What Is the Arms Index (TRIN)?

The Arms Index, also called the Short-Term Trading Index (TRIN) is a technical analysis indicator that compares the number of advancing and declining stocks (AD Ratio) to advancing and declining volume (AD volume). It is used to gauge overall market sentiment. Richard W. Arms, Jr. invented it in 1967, and it measures the relationship between market supply and demand. It serves as a predictor of future price movements in the market, primarily on an intraday basis. It does this by generating overbought and oversold levels, which indicate when the index (and the majority of stocks in it) will change direction.

The Formula for Arms Index (TRIN) is:


$\begin{aligned} &\text{TRIN}\ =\ \frac{\text{Advancing Stocks/Declining Stocks}}{\text{Advancing Volume/Declining Volume}}\\ &\textbf{where:}\\ & \begin{aligned} \text{Advancing Stocks}\ =\ &\text{Number of stocks that are higher}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Declining Stocks}\ =\ &\text{Number of stocks that are lower}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Advancing Volume}\ =\ &\text{Total volume of all advancing}\\ &\text{stocks}\end{aligned}\\ &\begin{aligned}\text{Declining Volume}\ =\ &\text{Total volume of all declining}\\ &\text{stocks}\end{aligned} \end{aligned}$​TRIN = Advancing Volume/Declining VolumeAdvancing Stocks/Declining Stocks​where:Advancing Stocks = ​Number of stocks that are higher​Declining Stocks = ​Number of stocks that are lower​Advancing Volume = ​Total volume of all advancing​​

How to Calculate the Arms Index (TRIN)

TRIN is provided in many charting applications. To calculate by hand, use the following steps.

1. At set intervals, such as every five minutes or daily (or whatever interval is chosen), find the AD Ratio by dividing the number of advancing stocks by the number of declining stocks.
2. Divide total advancing volume by total declining volume to get AD Volume.
3. Divide the AD Ratio by AD Volume.
4. Record the result and plot on a graph.
5. Repeat the calculation at the next chosen time interval.
6. Connect multiple data points to form a graph and see how the TRIN moves over time.

What Does the Arms Index (TRIN) Tell You?

The Arms index seeks to provide a more dynamic explanation of overall movements in the composite value of stock exchanges, such as the NYSE or NASDAQ, by analyzing the strength and breadth of these movements.

An index value of 1.0 indicates that the ratio of AD Volume is equal to the AD Ratio. The market is said to be in a neutral state when the index equals 1.0, since the up volume is evenly distributed over the advancing issues and the down volume is evenly distributed over the declining issues.

Many analysts believe that the Arms Index provides a bullish signal when it’s less than 1.0, since there’s greater volume in the average up stock than the average down stock. In fact, some analysts have found that the long-term equilibrium for the index is below 1.0, potentially confirming that there is a bullish bias to the stock market.

On the other hand, a reading of greater than 1.0 is typically seen as a bearish signal, since there’s greater volume in the average down stock than the average up stock.

The farther away from 1.00 the Arms Index value is, the greater the contrast between buying and selling on that day. A value that exceeds 3.00 indicates an oversold market and that bearish sentiment is too dramatic. This could mean an upward reversal in prices/index is coming.

Conversely, a TRIN value that dips below 0.50 may indicate an overbought market and that bullish sentiment is overheating.

Traders look not only at the value of the indicator but also at how it changes throughout the day. They look for extremes in the index value for signs that the market may soon change directions.

The Difference Between the Arms Index (TRIN) and the Tick Index (TICK)

TRIN compares the number of advancing and declining stocks to the volume in both advancing and declining stocks. The Tick index compares the number of stocks making an uptick to the number of stocks making a downtick. The Tick Index is used to gauge intraday sentiment. The Tick Index does not factor volume, but extreme readings still signal potentially overbought or oversold conditions.

Limitations of Using the Arms Index (TRIN)

The Arms Index has a few mathematical peculiarities that traders and investors should be aware of when using it. Since the index emphasizes volume, inaccuracies arise when there isn’t as much advancing volume in advancing issues as expected. This may not be a typical situation, but it’s a situation that can arise and could potentially make the indicator unreliable.

