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  • Arms' Ease of Movement: Adding Volume to the Equation

    by Wayne A. Thorp, CFA

    Arms' Ease Of Movement: Adding Volume To The Equation Splash image

    Technical analysis is the study of historical price and volume activity with the hope of identifying patterns or behavior that may predict future price movements. For many, however, volume is an afterthought, relegated to a small bar chart below the price chart.

    While price movement is of primary importance, volume analysis can play an important role in confirming price trends as well as price breakouts. High volume provides reassurance that a trend will continue while low volume is more prevalent during periods of indecision or consolidation.

    equivolume charting

    The singular role for the majority of chart types, such as line, bar, and traditional candlesticks, is to plot prices—open, high, low, close, etc. One exception to this is equivolume, which was introduced by Richard W. Arms Jr. This method is unique in that it places price activity and trading volume on an equal footing, combining these elements into two-dimensional boxes that represent each trading period. Figures 1 and 2 show bar and equivolume charts for General Dynamics.

    The bar chart in Figure 1 provides four price points for each trading period—the open, high, low, and close. While this chart is good at illustrating the relationship between the high and low prices as well as the open and close, it is lacking a key element of technical analysis—the trading volume behind this price movement.

    Comparing Figures 1 and 2, one can identify similarities as well as some distinct differences between the two. Similar to bar charts, the top and bottom of each equivolume box represent the high and low prices, respectively, for that period. However, one cannot readily discern whether the period was up or down—which can be done with bar charts.

    The unique element of equivolume charting lies in the way in which it represents volume. With bar charts and most other “traditional” chart types, the horizontal axis reflects time. However, with equivolume, the horizontal axis also represents the comparative trading volume for the period. In other words, the width of each box is a function of volume—the higher the volume for the period, the wider the box, and vice versa.

    Figure 2 includes daily volume bars to show the relationship between the width of the equivolume boxes and the corresponding volume. For the period shown, July 19 had the highest trading volume with 2,362,800 shares traded. On the chart, this date had the widest box as well as the highest volume bar. August 3 had the lowest trading volume for the period, with 476,600 shares traded. The chart also shows that this day had the narrowest box and shortest volume bar.

    Volume analysis and equivolume charting are useful in identifying levels of support and resistance as well as points where these levels are broken—breakouts. Figure 3 is an equivolume chart for Micron Technologies, which illustrates support and resistance levels as well as a power breakout to the upside.

    Beginning around early June of 1999, Micron began an upward move that lasted for the next four months. After falling off of its highs of September, Micron attempted a comeback as prices rebounded to Point 1. Here there is a short, wide box that is indicative of an intermediate top. At points such as this, buyers are willing to pay more and more for the stock, and prices are driven up. However, sellers are willing to satisfy this demand. The end result is heavy trading volume with little price movement.

    Points 2 and 4 are classic patterns exhibited on equivolume charts at intermediate bottoms. Arms points out that lows tend to differ from highs because they are more emotional. As the emotions of sellers take hold, this causes wider price movements coupled with higher volume. Such is the case at Points 2, 4, and to a lesser extent, 6. At Points 2 and 4, the boxes are taller and much wider than those found at the tops at Points 3, 5, and 7.

    After trading between $30 and $40 for a few months, Micron breaks above the resistance level. What makes this breakout different from the one just prior to Point 5 is the volume. The narrow box at this earlier breakout indicated a lack of buyer support, which led to its subsequent and immediate relapse below the resistance level. At Point 7, however, the bar is the tallest and widest on the chart—evidence of strong support behind this strong upward move. From there, the price rose over 75% in less then one month. Note too that the boxes during this period are much taller than those found within the trading range, yet are also relatively thin. Boxes such as these tend to be found in well-established trends.

    Ease of movement

    Beyond creating equivolume charting, Arms also introduced several technical indicators dealing with volume, including ease of movement (EMV). Like equivolume charting, the ease of movement indicator shows the relationship between volume and the price range for a given period. However, it takes the process a step further by providing an indication of how much volume is required in order to move prices.


    The components of EMV—price range, the movement in price from one period to the next, and the trading volume accompanying this price movement—should be understood before tackling EMV itself. This is illustrated using Table 1, which contains daily data for General Dynamics from June 18 to August 17, 2001.

    Price Range

    The price range is a straightforward calculation. It is simply the difference between the high and low prices for a given period so that:

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    Price Range = High Price – Low Price

    In our example, a daily EMV value is being calculated, so the daily high and low prices for the price range are used.

    Table 1 shows that the high and low prices for June 18 were $75.10 and $74.10, respectively. This results in a price range of $1.00 (75.10 – 74.10).

