True strength index
The True Strength Index (TSI) is a technical analysis indicator that functions as a momentum oscillator, designed to assess the strength and direction of price trends in financial securities by applying double exponential moving averages to price momentum data.[1] Developed to reduce noise and whipsaws compared to other momentum indicators like the Relative Strength Index (RSI), the TSI normalizes price changes relative to their volatility, producing values that oscillate between -100 and +100, with readings above +25 commonly indicating potential overbought conditions and below -25 suggesting oversold states.[2] This makes it particularly useful for identifying trend persistence, reversals, and divergences in stocks, forex, commodities, and other markets across various time frames, from intraday to long-term charts.[3] The TSI was created by William Blau, a technical analyst and trader, and first introduced in the November 1991 issue of Stocks & Commodities magazine, where it was presented as a refined tool for capturing underlying momentum without excessive short-term fluctuations.[1] Blau later expanded on the indicator in his 1995 book Momentum, Direction, and Divergence: Applying the Latest Momentum Indicators for Technical Analysis, emphasizing its role in quantifying the "true" strength of price movements by smoothing out irregularities in raw momentum data.[4] Unlike single-smoothed oscillators, the TSI's double-smoothing approach—typically using a 25-period exponential moving average (EMA) followed by a 13-period EMA—provides a more stable signal, making it suitable for confirming trends in volatile environments while minimizing false signals.[5] To calculate the TSI, the process begins with computing the momentum as the difference between the current closing price and the previous closing price, followed by applying a 25-period EMA to both this momentum value and its absolute counterpart to create smoothed lines.[6] These smoothed values are then further refined with a 13-period EMA, and the TSI is derived by dividing the double-smoothed momentum by the double-smoothed absolute momentum and multiplying by 100, yielding the final oscillator value.[7] A signal line, often a 7-period simple moving average (SMA) or EMA of the TSI itself, is commonly overlaid to generate buy or sell signals through crossovers.[5] In practice, traders interpret the TSI by monitoring its position relative to the zero centerline: values crossing above zero signal bullish momentum, while those below indicate bearish conditions, with extreme deviations from this line highlighting potential reversal points.[3] Bullish divergences occur when the TSI forms higher lows while prices make lower lows, suggesting weakening downward pressure, whereas bearish divergences show the opposite pattern.[7] The indicator's lagging nature due to smoothing can delay signals but enhances reliability in trending markets; it is often combined with other tools like moving averages or volume indicators for confirmation, and its parameters can be adjusted (e.g., shorter periods for day trading) to suit specific strategies.[5] Overall, the TSI remains a valued component in technical analysis for its balance of sensitivity and stability, aiding in both trend-following and contrarian approaches.[1]Introduction
Definition and Purpose
The True Strength Index (TSI) is a double-smoothed momentum oscillator that quantifies the rate of price change to assess trend strength and potential reversals in financial markets. Developed by William Blau in the 1990s, it applies exponential moving averages twice to momentum data, distinguishing it from simpler indicators by emphasizing sustained price movements over short-term fluctuations.[8][3] The primary purpose of the TSI is to filter noise from price data more effectively than single-smoothed momentum indicators, delivering refined signals for identifying overbought and oversold conditions while confirming ongoing trends. This makes it particularly valuable for traders analyzing volatile assets like stocks, forex, and commodities, where raw momentum can be misleading due to market noise.[1][9] The TSI oscillates within a bounded range of typically -100 to +100 and is centered at zero, allowing users to interpret positive values as bullish momentum and negative values as bearish, with extremes signaling potential exhaustion or reversal points in technical analysis.[10]Historical Development
