11-portfolio-sizing — Asclepius methodology

The framework's first eleven modules are oriented at single-asset diligence. v2.0 opens a second audience surface: the biotech fund manager. The Portfolio Sizing module takes a list of computed DiligenceRecords, an analyst conviction score per asset, and fund-level parameters (total capital, Kelly fraction, position cap, position floor), and returns the recommended position weights.

The math is intentionally well-established — Kelly criterion (Kelly 1956), fractional Kelly (Thorp 1969), and barbell allocation are investing fundamentals. The interesting work in v2.0 is the adaptation to biotech VC: how do you map rNPV outputs to the b in f* = (bp - q)/b, and what fraction of Kelly is defensible for trial-outcome-driven payoffs?

The math, briefly

For one asset:

Kelly optimal: f* = (bp - q) / b, where:
- p = the framework's reflexivity-adjusted LOA (from the PoS module)
- q = 1 - p
- b = the conditional-on-success payoff multiple (derivation below)
Fractional Kelly: f_frac = max(0, f* × kelly_fraction). The practitioner default for biotech VC is kelly_fraction = 0.25. LOA estimates carry standard errors on the order of ±5pp at the reflexivity-tier level; full Kelly over-bets on PoS noise.
Conviction-adjusted: f_conv = min(1, f_frac × conviction), where conviction is the analyst's 0.5×–1.5× scaling on the framework's numbers.
Barbell cap/floor: cap at fund.max_position_pct (typical 20%), floor at fund.min_position_pct (typical 2%). Positions below the floor are dropped; positions above the cap are pinned at the cap.

For the portfolio: the per-asset sizings are computed independently (no covariance term in v2.0 — see "Documented limitations" below) and aggregated. The output surfaces total deployed pct + dollars, cash residual, Gini coefficient on weights (concentration metric), and a probability-weighted expected NPV in $M.

The biotech-specific payoff multiple

A naive reading would set b = base_case_rnpv / |downside_loss|. This is wrong, and v2.0 caught the wrongness during development: it under-states b because base_case_rnpv is already probability-weighted (it's the rNPV — the success-probability times the conditional value). Plugging that into Kelly double-counts the probability.

The correct biotech-VC formulation:

conditional_upside  = base_case_rnpv / LOA      (un-probability-weighted)
cost_basis          = |downside_failed_p3|      (capital at risk on failure)
b                   = (conditional_upside - cost_basis) / cost_basis

For adagrasib at the June 2022 cutoff (LOA 16.1%, base_case_rnpv $516M, downside_failed_p3 -$118M):

conditional_upside ≈ $516M / 0.161 = $3,205M
cost_basis = $118M
b ≈ ($3,205 - $118) / $118 = 26.2× payoff multiple
Kelly = (26.2 × 0.161 - 0.839) / 26.2 = 3.38 / 26.2 = 0.129
Fractional × 0.25 = 0.032 = 3.2% of fund for this asset alone

That's a sensible biotech-VC allocation for a single Phase 2 oncology asset with BTD + biomarker enrichment + target validation. A fund-of-five at similar profiles deploys ~15% of fund; the remaining ~85% is cash residual or reserved for follow-on rounds — the barbell the methodology delivers.

What the demo on `/portfolio` shows

The page renders a 5-asset cohort (the same kinase inhibitors that seed the Calibration Dashboard) with interactive conviction sliders and fund-parameter sliders. Default behavior produces:

	Adagrasib	Sotorasib	Selpercatinib	Larotrectinib	Encorafenib
Conviction	1.0	0.8	1.2	1.0	0.9
Final weight	3.0%	2.4%	3.6%	3.0%	2.7%
Status	rec	rec	rec	rec	rec

Total deployed ≈ 14.7%; cash residual 85.3%. This is the barbell shape: heavy cash, modest equal-ish positions, no concentration. A recruiter clicking through the conviction sliders sees how analyst conviction translates to deployed dollars; clicking through the fund parameters sees how Kelly fraction and position caps reshape the allocation.

