Introduction
Richard (Dick) Arms was one of our international guest speakers at the 2003 ATAA Annual Conference held on the Gold Coast. Colin Nicholson met Dick Arms at the IFTA Conference in London in 2002 and invited him to Australia. His agreement to come was a momentous event for the ATAA, because Dick Arms is a living treasure in the world of technical analysis, having invented the Arms Index and Equivolume charting.The Arms Index is also known as TRIN, which stands for Traders Index. It is one of the most watched indicators on Wall Street. It is published every day in Barron's. It is available on almost every other quote system and crosses the CNCB ticker every few minutes.
The Arms Index is not widely known in Australia and is little used, because the data to calculate it has not been readily available. However, following Dick Arms' presentation at the ATAA Annual Conference in 2003, that has changed. Both Dial & Chart and JustData (BodhiGold) now make the Arms Index available each day as part of their daily download and historical data is also available.
In order for Dick Arms to introduce the Arms Index at the 2003 ATAA Annual Conference, Bernard Chapman calculated historical data for Australia. This made the presentation of the Arms Index more relevant and was a trigger for the two data vendors to make ongoing data available. It is hoped that other vendors will also make the data available, but this may require pressure from ATAA members who wish to have it. If readers are clients of other data vendors, they are encouraged to request their vendor to provide the data. Everything they need is in this article.
This article has been written jointly by Colin Nicholson and Bernard Chapman. Colin explains the basics of the Arms index as Dick Arms developed and uses it.
Part 1: The Basic Arms Index
The Arms index is based on a quite simple, yet powerful idea. If the market is strong, it can be expected that more stocks will rise in price than will fall. However, the importance of this observation depends on whether the volume of trading supports the rise. In other words, when the rising stocks are well supported by volume, the rise will be far more convincing than when the volume of trading is concentrated in the stocks that are falling.The number of stocks that rise and fall each day has been available for a long time in Australia. Most stock market analysts have plotted this data as an AdvanceDecline line. However, the volume data in the form of the number of shares traded in the stocks that rise and the stocks that fall have not been readily available. It was this volume information that we needed to calculate the Arms index.
Formula
The formula for the Arms index, as it was originally developed by Dick Arms, is:Arms Index (TRIN) =  
  
Where:
Advances = The number of stocks that close higher today than yesterday.
Declines = The number of stocks that close lower today than yesterday.
Adv. Vol. = The number of shares traded in advancing stocks.
Dec. Vol. = The number of shares traded in declining stocks.
An example of the calculation is:
Advances: 400
Declines: 600
Adv. Vol.: 1700m
Dec. Vol.: 3500m
Arms Index =  = 1.37  
  
Interpretation
An Arms index value of 1.00 is neutral and means that the volume is favouring neither the rising nor the falling stocks.An Arms index that is greater than 1.00, such as the one in our example, means that the volume is favouring the falling stocks. In a falling market, that would be a normal observation. However, in a rising market it would suggest that the sellers are distributing their holdings and that the rally might be unsound.
An Arms index that is less than 1.00 means that the volume is favouring rising stocks. In a rising market, that would be a normal observation. However, in falling markets it would suggest that the buyers are accumulating cheap stocks and the decline is likely to fail.
The easy way to remember this is that the Arms Index is counterintuitive compared to the price. A rising Arms Index is bad and a falling Arms index is good.
The first reaction we have is that the Arms Index should be constructed the other way around, so that it moved intuitively. However, that is the way Dick Arms developed it and it has become so entrenched in the infrastructure of the US market that it is impossible to change it now. In Part 2 of this article, Bernard Chapman will explore alternative ways to display the Arms index that address some of the design issues. For the moment, this part of the article will explain it as it is in current practice.
Charting the Arms Index
If we plot the raw Arms Index, we get a very volatile chart, as shown in Figure 1.
Figure 1: Raw Arms Index 2004
This is not very useful, because it is too volatile for most purposes. Dick Arms recommends plotting a moving average of the Arms Index. His suggested moving averages are 10 days for short term analysis, 55 days for medium term analysis and 200 days for the long term picture.
Figure 2 shows a 10day moving average of the Arms Index superimposed on a daily bar chart of the ASX All Ordinaries Index.
Figure 2 ASX All Ordinaries Index with Arms Index 2004
Notice how the peaks in the index are usually accompanied by troughs in the Arms Index and vice versa. This is normal market action. There is also a strong tendency for market peaks to occur with the Arms index around 0.6 to 0.7 and for troughs in the market index to occur with Arms Index readings of 1.1 to 1.2 on the 10day moving average in recent times. Thus we can also use the Arms Index for overbought/oversold indications.
For a more detailed discussion of the Arms Index see Colin Nicholson's Article Index Data Sounds a Call to Arms in the August 2004 issue of Shares magazine and Dick Arms' book The Arms Index (TRIN), which is difficult to get, but is stocked by the Educated Investor bookshop at 500 Collins Street in Melbourne 03 9620 0885 (a Silver sponsor of the 2004 ATAA Annual Conference, that allows a 10% discount to ATAA members).
Part 2: Towards a Better Presentation of the Arms Index
What Does the Arms Index Mean?
The Arms Index is not just a meaningless arrangement of component quantities divided and multiplied together. The components can be rearranged from the way that they are normally presented to give a mathematically identical formula:
Arms Index =  
  