Here are two examples of instances where problems may occur:

• Suppose that a very bullish day occurs where there are twice as many advancing issues as declining issues and twice as much advancing volume as declining volume. Despite the very bullish trading, the Arms Index would yield only a neutral value of (2/1)/(2/1) = 1.0, suggesting that the index’s reading may not be entirely accurate.
• Suppose that another bullish scenario occurs where there are three times as many advancing issues as declining issues and twice as much advancing volume than declining volume. In this case, the Arms Index would actually yield a bearish (3/1)/(2/1) = 1.5 reading, again suggesting an inaccuracy.

One way to solve this problem would be to separate the two components of the indicator into issues and volume instead of using them in the same equation. For instance, advancing issues divided by declining issues could show one trend, while advancing volume over declining volume could show a separate trend. These ratios are called the advance/decline ratio and upside/downside ratio, respectively. Both of these could be compared to tell the market’s true story.

What Is the 30-Year Treasury?

The 30-Year Treasury is a U.S. Treasury debt obligation that has a maturity of 30 years. The 30-year Treasury used to be the bellwether U.S. bond but now most consider the 10-year Treasury to be the benchmark.

Understanding the 30-Year Treasury

The U.S. government borrows money from investors by issuing debt securities through its Treasury department. Debt instruments that can be purchased from the government include Treasury bills (T-bills), notes, and Treasury Inflation-Protected Securities (TIPS). T-bills are marketable securities issued for terms of less than a year, and Treasury notes are issued with maturities from two to 10 years.

TIPS are marketable securities whose principal is adjusted by changes in the Consumer Price Index (CPI). When there is inflation, the principal increases. When deflation sets in, the principal decreases. U.S. Treasury securities with longer-term maturities can be purchased as U.S. Savings bonds or Treasury bonds.

Special Considerations

Treasury bonds are long-term debt securities issued with a maturity of 20 years or 30 years from the issue date. These marketable securities pay interest semi-annually, or every six months until they mature. At maturity, the investor is paid the face value of the bond. The 30-year Treasury will generally pay a higher interest rate than shorter Treasuries to compensate for the additional risks inherent in the longer maturity. However, when compared to other bonds, Treasuries are relatively safe because they are backed by the U.S. government.

The price and interest rate of the 30-year Treasury bond is determined at an auction where it is set at either par, premium, or discount to par. If the yield to maturity (YTM) is greater than the interest rate, the price of the bond will be issued at a discount. If the YTM is equal to the interest rate, the price will be equal to par. Finally, if the YTM is less than the interest rate, the Treasury bond price will be sold at a premium to par. In a single auction, a bidder can buy up to $5 million in bonds by non-competitive bidding or up to 35% of the initial offering amount by competitive bidding. In addition, the bonds are sold in increments of $100 and the minimum purchase is $100.

30-Year Treasury vs. Savings Bonds

U.S. Savings bonds, specifically, Series EE Savings bonds, are non-marketable securities that earn interest for 30 years. Interest isn’t paid out periodically. Instead, interest accumulates, and the investor receives everything when they redeem the savings bond. The bond can be redeemed after one year, but if they are sold before five years from the purchase date, the investor will lose the last three months’ interest. For example, an investor who sells the Savings bond after 24 months will only receive interest for 21 months.

Because the U.S. is seen as a very low-risk borrower, many investors see 30-year Treasury interest rates as indicative of the state of the wider bond market. Normally, the interest rate decreases with greater demand for 30-year Treasury securities and rises with lower demand. The S&P U.S. Treasury Bond Current 30-Year Index is a one-security index comprising the most recently issued 30-year U.S. Treasury bond. It is a market value-weighted index that seeks to measure the performance of the Treasury bond market.

What Is the Advance/Decline (A/D) Line?

The advance/decline line (or A/D line) is a technical indicator that plots the difference between the number of advancing and declining stocks on a daily basis. The indicator is cumulative, with a positive number being added to the prior number, or if the number is negative it is subtracted from the prior number.

The A/D line is used to show market sentiment, as it tells traders whether there are more stocks rising or falling. It is used to confirm price trends in major indexes, and can also warn of reversals when divergence occurs.

