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The concept of rate of change (ROC) is found almost everywhere in science and math. It's probably most often expressed as a rate of change of a property in a unit of time -- i.e., a time rate of change. The change might also be given with respect to some other property -- such as the rate of change in the northerly direction as compared to a unit of easterly change.

We encounter ROC in many forms. Driving speed, for example, is the distance traveled in an hour -- as kilometers per hour, say, or miles per hour. Acceleration, on the other hand, is often identified as the time rate of change of velocity.

In the stock market, rate of change normally refers to the change in the price of an equity over some period of time, like an hour, day, or week. Here we use it as well to apply to the change in trading volume.

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The rate of change in price of a stock (or an index of stocks) measures the amount that the equity changes, either by increasing or decreasing, over a trading period. It is often expressed as a percentage of the price, or sometimes as a proportion. It might be measured relative to a closing price, or to a day's high, or low, etc.

To calculate the rate of change of price, you need to decide on the reference for the change and on the interval of time over which the change is said to occur, a trading period -- whatever suits your requirements. You must also decide how to express the rate of change, either as a proportion or as a percentage.

Normally you'd like to know how much the price has changed during the most recent trading period, so you might compare the closing price (for the period prior to the selected period) with today's price. To calculate the proportional change, you take the difference between the two prices and express it as a ratio of the difference to the previous closing price.

To compute the percentage change, you would divide the difference in price by the closing price of the previous period and multiply the quotient by 100. This gives the percentage change from the previous (closing) price.

In symbols, the calculation for the rate of change, ROC, is as follows:

ROC = 100(Close_Today - Close_Previous)/Close_Previous)

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Trading volume gives mixed signals -- at least that's the way it seems to me.

Increasing volume in an up market (i.e., when prices are in an increasing trend) is bullish and portends still higher prices. However, there comes a time when the volume is so great that it reaches blow-off proportions. That's not bullish for the market and in fact portends a top. (Some technicians try to detect the top by using cycles).

Very often, too, after a pullback from the high, prices go even higher, but are accompanied by lower volume. This can happen in a double top or head and shoulders formation, for example. (These patterns are realized when prices break through the neckline to the downside.)

In a parallel way, increasing volume in a down market is bearish and portends lower prices, still. However, there comes a time when the volume on the downside is so great that it reaches blow-off proportions. That's not bearish for the market, and in fact portends a bottom. Very often, too, after a rebound from the low, market prices go even lower, but are accompanied by lower volume. This can happens in a double bottom or reverse head and shoulders formation.

Again, in a bull market, lower prices on decreasing volume is bullish. It shows that not many people are willing to sell at the lower prices -- selling pressure is diminishing. When the volume dries up, the advance normally resumes.

And in a bear market, increasing prices on decreasing volume is bearish. It shows that not many people are willing to buy at the higher prices. When the volume dries up, the decline normally resumes again.

It's instructive to compare this view with that of Charles W Smith.

At the top of a market, what normally occurs is distribution, which is to say that stocks are passing from strong hands to weak hands. At a bottom, it is accumulation, meaning stocks are passing from weak hands to strong hands. In either case the momentum is changing direction.

Accumulation and distribution are the basis for a divergence oscillator called the Chaikin Oscillator. Here's what Bauer and Dahlquist have to say about it:

The Chaikin Oscillator uses an accumulation/distribution line as the sum of the accumulation/distributions:

AD = åad_i, for i = 1 to P,

or for a predefined range, P. The terms ad_i over the period are defined as follows:

ad_i = (((Close_i - Low_i) - (High_i - Close_i))/(High_i - Low_i))/V_i:

Each day, for example, you take the difference between the closing price and the low, the difference between the closing price and the high, subtract the latter from the former, and divide by the difference between high and the low. This gives the fractional value that finishes above or below the close for the day. The value is then divided by the volume to yield the movement per unit volume.

A ten-period and a three-period exponential moving average of the accumulation/distribution line are calculated, and the difference between them is the Chaikin Oscillator:

CHA = 3-period moving average -10-period moving average.

When price movement and the Chaikin Oscillator movement diverge, a trading signal is generated.

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