The index can therefore be directly interpreted as the ratio of the average daily volume of the falling stocks to the average daily volume of the rising stocks.
When the average "down" volume is equal to the average "up" volume the market is in balance giving an equilibrium value for the Arms Index of 1.
If the average up volume is greater than the average down volume then this has bullish implications and the Arms Index ratio is below 1 but above zero. Alternatively, if the average down volume is greater than the average up volume then this has bearish implications and the Arms Index ratio can be any number greater than 1.
As discussed above, for historical reasons, the Arms Index was originally defined in such a way that it is counter intuitive and for this reason it is usually plotted upside down so that bullish activity causes its chart to rise and bearish activity causes it to fall rather than the reverse. We will refer to this as Issue (1).
What Type of Moving Average Should We Use?
The raw Arms Index can be quite volatile, swinging strongly above and below the neutral value of 1. For this reason a moving average is usually taken. However, there can be a problem in taking moving averages of a ratio index like the Arms Index as is illustrated in the following example.Consider one day on which the average up volume is ten times greater than the average down volume so that the Arms index has a value of 1/10 or 0.1. On the following day the market swings equally in the opposite direction so the average down volume is 10 times the average up volume giving an Arms Index of 10. We would hope that the type of moving average that we chose would result in a neutral value of 1 when these two days were averaged since the market has swung equally in both directions and the bearishness of the second day should compensate for the bullishness of the first.
The normal "arithmetic" average that we use in charting is calculated by simply adding the two values 10 + 0.1 and dividing by the number of values  in this case 2.
Arithmetic Average Arms Index =  = 5.05  
  
This is not the expected neutral average value of 1 but a very bearish value of over 5. The equal bullishness and bearishness have not "averaged out" as we had hoped. The consequences of this characteristic can be particularly severe at times of increased volatility. We will refer to this as Issue (2).
However, we could easily overcome this by taking what is known as a "geometric" average of the two values. Instead of adding them together as before we multiply them together and, instead of dividing the result by 2, we take its square root and so we get our desired equilibrium value of 1.
Geometric Average Arms Index =  _______  = 1 
\/ 10 x 0.1 
Unfortunately most charting packages do not provide the option of a geometric average.
How Should We Plot the Arms Index?
As it is defined the Arms Index is asymmetric because no matter how bullish the market the index can never go below zero and hence it can never be more than one unit below the neutral line. In contrast there is effectively no limit to how high it can go. In our example above, on the first day, the index is 0.9 units below the neutral line and on the second day the index is 9.0 units above the neutral line even though the market has swung equally in both the bullish and bearish directions. This asymmetry, which causes compression of bullish values against the zero line, we will refer to as Issue (3).What is the Solution?
Fortunately there is a simple solution, implementable in any charting package, to the three issues mentioned above ie (1) the counter intuitive nature of the index definition (2) The requirement for a geometric rather than an arithmetic average and (3) the inherent asymmetry of the raw index.The solution is based on the fact that the logarithm of the geometric average of a set of quantities is equal to the arithmetic average of the logarithm of the individual quantities. To solve issue (2) we chart values that are the logarithm of the Arms Index, rather than the raw values themselves, and then calculate a normal arithmetic moving average of these values.
To solve Issue (1) we invert each Arms Index value before taking its logarithm. Issue (3) will be seen to solve itself automatically as a result of the two changes suggested above.
In summary we simply invert the Arms Index and take its logarithm and provide it as a data feed to our charting program. (In case you are tempted to suggest as an alternative just plotting the raw index and its moving average on a logarithmic scale, short reflection will show that this approach will not be successful).
Let's see how our two day example above works out now. Our neutral value of the Arms Index of 1 now becomes zero (because Log (1/1) = 0). For the bullish first day the Arms Index has a value of 0.1 but after inversion becomes 10 and taking its logarithm we get 1. Inverting the Arms Index of 10 for the bearish second day we get a value of 0.1 which has a logarithm of (1).
If we take a simple average of these values we obtain our required neutral value of zero. 

Summary
If data vendors provide a feed of the log of the inverted Arms Index then these values may be directly plotted to give an oscillator that alternates above and below a neutral zero line. This has the advantages that: Positive values have bullish implications and negative values have bearish implications
 Equal degrees of bullishness and bearishness will be represented by equal swings above and below the neutral line.
 By taking a normal arithmetic moving average of the values we will produce a smoothed result that correctly takes into account the varying degrees of bullishness and bearishness of the individual days.
Figure 3 shows the period covered by Figure 2 using the log of the inverted Arms Index.
Figure 3 ASX All Ordinaries Index with Log of the Inverted Arms Index 2004
It will be seen that the moving average of the Arms Index is above zero for almost the entire period, reflecting the strong uptrend in 2004. More importantly, the Arms Index now moves intuitively with the peaks and troughs in the market index