# True Strength Index (TSI): Formula, Calculations, and Interpretation

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## What Is the True Strength Index (TSI)?

The true strength index (TSI) is a technical momentum [oscillator](https://www.investopedia.com/terms/o/oscillator.asp) used by technical analysts. The true strength index is used to identify trends and reversals in the market. The indicator may determine [overbought and oversold](https://www.investopedia.com/ask/answers/121214/what-are-best-indicators-identify-overbought-and-oversold-stocks.asp) conditions, indicate potential trend direction changes via centerline or signal line crossovers, and warn traders of trend weakness that may occur through [divergence](https://www.investopedia.com/terms/d/divergence.asp).

### Key Takeaways

*   The true strength index is a technical momentum oscillator used by technical analysts to identify market trends and reversals.
*   The TSI fluctuates between positive (bullish) and negative (bearish) territory.
*   When the indicator divergences with price, the TSI may be signaling the price trend is weakening and may reverse.
*   When the TSI crosses above the signal line, it can be used as a buy signal, and when it crosses below, a sell signal.
*   Overbought and oversold levels will vary by the asset being traded.

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## Formula and How to Calculate the True Strength Index (TSI)

The formula for calculating the TSI involves the following steps.

$\begin{aligned} &\text{TSI = (PCDS/APCDS) x 100}\\ &\text{PC = CCP }-\text{ PCP}\\ &\text{PCS = 25-period EMA of PC}\\ &\text{PCDS = 13-period EMA of PCS}\\ &\text{APC = AVCCP }-\text{ PCP}\\ &\text{APCS = 25-period EMA of APC}\\ &\text{APCDS = 13-period EMA of APCS}\\ &\textbf{where:}\\ &\text{PCDS = PC double smoothed}\\ &\text{APCDS = Absolute PC double smoothed}\\ &\text{PC = Price change}\\ &\text{CCP = Current close price}\\ &\text{PCP = Prior close price}\\ &\text{PCS = PC smoothed}\\ &\text{EMA = Exponential moving average}\\ &\text{APC = Absolute PC}\\ &\text{APCS = Absolute PC smoothed}\\ \end{aligned}$

The main skill required in computing the TSI is the ability to [calculate an exponential moving average (EMA)](https://www.investopedia.com/ask/answers/122314/what-exponential-moving-average-ema-formula-and-how-ema-calculated.asp).

1.  Record price changes and absolute price changes to calculate an EMA for both these values.
2.  Calculate the price change 25-period EMA and the absolute price change 25-period EMA.
3.  Smooth both of these EMAs by applying a 13-period EMA to each of them.
4.  Compute the TSI value by plugging the now double-smoothed price change and double-smoothed absolute price change into the TSI formula.

## How the TSI Works

[Technical analysis](https://www.investopedia.com/terms/t/technicalanalysis.asp) is a trading strategy that is used by certain traders to identify entry and exit opportunities. This is done by researching and evaluating the past performance of an [asset](https://www.investopedia.com/terms/a/asset.asp), security, or market and making predictions about its direction. Traders use different tools and techniques to pinpoint opportunities. This includes the true strength index, which was created by author and trader William Blau in 1991.

The TSI is an oscillator that measures the strength of an asset or market's price movement over time as well as any directions in that price. The index is primarily used to identify overbought and oversold conditions in an asset's price. It also helps traders spot divergence, identify [trend](https://www.investopedia.com/terms/t/trend.asp) direction and changes via the centerline, and highlight short-term price momentum with [signal line](https://www.investopedia.com/terms/s/signal_line.asp) crossovers.

Since the TSI is based on price movements, oversold and overbought levels tend to vary according to the asset being traded. Some stocks may reach +30 and -30 before tending to see [price reversals](https://www.investopedia.com/terms/r/reversal.asp), while other stocks may reverse near +20 and -20.

On the asset being traded, trades can mark extreme TSI levels to see the points that represent where assets are overbought and oversold. Traders typically watch for other signals to trigger a trade decision. For example, they may wait for the price or TSI to start dropping before selling in overbought territory. Alternatively, they may wait for a signal line [crossover](https://www.investopedia.com/terms/c/crossover.asp).

> **Important**
>
> Being oversold doesn't necessarily mean it is time to buy, and when an asset is overbought it doesn't necessarily mean it is time to sell.

## How to Interpret the TSI

As noted above, the TSI can help traders identify trends and patterns based on different levels, crossovers, and divergence. Below, we explain how it applies to signal line crossovers and centerline crossovers as well as [breakouts](https://www.investopedia.com/terms/b/breakout.asp) and divergence.

### Signal Line Crossovers

The TSI has a signal line, which is usually a seven- to 12-period EMA of the TSI line. A signal line crossover occurs when the TSI line crosses the signal line. When the TSI crosses above the signal line from below, that may warrant a [long position](https://www.investopedia.com/terms/l/long.asp). When the TSI crosses below the signal line from above, that may warrant selling or [short selling](https://www.investopedia.com/terms/s/shortselling.asp).

