How Preflop sets the discount rate r that prices every token

Three components. Cohort-conditional via $\beta_c$ only. The other two are universal across cohorts.

Mortality is not a fourth term. Mortality rates vary by an order of magnitude across age (a 22-year-old has $q_x \approx 0.001$, a 65-year-old has $q_x \approx 0.013$), so embedding mortality in a flat r mis-prices both ends. Instead, mortality enters the V_HC integration as a term-structured survival function:

where $S(t)$ is the survival probability from age at issuance to age at time t, sourced from SSA Period Life Tables with a selection multiplier $\theta_{\text{health}} = 0.85$ (PreFlop issuers self-select toward audit-clean, attestation-willing applicants — empirically healthier than full population).

Coordinated extension — Cohort Priors v2 —The V_HC integration gains a second multiplicative term — cohort-stay survival $P_{\text{stay}}(t)$ + exit-cohort fallback — under Cohort Priors v2 Design v2 — In progress. The two specs are designed to ship together (engine v2.2.0 + v2.3.0): DR-v1 adds mortality survival$\, S_{\text{mort}}(t)$; CP-v2 adds cohort-stay survival $P_{\text{stay}}(t)$ and the (1 − P) exit-fallback term. Multiplicative composition; orthogonal by construction.

The structural insight —A flat r conflates four mechanisms — opportunity cost, systematic risk, illiquidity, and mortality probability. The first three share the property that they discount future cash flows at a uniform time-rate; mortality is a probabilistic multiplier on the flow itself, term-structured by age. Conflating them was always numerical convenience, not modelling clarity.

The math foundation Part 3.6 originally proposed five terms: $r_f$, $\lambda_{\text{income}}$, $\lambda_{\text{liquidity}}$, $\lambda_{\text{MH}}$, and an implicit risk premium. v1 of this spec rejects two of those and moves a third out of r entirely.

The parsimony bias —Three components, each provably orthogonal to the others and to the forecast engine’s outputs. No component included for completeness; every component defended by a magnitude in §6 below.

The five priority cohorts plus fallback at canonical parameters $r_f = 4.0\%$, $\text{ERP} = 4.5\%$, $\pi_{\text{illiq}} = 4.0\%$:

Extended cohort grid (full v1 prior assignments):

Recalibration —Cohort betas are literature-anchored cold-start priors, not calibrated against PreFlop’s own outcomes (none yet exist). Recalibration is annual against realized cohort TEB returns vs S&P TR — first refit fires once each cohort accrues ≥ 50 issuer-quarters of observed data.

For every parameter, the question is: why this number, and not the next one over? Each defended below.

$r_f = 4.0\%$

• —Source. US Treasury 10-Year constant-maturity yield (FRED DGS10), 12-month trailing average.
• —Why 10Y. Matches the dominant covenant-window integration horizon. 30Y over-discounts near-term; 2Y under-discounts perpetuity tail.
• —Why 12-month trailing. Smooths day-of-quote noise without losing macro responsiveness. Shorter windows (6-month) are noisier; longer (24-month) lag.
• —Defensibility. Publicly verifiable on FRED. Anyone can replicate. Recalibrated quarterly.

$\text{ERP} = 4.5\%$

• —Source. Damodaran’s implied ERP for the US S&P 500, 10-year median (pages.stern.nyu.edu/~adamodar/).
• —Why implied not historical. Historical (Ibbotson) ERP is backward-looking and biased high in periods of expanding multiples. Implied (Damodaran) is forward-looking, conditions on current market levels — the right input for pricing a forward-looking asset.
• —Range. Damodaran’s 2014–2025 series spans 4.0%–6.5%; we use the 10-year median.
• —Population fit (residual risk). ERP measured on US public equity. PreFlop tokens are claims on individual human capital — single-name concentration, no rebalancing. Residual mis-application: $\beta_c \cdot \text{ERP}$ may understate true systematic premium for very-high-concentration cohorts. v2 may layer a concentration premium.

$\beta_c$ — per-cohort

• —Sources. Triangulated from three labor-economics studies plus sector-equity-beta analogues for modern cohorts.
• —Mayer (1996), “Wages and Equity Premia” — labor-income beta to market across US occupations, range 0.20–0.55, mean 0.35.
• —Lustig & Van Nieuwerburgh (2008), “The Returns on Human Capital” — aggregate human-capital beta ~0.30–0.40 with substantial cross-occupation heterogeneity.
• —Palacios-Huerta (2003) — occupational betas from PSID; 0.15–0.80 range.
• —Why not all 1.0. Human capital is empirically less volatile than equity (sticky wages, employment stability). Defaulting to 1.0 over-discounts non-cyclical careers.
• —Why not all 0.5. Founders, creators, and tech employees with heavy equity comp are demonstrably above 0.5.

