The $Arms Index aka$TRIN

Abstract

This is the second part of our research on the Arms Index which was published in “The Arms Index aka TRIN” (DOI) and it defines and introduces an improvement of the regular Arms Index calculation. We highlight the flaws of the existing Arms Index calculation which is so widely referenced and propose an weighted and normalized Index that that is not distorted by the prices of the stocks in the way the regular Arms Index is. We also show some inconsistencies of the published Wall Street Journal Arms Index values.

Full text

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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The $Arms Index aka $TRIN
Andreas A. Aigner1 & Walter Schrabmair2
TradeFlags, Vienna, Austria; Medical University Graz, Graz, Austria
25 Sept 2019
This is the second part of our research on the Arms Index which was published in “The Arms
Index aka TRIN” (DOI) and it defines and introduces an improvement of the regular Arms Index
calculation. We highlight the flaws of the existing Arms Index calculation which is so widely
referenced and propose an weighted and normalized Index that that is not distorted by the
prices of the stocks in the way the regular Arms Index is. We also show some inconsistencies of
the published Wall Street Journal Arms Index values.
Introduction
You have read the detailed analysis of the Arms Index (TRIN) . In one of the
sections we describe one of the criticisms of the regular TRIN calculation. In this
article we deduce and analyze an improvement over the regular Arms Index,
which we call the $Arms or $TRIN respectively.
The regular calculation uses the net Volume of all advancing and all declining
shares of all stocks, for the NYSE TRIN all the stocks listed on the NYSE. This is
a sum over all shares regardless of the dollar value of a single share. Whether it
is 1$ or 100$ one share of either is treated as equal and summed over. This is
equating smaller dollar value shares with high dollar value shares. You might
deduce that this is the same as equating all smallcap stocks with bigger market
cap stocks, but that is not the case. The price of a share doesnt necessarily mean
its marketcap is small or big. It is equating the dollar value only.
Since the index is counting each share up or down equally for the first ratio in
the calculation, the ratio of advancing to declining issues, it only seems logical to
do the same for the volume. In the end same way that you dont want to give the
smaller dollar stocks more weight in the first ratio you want to avoid this in the
volume ratio as well!
Funnily Richard Arms himself is suggesting this unknowingly in his book "The
Arms Index" from 1989. At the very end of the book he is giving an analogy of
distributing cookies to a group of boys and girls. They boys and girls
representing the two camps of advancing and declining issues and the amount
of cookies corresponding to the volume. If all the girls got two cookies and the
boys all got 1 cookie you would notice a bigger weight towards the girls since
the volume would tell you so. In Richards example he is taking a cookie as a
standard unit, this cookie is the same everywhere. Every boy and girl has a
certain quantity of this single unit thats identical for all kids. With the stock
market this cookie is different from one stock to the next, it would seem logical
to standardize this, ie. normalize this price and thereby the volume traded.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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For example the biggest dollar share is Berkshire Hathaway BRK-A which is
worth around 350,000 USD and makes up around 67% of all stock prices
because of this.
You can see that if you took the share volume of BRK-A and calculated the
Arms index normally you would equate this volume with the volume of a 10$
stock. While someone traded 350,000 USD you would bunch it together with
someone who traded 10$ in stock. It clearly has its flaw. It can be the case that
by calculating the Arms Index normally you get some kind of information as a
result which might be helpful, but you are obviously going to contaminate the
calculation with smaller dollar value stocks.
The new $Arms Index Calculation
Therefore we suggest to eradicate this unwanted contamination. You could do
this by normalizing each volume by the sum over all stock prices, or
alternatively you could simply use the $ notional traded of the advancing and
declining shares in the ratio, since you are only interested in the ratio of $
notionals traded. So essentially you want to use the traded USD notional
volume instead of the share volume.
Why has Richard Arms not used this ? Most likely this is due to the fact that it
was not readily available get the $notionals traded at a given time, or at end of
day even. We believe if he had had these numbers available, like they are readily
available nowadays he would have used them instead of the share volumes.
The following is what we call the $Arms or $TRIN index and we calculate it as
follows
$TRIN = A / D * NDV / NAV
where
A = Advancing Issues
D = Declining Issues
NDV = Notional of Declining Volume
NAV = Notional of Advancing Volume
Essentially NDV & NAV are a vector product of the $ share price vector with
the Volume vector.
NDV = S * V
and the $ share price vector is
S = fx * S.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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Comparison with the S&P500
In his book Richard plots a scatter plot of the S&P500 daily change versus the
TRIN index, where one sees for his data a nice cloud of datapoints decreasing
with increasing S&P changes and increasing with decreasing S&P changes. We
do this here as well and plot three groups of data. The normalized TRIN for our
US stocks, the regular TRIN for our US stocks and the official NYSE TRIN. The
S&P500 is a marketcap weighted index, similar to our $TRIN index which is
weighted according to the dollar notional traded each day. We have 500 big
names in the S&P500 and around 2700 names in our US population.
Figure 1: Plot of TRIN vs S&P500 Net Change. Courtesy The Arms Index by
Richard Arms Jr. (1989)
The plot is missing the x-axis in his book, which would have been nice to have as
well, but his chart suggests there is a kind of parabolic relationship between the
% Change and the TRIN index. Lets look at a plot of more recent data. Following
is a plot of the $TRIN

