📊 OBV — On-Balance Volume

OBV builds a single running total that adds a session's entire volume when price closes up, and subtracts it when price closes down. It is the oldest and simplest way to fold trading activity into a directional signal.

💡 Financial Meaning

The core idea, from Joseph Granville, is that volume precedes price: smart money accumulates or distributes before the broader move becomes visible on the price chart. Traders watch for divergence — price drifting sideways or making lower highs while OBV keeps climbing suggests quiet accumulation and a potential upside breakout; the mirror case suggests distribution ahead of a decline. It is the slope and shape of OBV that carries the signal, not its absolute value.

🔢 Mathematical Formula

\[ OBV_t = OBV_{t-1} + \begin{cases} +V_t & \text{if } C_t > C_{t-1} \\ -V_t & \text{if } C_t < C_{t-1} \\ 0 & \text{if } C_t = C_{t-1} \end{cases} \]

where \(V_t\) is the traded volume at time \(t\). OBV is a pure running (cumulative) sum — there is no window, no decay, and no smoothing constant anywhere in the formula.

⚙️ Parameters

OBV takes no parameters. It has no period, threshold, or smoothing setting to configure.

Rebased to the chart range

OBV is mathematically a cumulative sum starting from the beginning of an asset's history, so its absolute level has no intrinsic meaning. LibreFolio rebases the displayed OBV series to zero at the first session of the currently requested chart range, so what you read on screen is always "net signed volume accumulated since the left edge of the chart" — comparable regardless of how far back the underlying data goes.

🎛️ Signal Processing Equivalent — Signed Integrator

OBV is a discrete-time integrator (an accumulator, the digital equivalent of \(\int V(t)\, \text{sign}(dC/dt)\, dt\)) driven by a bang-bang signed input: \(+V_t\), \(-V_t\), or \(0\). An integrator has an infinite DC gain and no cut-off frequency of its own — it never forgets, which is exactly why the rebasing window matters so much for interpretation.

flowchart LR
    C["💹 Close"] --> SGN["➕➖0️⃣ sign(ΔClose)"]
    V["📦 Volume"] --> MUL["✖️ signed volume"]
    SGN --> MUL
    MUL --> ACC["🔁 Running sum (integrator)"]
    ACC --> OBV["📊 OBV(t)"]
    ACC -.->|"feedback"| ACC

On-balance volume on Wikipedia