Signal line crossovers occur frequently, so should be utilized only in conjunction with other signals from the TSI. For example, buy signals may be favored when the TSI is above the centerline (above zero). Or [sell signals](https://www.investopedia.com/terms/s/sell-signal.asp) may be favored when the TSI is in overbought territory.

### Centerline Crossovers

The centerline crossover is another signal the TSI generates. Price [momentum](https://www.investopedia.com/terms/m/momentum.asp) is positive when the indicator is above zero and negative when it is below zero.

Some traders use the centerline for a directional [bias](https://www.investopedia.com/terms/b/bias.asp). For example, a trader may decide only to enter a long position if the indicator is above its centerline. Conversely, the trader would be bearish and only consider short positions if the indicator's value is below zero.

### Breakouts and Divergence

Traders can use support and resistance levels created by the TSI to identify [breakouts](https://www.investopedia.com/terms/b/breakout.asp) and price momentum shifts. For instance, if the indicator breaks below a [trendline](https://www.investopedia.com/terms/t/trendline.asp), the price may see continued selling.

Divergence is another tool the TSI provides. If the price of an asset is moving higher while the TSI is dropping, that is called [bearish](https://www.investopedia.com/terms/b/bear.asp) divergence and could result in a downside price move. Conversely, if the TSI is rising while the price is falling, that could signal higher prices to come. This is called bullish divergence.

Divergence is a poor [timing](https://www.investopedia.com/terms/m/markettiming.asp) signal, so it should only be used in conjunction with other signals generated by the TSI or other technical indicators.

> **Tip**
>
> The TSI should be used in conjunction with other forms of analysis, such as price action analysis and other technical indicators.

## The TSI vs. the Moving Average Convergence Divergence (MACD) Indicator

The TSI is just one tool that traders can use to identify trends, patterns, and changes in the market. Another tool commonly used by technical analysts is the [moving average convergence divergence (MACD)](https://www.investopedia.com/terms/m/macd.asp).

Both indicators are used in similar ways for trading purposes, yet they are not calculated the same and will provide different signals at different times. The TSI [smooths](https://www.investopedia.com/terms/d/data-smoothing.asp) price changes to create a technical oscillator. The MACD indicator, on the other hand, measures the separation between two moving averages.

## Limitations of the TSI

Many of the signals provided by the TSI are commonly [false signals](https://www.investopedia.com/terms/f/false-signal.asp). This means the price action will be different than expected following a trade signal. For example, during an [uptrend](https://www.investopedia.com/terms/u/uptrend.asp), the TSI may cross below the centerline several times, but then the price proceeds higher even though the TSI indicates momentum has shifted down.

Signal line crossovers also occur so frequently that they may not provide a lot of trading benefits. Such signals need to be heavily filtered based on other elements of the indicator or through other forms of analysis. The TSI will also sometimes change direction without the price changing direction, resulting in trade signals that look good on the TSI but continue to lose money based on price.

Divergence also tends to be unreliable on the indicator. Divergence can last so long that it provides little insight into when a reversal will occur. Keep in mind that divergence isn't always present when price reversals do occur.

## Who Created the True Strength Index?

The true strength index was created by author and trader William Blau. It was introduced in the _Stocks & Commodities_ magazine in November 1991. Blau commented on how it was "a smooth momentum indicator stripped of high-frequency noise useful for expressing the direction of market trends."

## What Is Technical Analysis?

Technical analysis is a trading discipline that uses different tools and techniques to identify trading patterns and trends in the market. Technical analysts use historical data, indexes, signals, graphs, and charts to make future predictions about the movement of assets and markets. it is the opposite of [fundamental analysis](https://www.investopedia.com/terms/f/fundamentalanalysis.asp), which measures an asset or market's fair value based on intrinsic factors, including financial and economic factors.

## How Do You Calculate the True Strength Index?

You can use the following steps to calculate the TSI:

1.  Record price and absolute price changes to calculate an exponential moving average for both values.
2.  Calculate the price change 25-period EMA and the absolute price change 25-period EMA.
3.  Apply a 13-period EMA to each to smooth them.

## The Bottom Line

The true strength index is a technical oscillator that can help you identify market trends, signals, and patterns. Using the formula above, you can calculate the TSI. But as with anything else, do your due diligence when using the TSI as part of your investment strategy. Do your research before you adopt any investment strategy or tool. When you're sure it fits your goals, make sure you combine it with other tools to help mitigate any losses.

> **Article Sources**
>
> 1.  Technical Analysis of Stocks & Commodities. "[V.10:5 (214-219): Trading With The True Strength Index by William Blau](https://store.traders.com/-v10-c05-trading-pdf.html)."