Proving the Deflated Sharpe Ratio in zero-knowledge

A good backtest is not evidence. If you try five hundred variations of a strategy and keep the best, its Sharpe ratio is inflated by the search itself: you have found the luckiest configuration, not the truest. Every serious allocator knows this, which is why a raw backtest Sharpe is quietly discounted toward zero. The discipline's answer to this problem is one of the most important results in quantitative finance of the last decade. Our contribution is to make that answer unfakeable.

01The statistic

In 2014, David H. Bailey and Marcos López de Prado introduced the Deflated Sharpe Ratio (DSR): a correction that shrinks an observed Sharpe according to the number of trials that were run to find it, the length of the track, and the non-normality of its returns. Pass the deflation and the edge is probably real skill. Fail it, and the "edge" is a statistical fluke dressed up as a discovery. Alongside the Probability of Backtest Overfitting (PBO) and combinatorial purged cross-validation (CPCV), it forms the modern standard for telling a genuine strategy from a lucky one.

The framework is published, peer-reviewed, and widely adopted. But it has a soft underbelly that has nothing to do with the mathematics.

02The soft underbelly: who counts the trials?

The Deflated Sharpe depends on N, the number of configurations the researcher searched. And in every conventional workflow, the researcher reports N themselves. Nothing binds it. A quant who tried two hundred variations can declare they tried five, apply a gentle deflation, and present a "statistically significant" result that is nothing of the kind. The correction that exists to defeat selection bias is, in practice, chosen by the person with every incentive to understate it.

The statistic that corrects for cherry-picking is, in every ordinary workflow, computed by the cherry-picker.

This is not a flaw in Bailey and López de Prado's mathematics. It is a flaw in trust, the same flaw that makes every self-reported track record suspect. And it is exactly the flaw a proof can close.

03The contribution: enforce it in a proof

MIZAN computes the Deflated Sharpe Ratio inside a zero-knowledge proof (a STARK, via the RISC Zero zkVM). Three things change, and they change everything:

One — N is committed, not claimed. You commit the trial ledger up front. You cannot later shrink it: the proof binds your winning strategy to be provably the best of the N configurations you actually declared. Understating the search is no longer a matter of honesty; it is cryptographically impossible.

Two, the deflation is computed in-circuit. The Sharpe, the effective sample size (AR(1)-corrected for autocorrelation), and the deflation are all recomputed inside the proof from your committed positions on pinned prices, net of a cost model the credential discloses. The fee and slippage are applied in-circuit and recorded in the credential, never hidden — a frictionless Sharpe cannot be passed off as a traded one, and a verifier can reject any credential whose disclosed costs fall below a required floor. You do not report the number; the engine derives it, and the derivation is what gets proven.

Three — nothing is revealed. The strategy that produced the positions never leaves your machine. What the world sees is the verdict and the metrics, cryptographically bound to the engine's fingerprint, the pinned dataset, and your committed trial ledger. Prove the edge; reveal nothing.

04A worked example — recompute it yourself

Theory is cheap; this is a verification company. So here is a real, live credential, and the arithmetic behind it, which you can reproduce on your own machine in ~200 lines of dependency-free Python, trusting none of our software.

Take our flagship BTC trend book. Its raw in-sample Sharpe looks attractive. Run it through the committed-N deflation, and the honest verdict comes back:

Contrast the flagship's failing verdict with strategies that clear the bar. On the same locked engine, some of our strategies pass their deflation and some do not — and we publish the ones that do not:

Every credential shown here is one of our own mints. We do not present our own credentials as third-party validation — the registry records who minted each, and anyone can verify it. Independent quants minting on the engine is what we are building toward, not something we will fake.

The point is not which strategy wins. The point is that the same locked engine judges every credential the same way, the failing verdict is published as readily as the passing one, and each number is bound to a committed trial ledger its author could not understate.

the recomputation

Every committed number is reproducible from the pinned dataset alone. Our public recompute script re-implements the in-circuit backtest, integer-faithful down to the truncating division and fixed-point equity the circuit uses, and reproduces each metric to the printed digit:

You do not have to trust our verifier to trust the arithmetic — download the script and the pinned data and run it yourself, offline, no MIZAN binary, no network. That is the entire posture of the company, applied to a single number.

05Does the overfitting test have teeth?

A skeptic should ask whether the accompanying PBO statistic actually catches overfitting or blesses everything put in front of it. It has teeth, and this too is demonstrable rather than asserted. Run the exact combinatorially-symmetric cross-validation — all 12,870 splits — on two scenarios where the truth is known by construction: a pure-noise search (the winner is luck) and a genuine-skill search. The pure-noise search is flagged overfit; the skilled one clears. Our flagship's composed-PBO credential reads PBO 0.0759, not overfit, sitting squarely in the skill regime. The statistic separates luck from skill by construction.

06The boundary — what this does not prove

We state this plainly because a verification layer that oversells its own guarantees is worth nothing. A credential is only worth what its issuer refuses to certify.

07Why it matters

Bailey and López de Prado gave the field the mathematics to distinguish real edges from statistical mirages. What the mathematics could not do on its own was compel compliance, because the person applying the correction was also the person it constrained. Cryptographic proof closes that gap. The Deflated Sharpe stops being a statistic a manager can quietly soften, and becomes a property of a credential that anyone, anywhere, can check in seconds without seeing the strategy.

The framework told us how to tell skill from luck. Proof is what makes the answer unforgeable.