$\pi_{\text{illiq}} = 4.0\%$

• —Source. Franzoni, Nowak, Phalippou (2012, Journal of Finance), “Private Equity Performance and Liquidity Risk” — estimates 300–500bp liquidity premium for PE funds with 7–10 year lockups. PreFlop covenants are 7–12 year terms with optional early unlock. Use the midpoint.
• —Why a single platform-wide value, not cohort-conditional. Illiquidity is a function of the platform’s secondary-market depth, not the issuer’s cohort. v2 may differentiate (high-trading cohorts get lower π).
• —Population fit (residual risk). PE has fund-level diversification; PreFlop tokens are single-issuer concentration. Net: FNP’s 300–500bp range likely understates PreFlop’s true illiquidity premium. We use the midpoint as a conservative-low prior.

Survival function $S(t)$

• —Source. SSA Period Life Tables, 2021 release (ssa.gov/oact/STATS/table4c6.html). Public, free, full-population US.
• —Methodology. Per issuer, lookup mortality rate $q_x$ for each future age; compute survival to age x as $S(x) = \prod_{i = a_0}^{x-1} (1 - q_i)$; multiply each future TEB(t) by survival before discounting.
• —Selection multiplier $\theta_{\text{health}} = 0.85$. SSA tables are full-population; PreFlop issuers self-select toward audit-clean, attestation-willing applicants — empirically healthier (BLS Annual Survey of Insured Worker Mortality shows insured workers 10–20% below population). Adjusted: $q'_x = 0.85 \cdot q_x$.

Each component of r must be provably orthogonal to (a) every other component of r, and (b) what the Forecast Engine’s growth bands and segments already capture. This is the discipline that prevents silent double-discounting of risk.

Within-r orthogonality

r components vs Forecast Engine outputs

This is where the deepest trap lives — a component of r that duplicates what the cohort growth bands or segments already encode would silently double-discount risk. For each r component, the question is: does the Forecast Engine already capture this?

The shift-equivalence test —For each component, we asked: if you removed it from r and added an equivalent shift to the forecast bands, would the output be the same? All five mechanisms (three r components + survival + forecast bands) pass — none is redundant, none is hand-wavy relabeling.

For each parameter we proposed, must move V_HC by >5% for at least one cohort. Components that fail this don’t earn their place. Magnitudes computed for three canonical issuers under v1 priors:

Interpretation.

• —The three r components each move Maya’s V_HC by ~10% per 1pp, Amara’s by ~7%, athlete’s by ~5%. Maya is most sensitive because more of her V_HC is in the perpetuity tail (Phase 2-dominant); Amara’s V_HC is more near-term-weighted (Phase 1 dividend stream dominates).
• —Switching from no-mortality to survival-adjusted V_HC moves Amara’s V_HC by ~18% — large. Moves Maya’s by only ~5% — small (her remaining lifespan is long, mortality discount is in the back tail which is already heavily r-discounted). Mortality is a meaningful term-structure for older issuers; small for younger.
• —The selection multiplier $\theta_{\text{health}}$ moves things by 1–4%. Below the 5% parsimony threshold for the youngest issuer, but above for older ones. Decision: keep. Removal would over-discount older issuers; the 5% threshold is soft.

Robustness — what happens if the priors are wrong

Largest single-parameter risk —$\beta_c$ assignments. v2 calibration plan must prioritize beta refit. Cohort betas are the cold-start prior most likely to drift once realized data accrues.

Illustrative — implementation pending —The numbers below show what the engine will produce once v2.2.0 ships. The live engine still uses $r = 12\%$ flat; site pages displaying Maya / Amara / athlete numbers continue to reflect the live engine output. No site reconciliation in this session.

Maya — founder, age 22, $60K canonical covenant target

Maya moves from anchored (κ ≤ 1.2) into modest premium (1.2 < κ ≤ 2.0) tier. κ-tier classification changes; tier thresholds do not need to move.

Amara — surgeon, age 45F, $400K Direct Listing target

Amara needs survival-adjusted V_HCbecause she’s 45. Use $\theta_{\text{health}} = 0.85 \cdot q_x$ from SSA female 2021 tables.

Amara remains comfortably anchored. Her V_HC rises substantially — she’s structurally under-priced today. Net effect: r-shift +25% (lower r), survival-shift −18%, net +10%.

