If you spend enough time with market technicians, chances are that you’ll hear them talking about TRIN. What they’re referring to is the so called Arms’ Index. Created by Richard W. Arms Jr. in the 1960s, the Arms’ Index, is one of the most popular breadth indicators out there. Its approach is simple, but yet, quite effective: By compressing two dimensions of market breadth, namely participation and intensity, into a single ratio, the indicator provides a snapshot of market pressure efficiency. Its formula is deceptively simple: TRIN is calculated as the ratio of advancing to declining issues divided by the ratio of advancing to declining volume. When the TRIN value is below 1, it indicates bullish pressure as volume disproportionately supports advancing stocks. Conversely, values above 1 suggest bearish pressure, with extreme readings above 1.5 traditionally signaling panic selling, and values below 0.7 indicating a buying climax.
However, from a purely mathematical standpoint, TRIN’s formula has its own set of issues. In this article we will review these issues and propose solutions to them
A Double Division: Does It Make Sense?
As mentioned earlier, TRIN’s formula contains a double division. If we follow a mathematical approach to the double division, we arrive at this formula:
TRIN = Advancing Stocks * Declining Volume / Declining Stocks * Advancing Volume
Now let us move another step forward, in the same algebric fashion. If we rearrange the formula, we get this version:
TRIN = Average Volume per Declining Issue / Average Volume per Advancing Issue
If we would like to describe this version of TRIN’s formula, we could say that TRIN measures how concentrated is the trading activity in advancing or declining stocks. In reality, Arms’ Index shows us if trading activity is evenly distributed across the market’s issues. Now, for the sake of illustration, let us assume two hypothetical examples. In the first example, 70% of a market’s stocks are rising, with their trading activity representing 70% of total trading activity for the day. In this case, we would have a strong participation day in which TRIN should show a neutral reading around 1.
In our second example, let use consider a market, in which, during a specific trading day, 55% of its total issues rise but with 80% of the total volume for the day going into them. It is obvious that in our second example, we have an imbalance between the number of issues and their respective volume. However, in this case, TRIN would signal a more bullish market, as it would be well below 1.
However, if you ask 10 traders out there, in which example they think the market is more bullish, chances are you’re going to get mixed answers. On the other hand, TRIN has already decided: In our second example the market is more bullish, and that happens because it measures average volume per stock group and their relationship. However, the existence of an imbalance in this relationship doesn’t always point to a strong market.
A Division That Wanted To Become Multiplication
Now let’s revisit the first variation of TRIN’s formula:
TRIN = Advancing Stocks * Declining Volume / Declining Stocks * Advancing Volume
Now imagine a market which receives some great news. Let’s say an armed conflict has ended (or started), or an institutional credit rating has been upgraded, or non-farm payrolls announcement was better than expected. In all these scenarios, volume spikes should be anticipated. In such cases, Arms’ Index moves dramatically in either direction and its interpretation isn’t to be trusted. If we also add the capitalization concentration that is found in most famous indices today, we can see how this issue is further exaggerated.
A subtle but critical issue is the mathematical instability of TRIN’s formula. When declining volume approaches zero, TRIN can spike dramatically even if market pressure is not extreme. One solution to this problem would be to apply a logarithmic transformation, which will stabilize the distribution, making TRIN symmetric around zero and variance more manageable. This transformation also improves comparability across market regimes and avoids overreaction to low liquidity issues. By calculating ln(TRIN), extreme values are compressed, sensitivity to small denominator changes is reduced and distribution around zero is normalized. Positive values indicate selling pressure, negative values indicate buying pressure, and the scale becomes more consistent across different liquidity regimes.
Another, much simpler solution to the problem would be to smooth TRIN’s movements using a moving average. This is actually a very effective strategy to filter out such spikes. In addition, using an alternative breadth indicator, such as Advance / Decline Line, as a complementary tool, could work wonders in gauging long term market breadth and not being caught in TRIN’s wide fluctuations.
Bottom Line
In conclusion, Arms’ Index hasn’t lost its relevance, although market transformation through the years has changed the way it should be interpreted. Its core purpose remains measuring how efficiently capital commits to market direction. By knowing its structural deficiencies and how to treat them, we can keep using a valuable tool that many consider outdated.
