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Allan's Substack · Jan 1, 2026

Regulatory Risk Is a Sizing Problem: Applying the Kelly Criterion to Capital Allocation Under Uncertainty

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Allan Duarte · Allan's Substack

The fastest way to go broke in fintech or AI is sizing positions as if regulators don’t exist

That’s where the Kelly criterion enters.

In a world of regulatory uncertainty, it becomes a discipline for surviving long enough to be right.

Regulation doesn’t just change rules. It changes payoff distributions. And most investors still size positions as if the distribution is stable.

Here’s the problem.

When outcomes depend on regulators, your edge isn’t perfectly predicting their move.

Your edge is designing asymmetry: large upside on approval, bounded loss on rejection, and controlled loss on delay.

That last part matters because “delay” is usually the silent killer in fintech/AI: it turns into burn, dilution, and lost distribution windows.

Kelly is the cleanest way I know to translate that into sizing.

The core idea is simple:

  • You don’t allocate based on feeling.

  • You allocate based on the ratio between expected edge and variance.

When regulation is uncertain - and it usually is, variance dominates.

Kelly is a position sizing rule designed to maximize long-run compounded growth.

Not quarterly returns.

Not “being right.”

Compounding.

The intuition: if you repeatedly place bets with an edge, the best long-run outcome comes from sizing that protects you from large drawdowns while still letting your edge compound.

In the simplest (binary) form, Kelly tells you the optimal fraction of capital to risk:

If you win with probability p, lose with probability q = 1 − p, and your win pays b times what you risk (net odds), then:

f* = (b·p − q) / b

Two immediate implications matter in regulated markets:

  1. If your edge is small, Kelly forces small sizing.

  2. If your downside is large or your probabilities are uncertain, Kelly collapses sizing quickly.

That’s exactly the behavior you want when regulators can flip the payoff distribution.

Regulatory environments create three features that standard sizing approaches underestimate:

The world doesn’t move smoothly from “good” to “bad.”

It jumps between states: licensed vs not, permitted vs restricted, allowed-but-delayed vs fully blocked.

Those are step-functions in value.

Kelly naturally pushes you to model states explicitly instead of smoothing them away.

A regulatory “delay” is not neutral.

Delay burns cash, raises dilution risk, shifts competitive dynamics, and can destroy optionality.

When you model “delay” as its own branch, sizing changes.

In most markets, your inputs are noisy.

In regulated markets, your inputs are noisy and unstable.

That’s why fractional Kelly is not a preference. It’s the correct response to uncertainty about your own model.

Full Kelly is mathematically clean, but practically fragile.

It assumes you know probabilities and payoffs well.

Under regulatory uncertainty, you usually don’t.

Fractional Kelly simply means you size at a fraction of the full-Kelly result.

Typical operating ranges:

  • 1/2 Kelly when you have strong base rates, good precedent, and limited tail risk

  • 1/3 Kelly when your probability estimates are plausible but not robust

  • 1/4 Kelly when the downside branch is ugly, time risk is high, or correlation is hidden

If you remember one sentence: Fractional Kelly is what you do when you believe you have an edge but you don’t trust your own precision.

Map outcomes as discrete states (approve, delay, restrict, ban, partial permission).

Assign probabilities. If you can’t assign probabilities, you don’t have a position-sizing problem. You have a research problem.

Your payoff is not “market up vs down.”

It’s “what happens to unit economics, distribution, compliance cost, and time-to-revenue” in each state.

Full Kelly assumes you know the probabilities and payoffs with high confidence.

Regulatory environments are exactly where you don’t.

So you size at 1/2 Kelly, 1/3 Kelly, sometimes 1/4 Kelly.

This is not being conservative.

This is acknowledging estimation error.

Keep it small. Four to six branches is enough.

Approve, delay, restrict, block is a good default.

Before price, write what changes operationally:

  • Unit economics

  • Distribution access

  • Compliance cost

  • Time-to-revenue

  • Dilution risk

Then translate to returns.

