# Rate of Change Indicator

## by CI Staff

The term “momentum” is used frequently in investing. In fundamental analysis, it can refer to strong and/or growing sales, earnings, etc. In technical analysis, it is used to describe the speed or force of price movement. Common momentum indicators measure the change in price from one period to another or the percentage change in price from one period to another. In this installment of Technically Speaking, we focus on the momentum indicator called rate of change (ROC).

The rate of change (ROC) indicator is a pure momentum oscillator that measures the percent change in price over the last n periods. In other words, the indicator compares the latest price (typically the closing price) with the (closing) price n periods ago. The resulting oscillator fluctuates above and below the zero line, indicating shifts from positive to negative. Similar to other oscillators, ROC signals include centerline crossovers and overbought/oversold conditions.

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## Calculation

The formula for rate of change is:

ROC = [(C[0] ÷ C[n]) – 1] × 100

Where:

C = closing price

0 = the latest period

n = a specified number of periods in the past

Figure 1 is a daily price chart for Apple Inc. (AAPL) for the period December 14, 2012, through February 15, 2013, with the 12-day ROC plotted below the price chart (see the box below for an illustration of how ROC was calculated for AAPL over this period). When the ROC is above the zero line (positive), prices are rising. Conversely, when the ROC goes negative and crosses below the zero line, prices are falling. The stronger the momentum to the upside or downside, the more ROC advances into positive or negative territory, respectively. The ROC is not bounded on the upside, as there is no theoretical limit on prices. However, ROC is limited on the downside since securities can only decline 100%.

## Overbought/Oversold Conditions

Besides identifying the overall direction of the underlying trend in a security’s price, we can also use oscillators such as ROC to identify overbought and oversold conditions. However, they work best when prices are fluctuating. For example, while we have shown that Apple’s stock price has experienced strong and prolonged trends over the last several years, prices do fluctuate even when trending.

A typical uptrend consists of a series of higher highs and higher lows, with occasional pullbacks from the intermediate highs. Likewise, a downtrend generally consists of lower lows and lower highs, with retracements taking place from the intermediate lows. Following the movement of ROC as prices fluctuate can alert us to levels that, historically, have preceded a reversal.

Figure 2 is a daily price chart for Microsoft Corp. (MSFT) for the period June through December of 2010, along with a 20-day ROC. Depending on your charting service, you should be able to modify the number of periods used to calculate the indicator. The “optimal” number of periods will depend on the security you are analyzing and your desired trading time frame. Three times the ROC peaked around 13%: late July, early November and late December. This means that MSFT shares had risen roughly 13% over the previous 20 trading days. On the first two occasions, the price fell approximately 10% and 7% within a month of ROC hitting its max. While not shown in the chart, following the third ROC overbought condition in December, the price trended sideways before breaking above the December high.

Lastly, in Figure 3 we plotted Chevron Corp. (CVX) on a daily basis over a year ending February 15, 2013. Here we see where the 21-day ROC bottomed out near –10% on three occasions in 2012; mid-April, early June and November. The first time, Chevron rebounded roughly 8% over the next couple of weeks; the second time, the price rebounded roughly 23%; and the third time, where ROC reached its low a little before the shares reached their bottom, the price recouped approximately 15%.

## Conclusion

The rate of change (ROC) indicator shows you the speed at which prices are changing. An upward swing in ROC indicates that prices are moving upward at a faster rate. In contrast, a downward move in ROC indicates that prices are declining more rapidly. However, like all technical indicators, the ROC isn’t intended to be a stand-alone analysis tool. Using it in conjunction with other indicators will either confirm the signal or prevent you from acting on a false positive.

## Calculating Rate of Change

Table 1 illustrates the calculation of the 12-day rate of change for Apple Inc. (AAPL) for the 20-day period ending February 15, 2013. The greens cells show the prices used to arrive at the February 15, 2013, ROC of 1.32, which indicates that the closing price on February 15 is 1.32% higher than the close on January 30. The red cells show the 12-day ROC from January 18, 2013, until February 6, 2013. Note that the prices are adjusted to reflect the \$2.65 dividend payment on February 7.

 Date Closing Price* 12-day ROC 1 18-Jan-13 497.10 Close 12 days ago 2 22-Jan-13 501.85 3 23-Jan-13 511.03 4 24-Jan-13 447.89 5 25-Jan-13 437.33 6 28-Jan-13 447.22 7 29-Jan-13 455.61 8 30-Jan-13 454.18 Close 12 days ago 9 31-Jan-13 452.85 10 1-Feb-13 450.99 11 4-Feb-13 439.75 12 5-Feb-13 455.19 13 6-Feb-13 454.70 -8.53 Close 14 7-Feb-13 468.22 -6.70 15 8-Feb-13 474.98 -7.05 16 11-Feb-13 479.93 7.15 17 12-Feb-13 467.90 6.99 18 13-Feb-13 467.01 4.43 19 14-Feb-13 466.59 2.41 20 15-Feb-13 460.16 1.32 Close *Prices adjusted for \$2.65 dividend on 7-Feb-13.

## Discussion

Yusuf Qamar from Kansas posted 11 months ago:

No graphs, no charts. Not very helpful

Karl Lawson from Colorado posted 11 months ago:

Your article: RATE OF CHANGE INDICATOR, CI 2Q-2013, Pg 30, last paragraph, promises to show me how the ROC was calculated. I've looked all over but cannot find it???!!! Please send instructions on how to construct this tool?

Thank you, Karlwlawson@comcast.net
10673086 36 April 7, 2013

Jay Lagree from Delaware posted 10 months ago:

http://stockcharts.com/help/doku.php?id=chart_school:technical_indicators:rate_of_change_roc_a

Sunny

jbkemp from Texas posted 9 months ago:

I really like ROC, next to MACD, and I can see bottoms and tops much easier and I buy close to the bottom more often and I can sell just below the peaks more often...I really appreciate AAII.