The Formula for Advance/Decline (A/D) Line Is:


$\begin{aligned} &\text{A/D} = \text{Net Advances} + \begin{cases} \text{PA, if PA value exists} \\ \text{0, if no PA value} \\ \end{cases} \\ &\textbf{where:} \\ &\text{Net Advances} = \text{Difference between number of daily} \\ &\text{ascending and declining stocks} \\ &\text{PA} = \text{Previous Advances} \\ &\text{Previous Advances} = \text{Prior indicator reading} \\ \end{aligned}$​A/D=Net Advances+{PA, if PA value exists0, if no PA value​where:Net Advances=Difference between number of dailyascending and declining stocksPA=Previous AdvancesPrevious Advances=Prior indicator reading​

How to Calculate the A/D Line

1. Subtract the number of stocks that finished lower on the day from the number of stocks that finished higher on the day. This will give you the Net Advances.
2. If this is the first time calculating the average, the Net Advances will be the first value used for the indicator.
3. On the next day, calculate the Net Advances for that day. Add to the total from the prior day if positive or subtract if negative.
4. Repeat steps one and three daily.

What Does the A/D Line Tell You?

The A/D line is used to confirm the strength of a current trend and its likelihood of reversing. The indicator shows if the majority of stocks are participating in the direction of the market. 

If the indexes are moving up but the A/D line is sloping downwards, called bearish divergence, it’s a sign that the markets are losing their breadth and may be about to reverse direction. If the slope of the A/D line is up and the market is trending upward, then the market is said to be healthy.

Conversely, if the indexes are continuing to move lower and the A/D line has turned upwards, called bullish divergence, it may be an indication that the sellers are losing their conviction. If the A/D line and the markets are both trending lower together, there is a greater chance that declining prices will continue.

Difference Between the A/D Line and Arms Index (TRIN)

The A/D line is typically used as a longer-term indicator, showing how many stocks are rising and falling over time. The Arms Index (TRIN), on the other hand, is typically a shorter-term indicator that measures the ratio of advancing stocks to the ratio of advancing volume. Because the calculations and the time frame they focus on are different, both these indicators tell traders different pieces of information.

Limitations of Using the A/D Line

The A/D line won’t always provide accurate readings in regards to NASDAQ stocks. This is because the NASDAQ frequently lists small speculative companies, many of which eventually fail or get delisted. While the stocks get delisted on the exchange, they remain in the prior calculated values of the A/D line. This then affects future calculations which are added to the cumulative prior value. Because of this, the A/D line will sometimes fall for extended periods of time, even while NASDAQ-related indexes are rising.

Another thing to be aware of is that some indexes are market capitalization weighted. This means that the bigger the company the more impact they have on the index’s movement. The A/D line gives equal weight to all stocks. Therefore, it is a better gauge of the average small to mid-cap stock, and not the fewer in number large or mega-cap stocks.

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What Is Alpha?

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market, or its “edge.” Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market’s overall volatility or risk, known as systematic market risk.

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Understanding Alpha

Alpha is one of five popular technical investment risk ratios. The others are beta, standard deviation, R-squared, and the Sharpe ratio. These are all statistical measurements used in modern portfolio theory (MPT). All of these indicators are intended to help investors determine the risk-return profile of an investment.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

In other words, alpha is the return on an investment that is not a result of a general movement in the greater market. As such, an alpha of zero would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any additional value compared to the broad market.

The concept of alpha became more popular with the advent of smart beta index funds tied to indexes like the Standard & Poor’s 500 index and the Wilshire 5000 Total Market Index. These funds attempt to enhance the performance of a portfolio that tracks a targeted subset of the market.

Despite the considerable desirability of alpha in a portfolio, many index benchmarks manage to beat asset managers the vast majority of the time. Due in part to a growing lack of faith in traditional financial advising brought about by this trend, more and more investors are switching to low-cost, passive online advisors (often called roboadvisors​) who exclusively or almost exclusively invest clients’ capital into index-tracking funds, the rationale being that if they cannot beat the market they may as well join it.

Moreover, because most “traditional” financial advisors charge a fee, when one manages a portfolio and nets an alpha of zero, it actually represents a slight net loss for the investor. For example, suppose that Jim, a financial advisor, charges 1% of a portfolio’s value for his services and that during a 12-month period Jim managed to produce an alpha of 0.75 for the portfolio of one of his clients, Frank. While Jim has indeed helped the performance of Frank’s portfolio, the fee that Jim charges is in excess of the alpha he has generated, so Frank’s portfolio has experienced a net loss. For investors, the example highlights the importance of considering fees in conjunction with performance returns and alpha.

The Efficient Market Hypothesis (EMH) postulates that market prices incorporate all available information at all times, and so securities are always properly priced (the market is efficient.) Therefore, according to the EMH, there is no way to systematically identify and take advantage of mispricings in the market because they do not exist.

If mispricings are identified, they are quickly arbitraged away and so persistent patterns of market anomalies that can be taken advantage of tend to be few and far between.

