A Sharpe 2 signal needs a 7.245-year alpha half-life to survive a Bonferroni search across 100 candidates at 5% error and 90% power. Nicolò Bonacorsi calculates that hurdle before a backtest begins.
The information budget
Bonacorsi measures a signal's usable lifetime with an information clock: accumulated squared signal-to-noise. The Kullback-Leibler (KL) divergence between the true-drift model and the economic-boundary model equals half that clock. His Certified Alpha Capacity (CAC) compares the information generated before decay with the amount required by a declared certification rule. The rule specifies a false-deployment rate, a power target and a multiplicity correction.
For Gaussian returns, known noise scale and a deterministic lifetime, the best achievable deployment probability among level-α rules is Φ(√A − z₁₋α). Certification requires A ≥ (z₁₋α + z₁₋β)². Set false deployment at 5% and power at 90%: the hurdle is 8.5638 units of information time, or 4.2819 nats. The threshold is exact under those three assumptions. Elsewhere, the paper uses a KL data-processing bound, which establishes a necessary minimum of kl(0.9, 0.05) = 2.3762 nats.
The clock also prices the opportunity. With quadratic trading costs, each nat is worth σ²/γ relative to the position optimal at the boundary. Bonacorsi allows arbitrage to shorten signal lifetimes; as research costs fall to zero, competitive entry drives residual information toward the certification threshold. In the linear-crowding benchmark, N symmetric desks conducting costless research leave one Nth of the original excess information.
The paper cites work on sequential testing under deadlines and on multiple-testing haircuts. Its contribution is to put decay, search and deployment value on the same scale. Persistence becomes a feasibility constraint.
What does a wider search demand?
For alpha that decays exponentially toward a zero boundary, lifetime information is S²h/(4 log 2), where S is instantaneous Sharpe and h is half-life. The following hurdles use 5% familywise false deployment and 90% power. At Sharpe 2, a single candidate needs 2.968 years of half-life. Bonferroni raises the requirement to 5.157 years over 10 candidates, 7.245 over 100 and 9.271 over 1,000. At Sharpe 1 and 1,000 candidates, it reaches 37.085 years. The leading information cost grows like log M.
Those floors rely on the friendly model. In the appendices, an exponentially random lifetime makes a constant-threshold rule require about 26.47 nats of mean lifetime information, versus 4.28 for a fixed lifetime. That simple rule therefore needs about six times the budget. Unknown variance changes it too: with 12 observations, the t-test equivalent is 4.888842 nats. Bonferroni can overstate the burden if dependence information permits less conservative allocations, lowering the half-life hurdles. Both S and half-life must also be estimated. The required minimum scales as 1/S²; cutting Sharpe from 2 to 1 raises it fourfold, from 2.968 to 11.872 years.
This frontier is the paper's most usable result. A desk can enter its estimated Sharpe, decay model and search breadth, then reject candidates below the feasibility threshold.
Crowding has yet to show up
The equilibrium says that opportunities with more excess information should face stronger compression. The equity check finds nothing. Bonacorsi examines 205 Open Source Asset Pricing predictors, using half the squared originally reported in-sample t-statistic, scaled by the threshold, as a proxy. Its Spearman correlation with normalized post-publication attenuation is 0.059; the cluster-bootstrap interval is [-0.086, 0.199]. The OLS slope on log(1+proxy) is 0.0058, with HC3 standard error 0.0240 and t = 0.24. A publication filter acts on those in-sample t-statistics, likely inflating the proxy unevenly across predictors.
Bonacorsi says the pooled benchmark "contains little information" without an implementation coefficient. His proposition explains why: if that coefficient is sufficiently negatively related to excess information, the pooled slope can be zero or negative even when the proposed mechanism operates. The coefficient falls with turnover, borrow cost and impact, and rises with competitor count. The argument holds, but equity data leave the coefficient unobserved. His attempt to proxy it in a BTCUSDT holdout, by interacting excess certifiability with log market depth, fails.
The holdout contains 57 events. Both pre-specified coefficients have negative one-sided lower bounds, -3.002e-5 and -9857.24, so the joint criterion fails. The raw microstructure inputs are not redistributed.
Funding rates and gross persistence
Perpetual funding supplies the positive result. Bonacorsi uses BTC-USDT and ETH-USDT on six venues, sampled at eight-hour settlements, for 12 series. An event occurs when absolute funding reaches its trailing 95th percentile. A zero-intercept AR(1) fit to the prior 540 settlements supplies the lifetime score; 543 events have finite scores.
The score's Spearman correlation with next-seven-day signed funding is 0.4756, against 0.3833 for current edge magnitude and 0.3606 for the historical t-statistic. Lifetime score and edge themselves have a rank correlation of 0.7673. Residualizing on edge leaves the score at 0.2824 [0.128, 0.412]; dropping any one series leaves a range of 0.2529 to 0.3092. Add the historical t-statistic as a control and the figure falls to 0.1278, with a block-bootstrap lower bound of 0.012. In the top score quintile, 100 of 109 events had positive signed funding, averaging 16.97 of 21 same-sign settlements. The top edge quintile recorded 93 of 109 and 14.97.
On a series already known for persistence, a persistence estimate predicting further persistence comes close to a mechanical result. Bonacorsi limits the claim: "the reported quantities measure persistence". Net basis returns would also depend on fees, hedge drift, borrow, liquidation, slippage and venue credit risk. We did not find the sample dates.
We could not rerun either piece. We carry no perpetual-futures funding histories for these venues, while the equity version requires a per-anomaly implementation coefficient observed by neither us nor the paper.
The frontier is worth using as a screen: a 100-candidate search at Sharpe 2 demands 7.245 years of half-life. Bonacorsi ranks funding events by lifetime score, but never divides them at the frontier (score above or below one) and follows each side forward.