From the December 01, 2008 issue of Futures Magazine • Subscribe!

Measuring the big mo’

Over time, price changes. This fundamental attribute makes it possible to make money trading the markets. There are two general ways those price changes relate to time: direction and speed. Direction was largely addressed in our installments on trendlines and moving averages. This article will look at the speed — or velocity or momentum — of those movements.

Although there are variations on the specifics, it is generally assumed that momentum is greatest during the strongest part of a trend move. Before that trend ends and ultimately turns in the other direction, momentum should decrease. That is, price will begin advancing or declining at a decreasing rate. The concept is similar to that of a ball thrown into the air. Before arching and returning to earth, the ball’s assent will slow. Occurrences in the financial world are rarely so clean, but the analogy is sound.

Over the years, traders have developed many indicators to identify this change in speed so that their practitioners know when to take money off the table or, in some cases, initiate new trades. Referred to in a general sense as oscillators, this class includes rate of change, the relative strength index and stochastics.


Rate of change charts the close of the current period (minute, hour, day, week, etc.) as a percentage of the close a specified number of periods ago. An alternate calculation depicts rate of change by reporting the difference of the two closes as a percentage of the earlier close.

Here are the formulas:

ROC = (close_1 / close_n) * 100


ROC = ((close_1 - close_n) / close_n) * 100

Using the first calculation above as the basis, the interpretation is relatively simple. If the value on the oscillator is above 100%, this period’s close is greater than the close n periods ago. If the rate-of-change value is less than 100%, this period’s close is less than the close n periods ago. Clearly, the extent to which the reading is higher or lower than 100%, the stronger the trend.

One caveat to keep in mind for rate of change is that even though the direction of the indicator may change, the trend may be the same. In other words, if the rate-of-change reading has dropped from 125% to 105%, the trend is still, technically, up because the percentage is still higher than 100%. Its rate of increase, however, has indeed slowed and may indicate that price is primed for an actual turn. Trend analysis is necessary to determine how prices are trending (up, down or sideways).


The relative strength index (RSI) does not measure the relative strength of one market to another, as the name implies. Instead, it measures the internal strength of a single market. The indicator was introduced by J. Welles Wilder in the June 1978 issue of Commodities magazine (now Futures) and was expanded in Wilder’s book “New Concepts in Technical Trading Systems,” published that same year. RSI has since become one of the most popular technical indicators in use today.

According to Wilder’s original article:

RSI = 100 - 100 / 1 + RS, where

RS = Average of 14 days that closed up / Average of 14 days that closed down

In calculating the index, you start with 15 days of price data (not just 14 because the first day requires the previous close from which to determine the first up or down close value). Add up the amounts by which the market closed higher than the previous day and divide that by 14. Do the same with the amounts by which the market closed lower. Divide the average up close by the average down close to get RS. For example, if the sum of the day’s up closes divided by 14 is 0.95 and the sum of the day’s down closes divided by 14 is 0.33, RS is 2.9, and:

RSI = 100 - 100 / 1 + 2.9

RSI = 100 - 100 / 3.9

RSI = 100 - 25.6

RSI = 74.4

The RSI value for the next day, day 16, is calculated not simply by dropping the oldest up or down close and adding the most recent one, but by multiplying the previous average up and down closes by 13, adding either the new up close or the new down close, and dividing each value by 14. This effectively smoothes the oscillator, reducing noise.

Unlike rate of change, which can potentially escalate to infinity or drop to zero, at least in the initial calculation shown above, RSI will always oscillate between 0 and 100. As prices rise during an extended uptrend, the RSI value will rise as well. Likewise, in a downtrend, the RSI value will tend to drop along with price. Key levels, however, for indicating extreme conditions are 70 on the high side and 30 on the low side.

In other words, as the RSI value reaches these levels, the market may be overbought or oversold. Still, as with rate of change, it’s important to keep in mind that just because RSI is overbought or oversold doesn’t mean it will stop being so anytime soon. Markets can remain in both conditions for extended periods of time.

A relatively reliable, and much rarer, condition for RSI is known as divergence. Divergence refers to the indicator making a lower high or a higher low while price continues to rise or fall, respectively. If the indicator fails to confirm the continuation of the trend reflected in price, then there’s a fair chance that price is poised to retrace against that existing trend (see “Divergence comes calling”).


George Lane developed stochastics in the early 1960s. Stochastics is another sort of internal strength index that measures a market’s most recent close relative to its price range over a specified period.

The philosophy behind stochastics is as a market tops, closes will be closer to the high of the price range over a recent time period, and as a market bottoms, closes will be closer to the low of that price range. As with RSI and other oscillators, the price range is subjective, but generally ranges between nine and 20.

There are three values for stochastics, the first of which usually is omitted from charts but is necessary to calculate the second and third values. Raw K is the most basic stochastic value. The other values are smoothed versions of Raw K: %K is a moving average of Raw K, and %D is a moving average of %K.

The formulas for a nine-day stochastics oscillator is:

Raw K = 100 ((close_1 - low_9) / (high_9 - low_9)), where

Close_1 = current period’s close

High_9 = nine-day high

Low_9 = nine-day low

%K = %Kt-1 + (0.5 (Raw K - %Kt-1))

%D = %Dt-1 + (0.5 (%K - %Dt-1))

Note that 0.5 is a smoothing constant derived from the formula 2 / (Z + 1), where Z is the number of periods used for smoothing, in this case 3.

The formulas for calculating %K and %D are simply exponential moving averages of Raw K and %K, respectively. There are other ways to calculate %K and %D, but the concept remains the same: The two are smoothed, less noisy and, presumably, more useful versions of Raw K.

The interpretation of stochastics generally focuses on the relationships between %K and %D. When the fast line, %K, crosses the slow line, %D, a potential change in trend is indicated. A cross below suggests a new bear move is on tap. A cross above suggests a bullish move is imminent. As with RSI and rate of change, stochastics, particularly in relation to the slowest line (%D), is helpful as a divergence indicator (see “The fall before the fall”).


Although clean, obvious, well-chosen examples can be found, momentum oscillators generally work poorly for initiating new positions. That said, they are considered relatively reliable indicators for foretelling the end of a trend move. In other words, if you’re long and you notice a classic RSI divergence on a higher high, it may be time to take some money off the table, or at least tighten up your trailing stops.

Along those lines, oscillators also are strong candidates for confirmation. When used in conjunction with other indicators covered in this series — from trendlines to chart patterns — oscillators can help complete the picture of what the market is trying to say (or trying to hide). That said, there certainly are creative ways to employ these indicators on their own, even to the extent of using them in mechanical trading systems (see “RSI: A systematic approach” ).

The best analysis in the world, however, does not mean you will be a successful trader. Many traders with superior price forecasting skills have been tripped up by basic market logistics. The markets have their own mechanics, some simple and some complicated, but any one of them can throw a wrench into an otherwise well-oiled analytical machine.

The best approach to any indicator is simple: practice doesn’t make perfect, but it helps. As you explore what’s available in technical analysis — from trend detection to price patterns to momentum oscillators — maintain an open mind and a critical eye.

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