PSR and DSR: read the assumptions before the score

Last Updated: 2026-10-26

A high score is not a certificate of trading skill, and a low score is not proof of fraud or incompetence. The useful question is narrower: what return series, benchmark and selection process produced the statistic?

This guide uses transparent hypothetical inputs. The separate August scan record retains its historical figures and unresolved provenance. Its maximum PSR and DSR must not be treated as two measurements of the same candidate without matching row identifiers.

The benchmark changes the question

PSR evaluates an observed Sharpe against a specified benchmark with sample-length and return-shape assumptions. The benchmark need not be zero. DSR applies a selection-adjusted benchmark; the trial set and its dependence matter. See the original DSR methodology, especially its treatment of trial variation and independent trials. These statistical outputs should not be read as the posterior probability that a particular person possesses skill.

A simple thought experiment illustrates selection without pretending to calculate DSR. Suppose each of several independent tests has a 5% false-positive probability under its null model. The chance of at least one false positive is 1 - 0.95^N:

Scroll sideways to see every column. Keyboard: focus the table region and use the arrow keys.

This is elementary probability under deliberately strong assumptions, not the chance that a selected trader is unskilled. Correlated tests do not satisfy the independence calculation. A referral also does not erase the earlier search that produced the referral.

Work one score with visible inputs

For the illustrative PSR calculation below, let s be the observed Sharpe per observation, b the benchmark in the same units, T the number of observations, g3 skewness and g4 full kurtosis. The calculation is:

denominator = sqrt(1 - g3*s + ((g4 - 1)/4)*s*s)
z = (s - b)*sqrt(T - 1) / denominator
score = standard_normal_CDF(z)

Use invented summary inputs s=0.20, T=100, g3=0, g4=3. The denominator is sqrt(1.02). Changing only the benchmark gives:

Scroll sideways to see every column. Keyboard: focus the table region and use the arrow keys.

These are benchmark-sensitivity examples, not DSR values. We have supplied neither a real return series nor a selection model for choosing those benchmarks. The table shows why changing a benchmark can change a score; it does not estimate any trader's probability of future profit.

For a DSR study, retain the actual set of tested Sharpe estimates, their variation, the dependence treatment and the resulting benchmark. Do not silently set trial variance to 1.0 or equate the visible leaderboard count with independent trials. Report sensitivity to uncertain inputs and leave the result unavailable when the inputs are not defensible.

Make the units and returns coherent

If T counts daily observations, use the matching daily return moments and a Sharpe in daily-observation units. An annualized Sharpe cannot simply be inserted alongside an unadjusted daily count. The usual square-root conversion itself depends on assumptions about the series; serial dependence needs treatment rather than a cosmetic unit label.

Cash movements are another common trap. In a synthetic account, opening equity is $1,000, a $500 deposit arrives at period end, and closing equity is $1,510. The raw equity change is $510, or 51% of opening equity. After removing that end-of-period deposit, the period's gain is $10, or 1% under this timing assumption. A deposit at the beginning or middle needs its own capital/timing treatment. Dollar-PnL differences alone do not document that normalization.

Specify whether returns include trading fees, funding, rebates and external costs; how open positions are valued; whether withdrawals and transfers are identified; and which periods are missing. Preserve raw observations before filtering. Zero volatility, an invalid denominator, too few observations or undefined moments should be unavailable states, not automatic perfect scores.

Keep the result separate from the allocation decision

Before looking at the scores, write down the comparison benchmark and threshold, the universe, excluded cases, parameter search and evaluation period. Keep later observations separate from tuning. A threshold chosen after seeing the maximum is not the same evidence as a predeclared test.

Report candidate identifiers with the unrounded values and their data window. A displayed 1.0000 may be rounded or numerically saturated; it is not certainty. A failure to meet a threshold is an insufficient-evidence result for that test, not a demonstration that the trader has no ability. Passing does not remove custody, concentration, capacity, execution or future-regime risk.

Longer history is useful only if its meaning remains coherent. More observations can reveal a hidden loss, change the estimated moments, or combine incompatible strategies. PSR and DSR do not necessarily converge to each other just because time passes. Keep the assumptions inspectable rather than replacing one leaderboard with another unexplained badge.

Method: independent calculations using the stated hypothetical inputs; no personal trading test or replication of the August scan. Primary methodology consulted on 26 October 2026. AITR may earn commissions from commercial links elsewhere; this explanation contains no platform recommendation. Trading can lose money.