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📐 PPO — Percentage Price Oscillator

PPO is MACD's twin, with one change that matters a lot in practice: it expresses momentum as a percentage of price instead of raw price units, making it directly comparable across assets of any price level.

💡 Financial Meaning

A €2 MACD reading means something very different for a €10 stock than for a €500 stock. PPO removes that ambiguity: a PPO of 2% is 2% regardless of the instrument's price, so screening a whole portfolio for "which assets have the strongest momentum right now" becomes meaningful with PPO in a way it is not with raw MACD.

🔢 Mathematical Formulas

  1. PPO Line — the same fast/slow EMA spread as MACD, but divided by the slow EMA and rescaled to a percentage:

    \[ PPO_t = 100 \cdot \frac{EMA_{fast}(C_t) - EMA_{slow}(C_t)}{EMA_{slow}(C_t)} \]

  2. Signal Line — an EMA smoothing of the PPO line itself:

    \[ Signal_t = EMA_{signal}(PPO_t) \]

  3. Histogram — the momentum-of-momentum:

    \[ Histogram_t = PPO_t - Signal_t \]

⚙️ Parameters

Parameter Key Default Description
Fast Period fastPeriod 12 Short-term EMA window (sessions).
Slow Period slowPeriod 26 Long-term EMA window (sessions), also the PPO's normalising denominator.
Signal Period signalPeriod 9 EMA smoothing applied to the PPO line (sessions).

🎛️ Signal Processing Equivalent — Gain-Normalised Band-Pass Filter

MACD's band-pass output (see MACD) has an amplitude that scales with the input's absolute level. PPO divides that same band-pass output by a low-pass estimate of the signal's own level (\(EMA_{slow}\)) — this is exactly Automatic Gain Control (AGC), a standard technique in signal processing for keeping a filter's output amplitude comparable regardless of the input's DC level.

flowchart LR
    C["💹 Close"] --> EF["📉 EMA fast"]
    C --> ES["📉 EMA slow"]
    EF --> DIFF["➖ EMA fast − EMA slow"]
    ES --> DIFF
    DIFF --> AGC["🎚️ ÷ EMA slow ×100 (AGC)"]
    AGC --> PPO["📐 PPO line"]
    PPO --> SIG["🔁 EMA(signalPeriod)"]
    PPO --> HIST["📊 Histogram = PPO − Signal"]
    SIG --> HIST

Same crossovers, different scale

Every crossover rule that applies to MACD (line crosses signal, histogram flips sign) applies identically to PPO — only the units change, from price to percent. Use PPO instead of MACD whenever comparing momentum across different instruments; use MACD when working on a single instrument in its native units.

Percentage Price Oscillator on StockCharts