Motivation
Basis points (bps) are a convenient way to express a 0.01% (= 1/10,000) change in a human‑readable way. However, once you introduce fixed costs, you can no longer scale this unit cleanly. Consider a case where there is always a fixed cost of $10, regardless of trade size:
Trade notional of $1,000 → cost is 1% = 100 bpsTrade notional of $1,000,000 → cost is 0.001% = 0.1 bpsEven though the fixed cost is always "$10", the number of bps changes with the notional.
This makes it hard to describe a fee structure with fixed costs in a consistent bps-based way.
To address this, this article proposes a new notation, bp/U (basis points per unit), which expresses fixed costs in bps relative to a chosen reference notional.
Definition: bp/U (Basis Points per Unit)
bp/U stands for "basis points per unit notional."
Traditional bps describe the ratio relative to the current notional, whereas bp/U expresses the cost relative to a chosen reference notional.
Formula
Let:
U= chosen reference unit (e.g., $1,000,000 for "per million")FixedCost= fixed dollar cost
Then:
bp/U = (FixedCost ÷ U) × 10,000
For example, if we set U = $1,000,000 (one million), we can write bp/M (bps per million):
- U: $1,000,000
- FixedCost: $100
So:
bp/M = ($100 ÷ $1,000,000) × 10,000 = 1 bp/M
Converting back to actual bps
The notation 1 bp/M does not change regardless of trade size.
To compute the effective bps for a specific trade, use:
effective bps = bp/U × (U ÷ Notional)
Using our 1 bp/M example:
- Trade notional $1,020
1 bp/M × (1,000,000 ÷ 1,020) ≒ 980.39 bps - Trade notional $34,554
1 bp/M × (1,000,000 ÷ 34,554) ≒ 28.94 bps - Trade notional $1,140,000
1 bp/M × (1,000,000 ÷ 1,140,000) ≒ 0.877 bps
Once you define bp/U:
- The notation itself (e.g.,
1 bp/M) stays fixed - You compute the effective bps based on the actual trade notional when needed
In this way, bp/U lets you express fixed costs in bps without depending on the actual trade size.