Use fractional Kelly, then apply constraints:

  • Max single-name exposure

  • Max exposure to one regulator pathway

  • Liquidity and time-to-exit constraints

  • “Cannot lose” constraints (capital you must preserve)

Kelly is a sizing engine, not a replacement for governance.

Regulatory markets reprice on small signals.

You’re not “changing your mind.”

You’re updating the tree.

Imagine a fintech or AI business where the next 12–18 months hinge on a regulatory outcome.

You model four branches:

  1. Approved / clear pathway, Return: +60%

  2. Delayed, Return: −10% (time risk, burn, dilution, slower distribution)

  3. Restricted (economics impaired), Return: −30%

  4. Blocked, Return: −70%

Now assign probabilities (your job is to be honest here):

  • Approved: 40%

  • Delayed: 30%

  • Restricted: 20%

  • Blocked: 10%

Kelly sizing (in this multi-branch case) is the fraction f that maximizes expected log growth across these outcomes.

When you run that optimization, full Kelly comes out around allocating ~39% of capital in this example.

That number surprises people. It shouldn’t.

The upside is large, the base case is not catastrophic, and the expected log-growth still favors meaningful exposure.

Now apply reality: If you’re wrong on probabilities, wrong on drawdowns, or wrong on correlation, full Kelly can hurt.

So you move to fractional Kelly:

  • 1/2 Kelly ≈ 19%

  • 1/3 Kelly ≈ 13%

  • 1/4 Kelly ≈ 10%

That’s what “disciplined aggression” looks like under regulatory uncertainty: meaningful exposure, sized to survive.

Regulatory uncertainty is not just “risk.” It is correlated risk across the portfolio.

A portfolio can look diversified by ticker and still be one trade.

If multiple holdings depend on:

  • the same agency interpretation

  • the same licensing pathway

  • the same court or enforcement posture

  • the same compliance architecture (partners, banks, rails, cloud approvals)

…then your outcomes are correlated.

In practice, that means your true risk is higher than position-level models suggest.

Portfolio implication: your “Kelly fraction” across the whole book should be lower than the sum of each single-name Kelly.

Translation: even if each position looks fine alone, the shared regulator is your hidden factor.

Delay is often the worst branch for companies with burn and fragile funding.

Model it explicitly.

If your inputs are uncertain, full Kelly is leverage in disguise.

Fractional Kelly is the adult choice.

A good story is not a good estimate.

Kelly punishes storytelling without measurement.

1. Design your business so the downside state is survivable.

If one adverse rule change kills the company, your real problem isn’t sizing. It’s fragility.

2. Build “regulatory optionality”:

  • multiple jurisdictions

  • modular product architecture

  • compliance-by-design,

  • contingency pricing.

3. Size the capital you allocate to any new product or feature that depends on regulatory approval using a Kelly-style discipline:

  • Treat approval, delay, restriction, and rejection as explicit branches

  • Assign probabilities

  • Map each branch to burn and payoff

  • Fund at fractional Kelly so a “No” doesn’t jeopardize the company

1. Stop asking “Do I believe in the thesis?”Ask “What fraction of capital can I allocate without risking ruin if the regulator chooses the worst plausible branch?

2. Make fractional Kelly your baseline and increase only when probability and payoff clarity improves.

3. Tie sizing to regulatory milestones, not time: stage exposure so you add risk only after specific signals (draft guidance, licensing progress, enforcement posture, court decisions) reduce variance.

In fintech, AI, and regulated deep tech, the edge is not predicting regulators perfectly.

The edge is sizing exposure so you stay solvent while the payoff distribution is still being written.

𝘈𝘯𝘺 𝘷𝘪𝘦𝘸𝘴 𝘰𝘳 𝘴𝘵𝘢𝘵𝘦𝘮𝘦𝘯𝘵𝘴 𝘦𝘹𝘱𝘳𝘦𝘴𝘴𝘦𝘥 𝘢𝘳𝘦 𝘮𝘪𝘯𝘦 𝘢𝘯𝘥 𝘯𝘰𝘵 𝘵𝘩𝘰𝘴𝘦 𝘰𝘧 𝘮𝘺 𝘦𝘮𝘱𝘭𝘰𝘺𝘦𝘳

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