The True Strength Index (TSI) was developed by William Blau, a prominent technical analyst and futures trader, in the early 1990s as a refined tool for assessing market momentum. Blau, who held a background in engineering and applied his expertise to financial indicators,[11] aimed to create an oscillator that could more effectively capture price trends while minimizing erratic signals common in volatile markets.[12] The indicator was first published in the November 1991 issue of Technical Analysis of Stocks & Commodities magazine, in an article simply titled "True Strength Index." In this seminal piece, Blau outlined the TSI's core methodology, emphasizing its ability to measure the relative strength of price movements through advanced smoothing techniques. This publication marked the TSI's introduction to the broader trading community, where it was positioned as an improvement over predecessors like the Relative Strength Index (RSI), which Blau critiqued for its sensitivity to short-term noise; the TSI addressed this by applying double exponential smoothing to both momentum and its absolute value, yielding clearer trend signals.[13][3] Following its debut, the TSI evolved through practical integrations and further documentation. Blau expanded on its applications in his 1995 book Momentum, Direction, and Divergence: Applying the Latest Momentum Indicators for Technical Analysis, where he detailed trading strategies and parameter optimizations, solidifying the indicator's role in momentum-based analysis. By the 2000s, the TSI had been incorporated into popular trading software, including MetaStock—where users began sharing custom formulas for its implementation—and later TradingView, which added it as a built-in oscillator to facilitate accessibility for retail and professional traders alike. These adaptations ensured the TSI's enduring relevance in technical analysis up to the present day.[14][6]Technical Formulation
Key Components
The True Strength Index (TSI) relies on foundational elements derived from price momentum to assess the strength and direction of market trends. Central to its construction is the price change (PC), defined as the difference between the current closing price and the previous closing price: PC_t = \text{Close}_t - \text{Close}_{t-1}. This raw momentum measure captures short-term price movements without additional filtering.[1] To account for the magnitude of these changes regardless of direction, the TSI incorporates the absolute price change (APC), calculated as the absolute value of PC: APC_t = |PC_t|. APC normalizes momentum by focusing on the intensity of price shifts, providing a basis for relative strength comparisons.[6] Smoothing is achieved through exponential moving averages (EMAs), which apply greater weight to recent data to reduce noise while retaining responsiveness. The EMA formula is given by: EMA_t = \alpha \cdot \text{Value}_t + (1 - \alpha) \cdot EMA_{t-1} where \alpha = \frac{2}{N + 1} and N is the smoothing period. This recursive structure ensures that older values influence the average exponentially less over time.[1] The core smoothing mechanism in TSI is double smoothing, involving the sequential application of two EMAs. First, an EMA with period r is computed on the PC (and separately on the APC) to dampen volatility. Then, a second EMA with period s is applied to the output of the first EMA, further refining the signal by eliminating short-term fluctuations while preserving underlying momentum trends. This layered approach enhances the indicator's sensitivity to sustained price movements.[5] Standard parameters for these EMAs are typically r = 25 for the first smoothing and s = 13 for the second, as originally suggested by developer William Blau. These values balance noise reduction and signal timeliness for daily charts, though shorter periods (e.g., r = 7, s = 5) may be used for intraday analysis to adapt to faster timeframes.[6]Step-by-Step Calculation
The True Strength Index (TSI) is computed using double-smoothed exponential moving averages (EMAs) applied to price changes and their absolute values, resulting in the following formula:\text{TSI} = 100 \times \frac{\text{Double-Smoothed PC}}{\text{Double-Smoothed APC}}
where Double-Smoothed PC = EMA_s(EMA_r(PC)) and Double-Smoothed APC = EMA_s(EMA_r(APC)), with PC denoting the price change, APC the absolute price change, r the first smoothing period (typically 25), and s the second smoothing period (typically 13).[1][15] To derive the TSI value for each period, follow these sequential steps:
- Compute the Price Change (PC) and Absolute Price Change (APC): For each period n, calculate PC_n = Close_n - Close_{n-1}, and APC_n = |PC_n|. This captures the raw momentum in price movements.[1][16]
- Apply the First EMA Smoothing: Compute the first EMA with period r on the PC series to obtain EMA_r(PC), and separately on the APC series to obtain EMA_r(APC). The EMA formula is EMA_t = \alpha \times Value_t + (1 - \alpha) \times EMA_{t-1}, where \alpha = 2 / (r + 1). This step reduces noise in the initial momentum data.[1][15]
- Apply the Second EMA Smoothing: Compute the second EMA with period s on the results from Step 2, yielding Double-Smoothed PC = EMA_s(EMA_r(PC)) and Double-Smoothed APC = EMA_s(EMA_r(APC)). Using \beta = 2 / (s + 1), this further smooths the series to emphasize sustained trends.[1][16]
- Normalize to Percentage Scale: Divide the Double-Smoothed PC by the Double-Smoothed APC and multiply by 100 to produce the TSI value, which oscillates around zero as a percentage-like measure of momentum strength.[1][15]