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“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/