Who Counts the Trials? A Committed Trial Ledger for Enforcing the Deflated Sharpe Ratio in Zero-Knowledge

Abstract

The Deflated Sharpe Ratio (Bailey and López de Prado, 2014) corrects an observed Sharpe ratio for the number of trials N behind it, separating genuine skill from the selection bias of a large backtest search. Its practical weakness is structural: N is supplied by the same researcher whose result it constrains. A search over a thousand configurations, reported as a single trial, satisfies the formula while defeating its purpose. The correction is sound; its input is self-reported. We present a construction that removes the researcher's discretion over that input. The trial set is committed to a Merkle tree before evaluation; the trial count N is the leaf count of the tree, not a reported scalar; and the winning strategy is bound, inside a zero-knowledge proof (a STARK), to be the maximum over the committed leaves. The deflation is then recomputed in-circuit on Merkle-pinned prices, net of a cost model the credential discloses, so the figure an allocator reads is derived by the circuit rather than asserted by the manager. The output is a credential, checkable by anyone, in seconds, without disclosure of the strategy, whose anti-overfitting correction cannot be understated within the committed search. We give the commitment scheme and its in-circuit binding; state precisely the manipulation it eliminates (understating N, cherry-picking a non-maximal winner, softening the cost model) and the residual trust it does not (off-ledger trials, closed only by forward pre-registration); and report a live implementation that additionally computes, in-circuit, the Probability of Backtest Overfitting over all C(16,8) = 12,870 combinatorially-symmetric splits (via recursive proof composition), together with the Probabilistic Sharpe Ratio and Hansen's Superior Predictive Ability. We demonstrate the system on its own flagship strategy, which it rules not significant (DSR 0.68, below the 0.95 bar), and publish that failure as the reference credential.