    Box Ratio

    The next step taken by Arms is to combine the “adjusted” price range and the volume for the same period into what he calls the box ratio (BR). Before doing so, he adjusts the volume by dividing each period’s volume by 10,000.

    The box ratio is calculated as follows:

    BR = Volume (in 10,000s)/Price Range

    For June 18, the volume of 58.48 is divided by the price range for the day of $1. Therefore, the box ratio (BR) for June 18 is 58.48.

    The box ratio provides an indication of how easily the price is moving. The lower the box ratio value, the “easier” the price is moving. Likewise, the more resistance the price is facing when making a move (up or down), the higher the box ratio. Breaking down the box ratio into its component parts provides a better understanding of why this is the case. Stocks facing heavy resistance, on either the upside or downside, typically experience heavy volume with little price movement. Circumstances such as this would result in a high numerator (volume) and a low denominator (price range). In contrast, stocks in established trends— again, in either direction—tend to move on relatively light volume.

    Midpoint Move

    Arms points out that it is not enough to know how “easy” or “hard” it is for prices to move. In order for this knowledge to be useful, one needs to know: 1) how much the price has moved, and 2) in what direction the price movement was. To determine these factors, he derived the midpoint move (MPM), which is the difference between the median price for one period and the median price of the next period. It is calculated as:

    MPM = (Today’s High + Today’s Low)/2 – (Yesterday’s High + Yesterday’s Low)/2

    Two period’s worth of data is required in order to calculate the midpoint move. Therefore, with the data in Table 1, the first day for which the midpoint move can be calculated is June 19 using the following data:

    Today’s High (19th) = $75.80

    Today’s Low (19th) = $74.17

    Yesterday’s High (18th) = $75.10

    Yesterday’s Low (18th) = $74.10

    MPM = (75.80 + 74.17)/2 – (75.10+74.10)/2

    MPM = 0.385


    Having derived all of its components, the ease of movement indicator can be calculated using the following formula:

    EMV = MPM/BR

    For June 19, the EMV value is:

    EMV = 0.385 / 60.37 = 0.00638

    interpreting emv

    A good way to understand EMV is to look at it in the context of two different stocks. Stock A and B have the same midpoint move value for a period, but Stock A had lower volume for the period. Stock A would then have a higher EMV (Stock B would have a lower EMV). Stock A’s price is seen as moving more easily because it took less volume to move the price the same amount as Stock B.

    smoothing EMV

    Table 1 shows the drastic variation in the daily EMV values for General Dynamics. These fluctuations make it difficult to discern a pattern that could be used when trading. To make the EMV more stable, and useful, most technicians employ an EMV moving average to “smooth” the data.

    There is no clear-cut number of periods one should use when calculating an EMV moving average. The number of periods used by one person probably will not be the ideal one for another. Factors such as investment horizon and the security being analyzed will affect this decision. Arms describes a process of trial and error to arrive at his own moving average period for EMV.

    As with all moving averages, the shorter the time period used in the calculation, the more responsive the average is to daily fluctuations. The key is to strike a balance—select a period that is short enough to generate timely signals, yet long enough to avoid false or meaningless signals.

    plotting emv

    Figure 4 is a daily equivolume chart for General Dynamics with a bar chart showing the 10-day simple moving average of ease of movement. Technicians focus on when EMV goes from positive to negative or negative to positive. When the EMV crosses above zero, this is an indication that prices are moving upward more easily, while a move below zero suggests that prices are moving more easily downward.

    In Figure 4, these occurrences are marked with arrows as well as numbers. Points 1 and 3 indicate where EMV went from negative to positive, which suggests a buying opportunity. Likewise, Points 2 and 4 show where the EMV went from positive territory to negative—potential sell points.

    Most indicators work best in particular markets. In the case of the EMV, it works best when the security experiences prolonged trends—either up or down. When this takes place, EMV is apt to stay positive or negative for an extended period of time. Such was the case between Points 1 and 2, where General Dynamics rose from a low of $63.30 to a high of $84.28 in the span of less than two months. When prices start moving in a sideways fashion, the indicator is more apt to bounce from positive to negative, providing no decisive signal in either direction.


    The EMV can be useful in pointing out possible buy and sell points, with movement above zero suggesting a buy and movement below zero, a sell.

    The trap you may fall into with technical analysis is believing that one indicator is the key to trading success. There is no such thing as one “all purpose” indicator that performs well in all market conditions. Some indicators perform well when prices are trending up or down, while others generate the best signals when prices are trading sideways.

    For this reason, it is best to use ease of movement in tandem with other indicators when formulating a trading strategy.

    Wayne A. Thorp, CFA is a vice president and the senior financial analyst at AAII and former editor of Computerized Investing. Follow him on Twitter at @WayneTAAII.


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