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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When we linearly interpolate the data we get negatively sloping lines for the
$TRIN and the NYSE TRIN, while for the regular TRIN we get a positively
sloping line. The change in slope is due to the normalization of the volume, ie.
using the dollar notional volume instead of the regular share volume. Now why
doesnt the NYSE TRIN not show such a positively sloping line? We cannot
answer this question. It could be due to nature of the set of stocks taken to
calculate the NYSE TRIN. We tried to replicate this NYSE TRIN but we
encountered problems in determining exactly what is used in the calculation.
Looking at the WSJ page for the TRIN we couldnt confirm or verify the volume
being used in the calculation of their TRIN when we compare the official volume
with the CBOE page for daily volume. The volumes dont line up, so we are lost
at how exactly is the WSJ TRIN calculated. Their volume numbers are off by up
to 30% compared to the official exchange volume published on the CBOE. We
leave this as further work since its really a separate study.
Comparison with the Nasdaq Composite
We continue looking at the $TRIN and regular TRIN compared to further
indices. Here is a plot versus the NASDAQ composite %Change. The Nasdaq
Composite has around 3300 names and is also market-cap weighted just like
the S&P500.
Comparison with the Russell 2000
This following plot shows the $TRIN and regular TRIN versus the Russell 2000
index. The Russell 2000 is composed of 2000 small-cap names free-float
weighted.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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Comparison with the Dow Jones Industrial Average
Here is a plot versus the Dow Jones Industrial Average which comprises 30
names and is price-weighted as compared to market cap weighted. You see the
relationship between the TRIN of 2700 names break down when mapped
against the 30 name DJIA. This is very likely due to the price-weighting of the
index which gives more weight to the index to stocks with bigger stock prices
as opposed to market caps.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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Comparison with the MSCI World
How does the $TRIN look like if we take the global stock market into account
and normalize all stock prices in USD and all notionals in USD. We are
comparing our global population of 4012 names with the MSCI World which
covers around 4500 stocks globally and is also market cap weighted.
You can again see a marked improvement in the negative slope of the linear
interpolation and a more pronounced wedge shaped cloud of data similar to
Richard Arms plot above.
We want to have a quick look an plot the three MSCI World ETF trackers
against the $TRIN and see what it looks like for those three ETFs against our
$TRIN. In theory they should all be identical.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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Comparison with the MSCI Hong Kong
Here is a plot of the $TRIN and regular TRIN for the Hong Kong stock market
compared to the ishares MSCI H0ng Kong ETF (EWH). It is not very pronounced
in this case but still the slopes are negative. The EWH is one of the oldest
country based ETF and comprises 53 names and is market cap weighted
compare this to our population of 81, it looks like smaller populations lead to
more noise.
Comparison with the MSCI Germany
Looking at the $TRIN and regular TRIN for the German stock market and
comparing this to the iShares MSCI Germany ETF (EWG) we get this chart. This
chart shows a very clear wedge shaped structure and both charts of the regular
and $TRIN are negatviely sloped and wedge-like, but you you clearly see the
wedge shape is more pronounced for the $TRIN. The MSCI Germany comprises
71 names market cap weighted and we compare it to our population of 161 the
noise is a lot less here and there is a clear relationship between them.

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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The $Arms and $TRIN time series
In the following we will chart some of the $TRIN time series. We plot three
moving averages (5, 10 and 100 day) and plot the 85% and 99.7% probability
averaged over 200 values, similar to how we dealt with the regular TRIN in the
first part of research here.
You can see the period around December 2018/ January 2019 is a lot more
pronounced towards the SELL side than before and we know from the charts
above it is working a lot better than non-normalized. Lets look further back
into the past we get this

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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Here you can see the Feb 2018 selloff peak very very clearly as a very extreme
level. So high that even the 5 day and 10 day average get pulled beyond a 97%
probability level. We also see the peak in September 2018 which is also a
significant date which kind of set the start off a broader selloff that peaked in
December/January of 2018/2019.
Following are a couple more charts of the $TRIN time series for different
regions. First the global $TRIN timeseries
the $TRIN for Germany

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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and Taiwan and Australia.
Conclusion
Based on the analysis of the conventional Arms Index (TRIN) calculation (Part 1)
we have deduced an improved version of the TRIN, which we showcase here
and compare it to data of the conventional TRIN. We show how a regular
weighted TRIN leads to a lot more noise given any number of stock underlyings
and leads to a more or less useless sloping data set and show that the improved
dollar weighted notional traded $TRIN has the expected behaviour of the TRIN
and doesnt lead to such distortions through price-effects. Furthermore we
expose flaws in the common published values for the TRIN (WSJ) and warn of
the dangers of using the commonly published figures, based on inconsistent
figures and a flawed weighting of the index.
References
[1] "The Arms Index" Richard W Arms Jr.
[2] "The New Arms Index Course" Richard Arms DVD Oct 2008

“The $Arms Index aka $Trin” Andreas A. Aigner & Walter Schrabmair, 25 Sep 2019
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[3] https://www.wsj.com/market-data/stocks/marketsdiary
[4] https://markets.cboe.com/us/equities/market_share/
[5] List of NYSE stocks http://www.eoddata.com/symbols.aspx
[6] List of NYSE stocks ftp://ftp.nasdaqtrader.com/symboldirectory/