Empirical evidence comparing historical returns of active mutual funds relative to their passive benchmarks indicates that fewer than 10% of all active funds are able to earn a positive alpha over a 10-plus year time period, and this percentage falls once taxes and fees are taken into consideration. In other words, alpha is hard to come by, especially after taxes and fees.

Because beta risk can be isolated by diversifying and hedging various risks (which comes with various transaction costs), some have proposed that alpha does not really exist, but that it simply represents the compensation for taking some un-hedged risk that hadn’t been identified or was overlooked.

Seeking Investment Alpha

Alpha is commonly used to rank active mutual funds as well as all other types of investments. It is often represented as a single number (like +3.0 or -5.0), and this typically refers to a percentage measuring how the portfolio or fund performed compared to the referenced benchmark index (i.e., 3% better or 5% worse).

Deeper analysis of alpha may also include “Jensen’s alpha.” Jensen’s alpha takes into consideration the capital asset pricing model (CAPM) market theory and includes a risk-adjusted component in its calculation. Beta (or the beta coefficient) is used in the CAPM, which calculates the expected return of an asset based on its own particular beta and the expected market returns. Alpha and beta are used together by investment managers to calculate, compare, and analyze returns.

The entire investing universe offers a broad range of securities, investment products, and advisory options for investors to consider. Different market cycles also have an influence on the alpha of investments across different asset classes. This is why risk-return metrics are important to consider in conjunction with alpha.

Examples

This is illustrated in the following two historical examples for a fixed income ETF and an equity ETF:

The iShares Convertible Bond ETF (ICVT) is a fixed income investment with low risk. It tracks a customized index called the Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index. The 3-year standard deviation was 18.94%, as of Feb. 28, 2022. The year-to-date return, as of Feb. 28, 2022, was -6.67%. The Bloomberg U.S. Convertible Cash Pay Bond > $250MM Index had a return of -13.17% over the same period. Therefore, the alpha for ICVT was -0 12% in comparison to the Bloomberg U.S. Aggregate Index and a 3-year standard deviation of 18.97%.

However, since the aggregate bond index is not the proper benchmark for ICVT (it should be the Bloomberg Convertible index), this alpha may not be as large as initially thought; and in fact, may be misattributed since convertible bonds have far riskier profiles than plain vanilla bonds.

The WisdomTree U.S. Quality Dividend Growth Fund (DGRW) is an equity investment with higher market risk that seeks to invest in dividend growth equities. Its holdings track a customized index called the WisdomTree U.S. Quality Dividend Growth Index. It had a three-year annualized standard deviation of 10.58%, higher than ICVT.

As of Feb. 28, 2022, DGRW annualized return was 18.1%, which was also higher than the S&P 500 at 16.4%, so it had an alpha of 1.7% in comparison to the S&P 500. But again, the S&P 500 may not be the correct benchmark for this ETF, since dividend-paying growth stocks are a very particular subset of the overall stock market, and may not even be inclusive of the 500 most valuable stocks in America.

Alpha Considerations

While alpha has been called the “holy grail” of investing, and as such, receives a lot of attention from investors and advisors alike, there are a couple of important considerations that one should take into account when using alpha.

1. A basic calculation of alpha subtracts the total return of an investment from a comparable benchmark in its asset category. This alpha calculation is primarily only used against a comparable asset category benchmark, as noted in the examples above. Therefore, it does not measure the outperformance of an equity ETF versus a fixed income benchmark. This alpha is also best used when comparing the performance of similar asset investments. Thus, the alpha of the equity ETF, DGRW, is not relatively comparable to the alpha of the fixed income ETF, ICVT.
2. Some references to alpha may refer to a more advanced technique. Jensen’s alpha takes into consideration CAPM theory and risk-adjusted measures by utilizing the risk-free rate and beta.

When using a generated alpha calculation it is important to understand the calculations involved. Alpha can be calculated using various different index benchmarks within an asset class. In some cases, there might not be a suitable pre-existing index, in which case advisors may use algorithms and other models to simulate an index for comparative alpha calculation purposes.

Alpha can also refer to the abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like CAPM. In this instance, a CAPM model might aim to estimate returns for investors at various points along an efficient frontier. The CAPM analysis might estimate that a portfolio should earn 10% based on the portfolio’s risk profile. If the portfolio actually earns 15%, the portfolio’s alpha would be 5.0, or +5% over what was predicted in the CAPM model.