Capacity Model

The capacity model estimates how much capital an opportunity can absorb before returns degrade due to crowding effects.

Capacity Concepts

Soft Capacity ( $C_{soft}$ )

The position size at which returns begin degrading. Below soft capacity, full expected return is achievable.

Hard Capacity ( $C_{hard}$ )

The maximum reasonable position size. Beyond hard capacity, the opportunity cannot absorb additional capital meaningfully.

Capacity Estimation

Capacity is derived from:

Open Interest (OI) — Total market size
Historical capacity utilization — How crowded is the opportunity
Funding sensitivity — How rates respond to position changes

Soft Capacity Formula

C_{soft} = OI \times \alpha_{soft}

Where $\alpha_{soft}$ is the soft capacity ratio (typically 0.5-2% of OI).

Hard Capacity Formula

C_{hard} = OI \times \alpha_{hard}

Where $\alpha_{hard}$ is the hard capacity ratio (typically 2-5% of OI).

Capacity Pressure Ratio

The capacity pressure ratio measures how much of available capacity is being used:

\rho_{cap} = \frac{PositionSize}{C_{soft}}

$\rho_{cap}$	Interpretation
< 1.0	Below soft capacity, no penalty
1.0 - 2.0	Moderate crowding, some penalty
> 2.0	Heavy crowding, significant penalty

Capacity Penalty

When position size exceeds soft capacity, returns are penalized:

P_{cap} = \min\left(1, \frac{C_{soft}}{PositionSize}\right)^{\gamma}

Where $\gamma$ is the penalty exponent (typically 0.5).

Penalty Curve

Position / $C_{soft}$	$P_{cap}$ ( $\gamma=0.5$ )
0.5	1.00
1.0	1.00
2.0	0.71
4.0	0.50
10.0	0.32

Edge Capacity

Edge Capacity is the position size at which edge value approaches zero:

C_{edge} = f(APR_{surv}, C_{soft}, Fees)

This accounts for the point where capacity penalties and fees consume all expected return.

24-Hour Edge Capacity

For a 24-hour horizon, edge capacity is the maximum size that still produces positive expected value after fees and capacity penalties.

Capacity-Adjusted PnL

After survivability adjustment:

PnL_{cap} = PnL_{surv} \times P_{cap}

Example

Given:

$PnL_{surv} = \$ 100$
$PositionSize = \$ 50,000$
$C_{soft} = \$ 25,000$

Then:

$\rho_{cap} = 50000 / 25000 = 2.0$
$P_{cap} = (25000 / 50000)^{0.5} = 0.71$
$PnL_{cap} = 100 \times 0.71 = \$ 71$

Capacity in Portfolio Context

When allocating across multiple opportunities:

Respect individual capacity — Don't exceed hard capacity per opportunity
Monitor aggregate capacity — Total portfolio shouldn't stress market
Diversify capacity — Spread across opportunities with different capacity profiles

Capacity Display

In the UI:

Display	Meaning
$C_{soft}$	"Soft Capacity" — where degradation begins
Utilization %	Current market utilization of capacity
Capacity Warning	Position exceeds soft capacity

Survivability Model Simulation Engine