trends and price bubbles.

### Understanding Rate of Change

Rate of change oscillator measures the pace at which prices of a security rise or fall. An upward ROC movement indicates a sharp price rise, while a downward ROC movement shows a steep price fall. The ROC value of a security hovers around 0 and means the following:

• ROC = 0 shows no change in the security price over a definite time.
• A positive ROC signals that the prices are rising.
• A negative ROC denotes that the prices are falling.

Thus, an investor must buy a security when the ROC is positive and sell when it turns negative. Hence, the purpose of the ROC oscillator is to recognize the overbought and oversold securities.

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### How does Rate of Change work?

Let’s see how the rate of change works. Suppose the stock prices are declining. In that case, the ROC is negative. The faster the pace of decline is, the greater the fall in ROC. However, when the rate of decline reduces, the ROC goes up. But it continues to be negative as the prices are still falling. When the security price touches the lowest price, ROC becomes 0. This is because the fall in prices has stopped.

For eg:
Source: Rate of Change (wallstreetmojo.com)

Now, if the stock price starts rising, ROC becomes positive. With a faster rise in price, the ROC rises sharply. However, the ROC declines when the pace of increase doesn’t keep its momentum. But it remains positive as the stock price is still going up. As the stock price reaches the highest price, ROC touches 0 again and becomes negative again when the stock price begins to decline.

Precisely put:

• If the ROC of a security is positive, it indicates a positive momentum or bullish trend in the market.
• If the ROC of a security is negative, it denotes a negative momentum or bullish trend in the market.

Thus, ROC is the best indicator of the extreme ends of a security’s overbought and oversold situations. It helps investors decide when to enter or exit a position in the Stock market.

### Rate of Change Formula

The ROC formula is simply the change in the value of a variable divided by the old value. It is usually expressed in percentages. Hence the formula is as follows:

For finding the ROC of a security’s price, use the following formula:

### Calculations

Let’s understand the rate of change calculation through the following example. Here is a list of prices of a stock over a period of 20 days. Generally, ROC is calculated for 12 days. Thus, the formula can be written as:

As evident, after a few days of rising, the stock prices fell and continued the downward trend. Hence, the ROC is negative on calculation. Moreover, as the decline in prices accelerates, the value of ROC becomes more negative. This gives a sell signal to investors.

### Finance Applications

There are important uses of rate of change in finance and investing. Some of the important finance applications are listed below:

#### #1 – Bubble spotting

The traders use ROC as a dynamic metric for bubble spotting. Usually, traders keep an eye on those securities that have high momentum. In other words, traders identify securities whose price accelerates over a period of time. So as soon as the ROC is at its highest, traders buy them, and then they sell these securities just before there is a decline in prices.

However, if the price of a security rises exponentially, much beyond its intrinsic value, it creates a price bubble. When the bubble bursts, the stock price steeply declines, resulting in major losses for the traders.

Traders can spot the bubbles in stock price by using the thumb rule, which says that the positive momentum will stop as soon as the ROC of security crosses the 50% mark.

#### #2 – Bull and bear markets

Traders use the ROC to identify the bull and bear market trends. Whenever the ROC is positive, the market will be bullish. Alternately, the market will be bearish when the ROC is negative. A bull market means when the prices are rising for an extended period. In contrast, the bear market indicates a decline in prices for a long time.

What does the rate of change (ROC) mean?

Rate of change means the change in the value of a variable during a given period with respect to the old value. In investing, ROC is a technical analysis tool to understand the momentum of a security’s price.

How to find the rate of change of a security?

Rate of change is calculated by subtracting the present value of a variable from the old value, dividing it by the old value, and multiplying the result by 100. For example, in the case of securities, subtract the current price of a security from its price a few days ago (old price) and then divide the difference by the old price. Then, to get the rate of percentage change, multiply the amount by 100.

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

The value of rate of change oscillates around 0. It can be negative or positive. A positive ROC indicates a rising trend, while a negative ROC displays a downward trend. If the ROC is zero, there is no change in the value over time.

This has been a guide to what is Rate of Change & its definition. We discuss how to find the rate of change & momentum, in finance using its formula. You can learn more from the following articles –