# Constance Brown Studies Also known as: Derivative Oscillator, Composite Index. A Momentum & Oscillators concept (Classic single-name oscillators) in the LuxAlgo Library, with 1 indicator implementation. ## What are the Constance Brown Studies? The Constance Brown Studies are a family of RSI-derived momentum tools from Constance Brown's Technical Analysis for the Trading Professional (1999), each built to repair a specific weakness of [RSI](https://www.luxalgo.com/library/concept/rsi/) rather than replace it. The best known is the Composite Index: as published, the 9-bar momentum of a 14-period RSI added to a 3-bar simple average of a 3-period RSI. Removing RSI's bounded 0-100 scale is the point; the unbounded line can keep stretching where RSI flattens, so it can print [divergences](https://www.luxalgo.com/library/concept/regular-bullish-bearish-divergence/) that RSI's compression near its extremes hides. The second study is the Derivative Oscillator: a 14-period RSI smoothed twice, with a 5-period and then a 3-period exponential average, minus a 9-period simple average of that double-smoothed line, plotted as a histogram. Brown also reframed how RSI's operating range shifts between bull and bear regimes; that thread of her work is covered under [RSI range rules](https://www.luxalgo.com/library/concept/rsi-range-rules/). The design problem behind the Composite Index deserves spelling out. RSI's averaging caps how far it can travel: in a runaway move the oscillator pins near its extreme and physically cannot make a higher high, so it prints divergence whether or not momentum is genuinely fading, and fails to print it when the fade is real but the scale is saturated. Bolting an unbounded momentum term onto the RSI stream removes the ceiling. When RSI and the Composite Index disagree at a price extreme, the disagreement itself is Brown's signal: the bounded line's testimony has been checked against a witness that cannot be silenced by its own scale. On the Library the studies live mostly as divergence engines: LazyBear's port pairs the Composite Index with RSI and its averages on one panel, and z3bazi's and shayankm's builds automate the divergence detection between the two lines. The honest caveats are those of any derivative-of-a-derivative: the Derivative Oscillator's double smoothing buys clean histogram flips with real lag, the Composite Index's unbounded scale means its levels only make sense relative to their own recent history, and every read remains a momentum read, needing price structure to convert warnings into trades. ## How to identify the Constance Brown studies Two constructions, both starting from RSI: one un-bounds it, the other smooths it into a histogram. 1. Composite Index, term one: compute a 14-period RSI, then its 9-bar momentum, the unbounded ingredient. 2. Composite Index, term two: a 3-bar simple average of a 3-period RSI, the fast bounded ingredient; sum the two terms. 3. Overlay the index's own moving averages, as Brown plotted them, so crosses of the study through its averages give mechanical triggers. 4. Derivative Oscillator: double-smooth a 14-period RSI with 5- then 3-period EMAs, subtract a 9-period SMA of the result, plot as a histogram. 5. Read the pair the intended way: Composite Index divergence checked at RSI's swing points, histogram zero-crosses and shrinking bars for timing. ## How it's calculated Two Constance Brown momentum studies built on the 14-period RSI: the Composite Index (line 1) and the Derivative Oscillator (lines 2 to 4). ``` CI_t = (RSI_14(t) - RSI_14(t - 9)) + SMA_3(RSI_3) S1_t = EMA_5(RSI_14) S2_t = EMA_3(S1) DO_t = S2_t - SMA_9(S2) CI_t: Composite Index value at bar t DO_t: Derivative Oscillator value at bar t RSI_14: Wilder relative strength index of close over 14 bars (default 14) RSI_3: Wilder relative strength index of close over 3 bars (default 3) SMA_n: simple moving average of a series over its last n values EMA_n: exponential moving average of a series with period n S1_t: first smoothing, the 5-period EMA of RSI_14 (default 5) S2_t: double-smoothed RSI, the 3-period EMA of S1 (default 3) n: smoothing length used in each SMA/EMA subscript t: current bar index ``` Composite Index defaults are 14, 9 and 3; it is usually plotted with 13-period and 33-period simple moving averages of itself as reference lines. Derivative Oscillator defaults are 14, 5, 3 and 9 and it is drawn as a histogram; some platforms use an EMA instead of an SMA for the 9-period signal. Both studies are published in Brown's Technical Analysis for the Trading Professional. ## How traders use it - Cross-checking divergence: the Composite Index is read at RSI's swing highs and lows, and a divergence that shows on one line but not the other is the warning, the Composite catching what RSI's bounded scale conceals. - Timing momentum flips with the Derivative Oscillator histogram: zero-line crosses and shrinking bars carry the same grammar as a [MACD](https://www.luxalgo.com/library/concept/macd/) histogram, applied to double-smoothed RSI. - Trigger construction: Brown plotted the studies with moving averages of themselves, so a study crossing its own average adds a mechanical trigger