Athlete — NBA veteran, age 31M, illustrative $5M DL target at e=2%

Athlete also under-priced today — their negative-systematic-beta (low $\beta_c = 0.60$) isn’t counted under flat 12%. r-effect +15%, survival-effect −5%, net +12%.

The systematic story

The flat 12% over-discounted defensive cohorts (medicine, law, athlete, academia) and under-discounted cyclical cohorts (founder, creator, quant). The shift is in the right direction in every case:

• —Founders’ V_HC drops 10–15% under the new r → their κ rises → listings face stricter scrutiny. This reflects the actual systematic risk founders carry.
• —Defensive cohorts’ V_HC rises 10–15% under the new r → their κ falls → they have more pricing room. This reflects the actual safety of their income streams.

The bar —This is the correct outcome for any market that takes risk-pricing seriously. A flat r is a placeholder; cohort-conditional r is the right operational treatment of cross-sectional risk.

The κ-tier table at /spec/human-capital uses these thresholds:

Question: do these thresholds need to shift now that r is cohort-conditional?

Answer: no. The tier thresholds remain in place. Three reasons:

1. κ has the same economic meaning. It’s still “market-implied valuation / engine fundamental valuation.” The thresholds are about how much premium over engine the market is paying — that’s tier-relevant regardless of how the engine itself is computed.
2. Cohort-typical κ shifts naturally. Founders’ κ rises by ~15% under the new r. So a founder targeting what previously cleared as “anchored” (κ=1.2) now clears as “modest premium” (κ=1.38). This is the correct outcome — founders’ raises are more speculative; the κ-tier boundary catches them.
3. The conviction-floor requirement is the right second filter. A founder bumped into “modest premium” (κ in 1.2–2.0 tier) needs Conviction ≥ 65. If their conviction score is 62 (Maya’s case), they cannot list at that κ — they must reduce raise target.

The cohort interaction is by design —Under cohort-conditional r, founders structurally land in higher κ tiers; defensive cohorts cluster at the floor. The system reads issuer pricing posture against engine, regardless of cohort. No threshold change needed; the document update is an implication note, not a recalibration.

What this spec is and isn’t

It is: a literature-anchored set of priors with documented sources for every parameter.

It is not:a calibration against PreFlop’s own realized issuer outcomes — because those don’t exist yet.

Residual uncertainty bounds

After this refit, residual uncertainty in cohort $r_c$:

Translated to V_HC uncertainty: ±15–25%. The forecast bands’ CI width (±15–60% per conviction tier) absorbs most of this. A backer reading “engine-mid V_HC = $3M, low band = $1.4M, high band = $4.6M” gets bands wide enough to account for discount-rate uncertainty.

Recalibration plan —Quarterly. Engine v2.1.0 (current) is unchanged: still r = 12% flat, calibrated against 0 realized outcomes (cold start). v2.2.0 ships cohort-conditional r with literature-anchored priors, still calibrated against 0 realized outcomes — the posture is unchanged; the priors are sharper. First refit: once each cohort accrues ≥ 50 issuer-quarters of observed data.

This page is the published methodology. Three streams of work flow from it but live in separate sessions:

• —Implementation. Library code in lib/conviction-engine-v2/discount-rate.ts and survival-aware integration in lib/obligation-ledger/math.ts. Ships under engine version v2.2.0. Backward-compatible default $r = 12\%$ and unit-survival preserve current 75-test obligation-ledger suite at default parameters.
• —Math foundation Part 9 reconciliation. Maya’s $V_{\text{HC}}^{\text{mid}}$ shifts from $3.01M to $2.68M under v1; Part 9 worked examples will need re-running. Separate vault session.
• —Quant review. This spec goes through a paid quant review (Two Sigma / Citadel / AQR background). Expected feedback areas: cohort-beta credibility, FNP 2012 applicability to tokenized-securities context, selection-multiplier methodology, whether mortality should remain in r or in the integration. Separate engagement.

The bar restated —A market-maker reads this spec, reviews the math, runs the sensitivity table, and concludes: “This is how I’d discount these cash flows. The decomposition is parsimonious — three components plus survival, each with a specific empirical anchor and a defended bound. The orthogonality argument holds. The cohort betas are triangulated from three labor-economics sources. The illiquidity premium uses FNP 2012’s midpoint with stated rationale. The mortality treatment is term-structured via SSA tables with a documented selection multiplier. The before/after analysis quantifies the shift on canonical issuers. The κ-tier regime holds without threshold changes. The cold-start posture is honest. I’d put capital on this.”