Participation Rate (Percent of Volume)

Formula

POV = V_own / V_market

Child quantity for one interval, given volume V printed in that interval:
  q = min(Q_remaining, ρ · V)

ρ is the target rate as a fraction (0.10 means ten percent of volume).
The child does not look ahead at volume that has not printed.

How the schedule behaves

• Busy intervals produce larger children. Quiet intervals produce smaller ones. The order slows down when the market does, which a TWAP slice will not.
• It does not finish by a deadline. If volume dries up, quantity is left over. A horizon with a hard end needs a different schedule, such as Almgren-Chriss or VWAP with a residual sweep.
• The realised rate is own fills over market volume, which includes your own prints if they are in the tape. Subtracting them is a policy choice and changes the number.

Pitfalls

• ρ is a fraction. Passing 10 thinking it means 10 percent requests ten times market volume. The code treats 10 as 1000 percent and will try to take all remaining quantity.
• The cap is the remaining parent, not a market-impact model. min(remaining, ρ·V) does not estimate how far the child moves the price. Impact still scales with participation; this function only sizes the child.
• Which volume. Lit continuous volume, auction volume and odd-lot volume are different denominators. The caller passes the volume number; the function does not classify prints.

Python reference implementation

Requires standard library only. Tested before publication; the generator re-executes it on every rebuild. MIT licensed. Download participation-rate.py · All snippets

def pov_child_qty(market_vol_interval, target_rate, remaining_qty) -> float:
    """Child quantity for a percent-of-volume slice.

    target_rate is a fraction of market volume (0.1 = 10%). The result is
    never larger than remaining_qty, and is zero when there is nothing to do.
    """
    if market_vol_interval < 0 or remaining_qty < 0:
        raise ValueError("volumes must be non-negative")
    if target_rate < 0:
        raise ValueError("target_rate must be non-negative")
    return float(min(remaining_qty, target_rate * market_vol_interval))

FAQ

Is participation the same as POV?

POV (percent of volume) is the schedule that tries to keep participation near a target. Participation rate is the realised or target ratio itself. People use the two names for both the ratio and the algorithm; the formula on this page is the ratio, and the function is the child size that targets it.

What rate is reasonable?

There is no universal rate. Higher participation finishes sooner and usually moves the price more. The function does not choose ρ. It only converts a chosen rate and an observed volume into a child quantity.