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The default approach, and why it's popular

Most PE secondary pricing leans on a deterministic age-curve roll-forward — commonly Takahashi–Alexander (TA) — that projects a fund's remaining cashflows from a fitted curve of how "typical" funds of its age and vintage behave. It's popular for a good reason: it's simple, explainable, and fits observed history closely. The problem is that "fits history closely" and "predicts the future reliably" are different claims, and the industry standard is rarely checked against the second one.

The test we run instead

Before a quantitative fund trusts a trading strategy with real capital, it doesn't just ask "does this look good on the backtest?" — it asks "how likely is it that this strategy only looks good because we tried enough variations until one of them fit the noise?" That's the question the Deflated Sharpe Ratio and a stationary-bootstrap confidence interval on the pricing edge are built to answer: adjust the raw performance measure downward for how many model variants were actually compared to find this one, then check whether the edge still holds up — via 5,000 Monte Carlo resamples per model — once you account for that search.

We run every pricing model we ship through that same battery before putting it in front of a user, instead of picking whichever model looks best in-sample and staying quiet about how it does out of it.

What we found

Held-out test: 801-813 funds per model, 5 hurdle-rate variants searched per model, 3,432 CPCV folds, 5,000 bootstrap resamples. PBO (Probability of Backtest Overfitting) asks whether the in-sample winner keeps winning out-of-sample; we flag anything at or above 50% as a red flag. All three models clear the Deflated Sharpe Ratio hurdle (DSR ≥ 0.95) on this panel — but DSR alone is the metric most pricing tools stop at, and it's exactly where the real differences between the three don't show up.

Equisect Cohort is the clean win here: its PBO is roughly half TA's (18% vs. 38%), and its bootstrap Sharpe lower bound — the number that actually says how much of the edge survives resampling — is nearly 3× TA's (0.32 vs. 0.12). Equisect Bayesian is a more honest story, and we're not going to hide the unflattering half of it: its Sharpe floor edges out TA's (0.15 vs. 0.12), but its own PBO (78%) is the highest of the three, crossing the same red-flag line we'd call out on anyone else's model. A model doesn't get to grade its own homework here, including ours. Most pricing tools ship the industry-standard age-curve model as their only option and never compute a PBO for it, let alone for their own model. We do, on every model we ship, and publish the result next to the price rather than just the claim.

What this means in practice

Takahashi–Alexander stays in Equisect as a transparent, auditable baseline you can sanity-check by eye; Equisect Bayesian and Equisect Cohort layer public-market-factor and cohort-quantile signal on top of it for the price we'd actually quote. It means a fair price is never just a single number: every result on Equisect ships with a calibrated P25–P75 range and each single-snapshot model's own verdict next to it, so you can see whether the number you're looking at has earned the right to be trusted before you rely on it.

The data behind it

We start from over 2,500 distinct funds spanning vintages back to 1976 and clean every one of them before a model ever sees it — reconciling duplicates, correcting restatements, matching each fund's history against itself point-in-time. What survives is the warehouse below.

Reproduce these numbers: python scripts/build_pe_oos.py
Every model figure on this page is regenerated by that command from the same artifacts the product prices from — so it can be checked, not just cited.

Research and software, not investment advice.