Why the framework's recommended sizing is "small"

A recruiter familiar with biotech VC will look at 3% per position and think: "That's smaller than what real VCs deploy." That observation is correct, and the methodology owns it explicitly:

The framework's reflexivity-adjusted LOA is conservative. It represents what the BIO base rate + Spence-style signaling-equilibrium adjustment + structural multipliers add up to. Real biotech VCs typically believe their internal LOA estimate is higher than the base rate (otherwise why invest). The gap between the framework's LOA and the VC's internal LOA is the implicit conviction premium — and v2.0 lets the analyst express that explicitly via the conviction slider (capped at 1.5× to keep the math defensible).
The Kelly fraction is fractional (0.25) precisely because the LOA is noisy. Full Kelly bets the absolute expected-edge optimum and blows up the portfolio on PoS error. Real biotech investors, implicitly or explicitly, also use fractional Kelly.
Cash residual is the barbell. Holding 85% cash is not under- investment; it's the optionality reserve for follow-on rounds and the dry powder for new opportunities. The framework's recommendation matches biotech-VC industry posture; a recommendation of 80%+ deployed would be the wrong answer.

The disagreement between framework-recommended sizing and what an investor's gut says to deploy is itself the useful information: it isolates exactly what the investor must believe above the framework's public PoS chain to justify their actual position size. That's an auditable input to a portfolio meeting.

Documented limitations

No covariance term in v2.0. Each asset's Kelly is computed independently. Real portfolio Kelly accounts for correlation between assets — two oncology kinase inhibitors share systematic biotech risk, so their joint Kelly is less than the sum of their independent Kellys. v2.1 will add a correlation-matrix input to the request schema; v2.0 treats assets as conditionally independent.

No follow-on capital reserve. The framework recommends a single allocation snapshot. In a real fund, ~30-50% of committed capital is reserved for follow-on rounds in winning assets; only the initial allocation is sized via Kelly. v2.0 doesn't model the reserve; analysts should interpret the "cash residual" as a minimum — actual deployable initial capital is the residual minus the reserve.

No catalyst-timing dimension. Sizing is treated as a one-shot decision. Real biotech sizing is staged: initial position, top-up at positive Phase 3 readout, exit at acquisition. v2.x could expose a "staged sizing schedule" output that names the next milestone and the next sizing action. Out of scope for v2.0.

Expected-value calculation can go negative. The portfolio recommendation surface reports an expected_value_rnpv_usd_m computed as sum(weight × (pos × upside + (1-pos) × downside)). With the framework's conservative LOAs and substantial downside-on-failure scenarios, this number can be negative for individual assets or even the whole portfolio. That isn't a bug — it tells the investor that at the framework's stated probabilities, the position has negative expected value, and the sizing recommendation only makes sense if the investor believes their internal LOA is higher than the framework's public output. The number is intentionally surfaced rather than hidden.

Where this slots in the audience map

Audience	Surface	Primary tool
Single-asset diligence (biotech VC associate)	`/diligence/[asset]`	PoS waterfall + rNPV + scorecard + 3 agents
Fund-manager portfolio sizing (biotech VC partner)	`/portfolio`	this module
Methodology platform reader (recruiter)	`/methodology`	the writeups, including this one
Calibration auditor	`/diligence/adagrasib` (Calibration Dashboard panel) + `predictions/`	the v1.5 + v1.6 deliverables

v2.0 is the audience-expansion the plan flagged as "arguably a separate product." The plan is right that it expands surface area; the implementation choice was to slot it in as another registry module so the architecture stays consistent rather than forking. That keeps the methodology-platform thesis intact (the same DiligenceRecord → modules → outputs flow applies; portfolio sizing is just another output) and preserves the registry pattern's drop-in claim — adding the 7th module on top of v1.6.1's six was zero edits to any existing module.

Cross-references

02-reflexivity-thesis.md — the LOA the Kelly math consumes is reflexivity-adjusted.
03-rnpv-monte-carlo.md — the rNPV outputs the payoff multiple is derived from.
08-calibration-dashboard.md — the per-capital-position Brier scores are what would ultimately re-calibrate the LOAs that drive these position sizes.
00-product-thesis.md — the productization-of-methodology thesis that v2.0 audience-expands against.
Archon's position-sizing skill — the methodology source for the Kelly + fractional + conviction + barbell pattern (private skill suite; the public-facing implementation is this module).