to the divergence read. - As automated divergence engines: detector builds flag disagreements between the Composite Index and RSI at swing points, converting Brown's visual cross-check into alerts. - Within regime context: the studies inherit Brown's range framework, so bullish divergences are weighted more when RSI is operating in its bull-regime range and faded reads are demoted when the regime disagrees. ## Constance Brown studies vs related momentum tools - **RSI** (https://www.luxalgo.com/library/concept/rsi/): The parent indicator, kept on the chart deliberately: the studies are read against RSI, not instead of it. The Composite Index exists precisely because RSI's bounded scale suppresses divergence information at the extremes where it matters most. - **Stochastic RSI** (https://www.luxalgo.com/library/concept/stochastic-rsi/): Both are RSI derivatives attacking different complaints. Stochastic RSI stretches the oscillator's range to amplify sensitivity, adding noise; the Composite Index un-bounds the scale to recover hidden divergence, adding stretch. Amplification versus liberation. - **MACD** (https://www.luxalgo.com/library/concept/macd/): The Derivative Oscillator borrows MACD's histogram grammar, zero-line crosses and fading bars, but builds it from double-smoothed RSI rather than price averages. Same reading skills transfer; the input stream and its saturation behavior differ. ## FAQ ### What is the Composite Index indicator? Constance Brown's Composite Index, as published, adds the 9-bar momentum of a 14-period RSI to a 3-bar simple average of a 3-period RSI. Because the momentum term is unbounded, the line can keep stretching where RSI flattens against its scale, so it can print divergences at price extremes that RSI itself fails to show. It is read alongside RSI, not instead of it. ### What is the Derivative Oscillator? Brown's Derivative Oscillator double-smooths a 14-period RSI with 5- and 3-period exponential averages, subtracts a 9-period simple average of that smoothed line, and plots the remainder as a histogram. Read it like a histogram of smoothed momentum: zero-line crosses mark direction flips and shrinking bars warn that thrust is fading. Its divergences carry the same caveats as any oscillator divergence. ### Why does the Composite Index need to be unbounded? Because RSI's boundedness is the failure being repaired. Near 0 or 100 the oscillator compresses: it cannot exceed its scale no matter how strong momentum gets, so divergences print spuriously at pinned extremes and fail to print when saturation hides a genuine fade. The unbounded momentum term keeps stretching with the move, so a divergence on the Composite Index reflects momentum, not scale arithmetic. ### What are the published settings for the studies? Composite Index: momentum over 9 bars of a 14-period RSI, plus a 3-bar simple average of a 3-period RSI, often plotted with short moving averages of itself. Derivative Oscillator: a 14-period RSI smoothed with 5- and 3-period EMAs, minus a 9-period SMA of that line. Ports occasionally expose the lengths; changing them changes behavior enough that Brown's published reads no longer apply verbatim. ### How are Composite Index divergences read? At RSI's swing points, as a cross-examination. Mark the swing highs or lows on RSI, then check whether the Composite Index confirms each one. RSI flat while the Composite makes a new extreme says the bounded scale was hiding strength; RSI making an extreme the Composite refuses says the move's momentum is thinner than RSI's scale suggests. The disagreement is the signal, and price structure still has to convert it into a trade. ### Do the Brown studies work on intraday charts? The arithmetic computes anywhere, but the published work and its calibrations grew from daily and weekly index and futures charts. Intraday, the same constructions inherit intraday noise: more swings, more divergences, lower average meaning per signal. Traders who port them down usually lengthen the smoothing or demand confluence with structure, and treat Brown's regime framing as the part that transfers least automatically. ## Implementations in the Library - Constance Brown Studies (LuxAlgo): https://www.luxalgo.com/library/indicator/constance-brown-studies/ ## Related concepts - Balance of Power: https://www.luxalgo.com/library/concept/balance-of-power/ - CCI: https://www.luxalgo.com/library/concept/cci/ - Williams %R: https://www.luxalgo.com/library/concept/williams-percent-r/ - Ultimate Oscillator: https://www.luxalgo.com/library/concept/ultimate-oscillator/ - True Strength Index: https://www.luxalgo.com/library/concept/true-strength-index/ - Relative Vigor Index: https://www.luxalgo.com/library/concept/relative-vigor-index/ - Awesome Oscillator: https://www.luxalgo.com/library/concept/awesome-oscillator/ - Accelerator Oscillator: https://www.luxalgo.com/library/concept/accelerator-oscillator/ - Gator Oscillator: https://www.luxalgo.com/library/concept/gator-oscillator/ - Elder Ray: https://www.luxalgo.com/library/concept/elder-ray/ --- Source: https://www.luxalgo.com/library/concept/constance-brown-studies/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/