Define the question before the average
A conditional return asks what happened over a specified horizon after observations assigned to a specified state. Define the instrument universe, return convention, observation frequency, horizon, and label timing before calculating it. A next-session total return and a same-session change answer different questions. A classification made after the session cannot establish that its return was available after the classification. The average describes the selected sample; it does not by itself establish predictability, economic causation, or a usable allocation rule.
Count rows, episodes, and elapsed coverage
Publish the number of usable returns alongside the number of distinct state episodes and the calendar coverage. A state can contribute many consecutive observations while appearing in only one economic setting. Episode counts are a useful concentration warning, not a replacement sample size: separate episodes can also share common influences. Show how much of the total comes from the largest episode. Report missing outcomes and incomplete forward horizons rather than quietly removing them from the denominator or interpreting them as zero returns.
Specify the averaging unit as well. Equal weighting of decision rows, instruments, and complete episodes produces different summaries. An episode with many instruments can dominate a pooled table even when all instruments respond to the same event. Present the chosen weighting and a concentration diagnostic rather than implying that every instrument-return row is independent.
Overlapping horizons repeat information
Rolling forward returns can reuse the same underlying sessions. That creates dependence even when the daily changes were independent. The NIST discussion of autocorrelation explains why relationships across time matter for statistical assumptions. Inspect dependence at lags relevant to the return horizon and label persistence. Possible sensitivity checks include nonoverlapping observations and resampling contiguous time blocks. These checks answer different questions and require their own design choices; neither more bootstrap draws nor a longer table creates additional independent market episodes.
Separate the estimate from its precision
For an independent sample under suitable assumptions, uncertainty in a mean depends on both dispersion and sample size, as described in NIST's confidence-limit reference. Do not transplant that formula unchanged into dependent regime observations. Use an uncertainty method justified for the sampling process, and state its assumptions. There is no universal minimum row count that makes every regime comparison reliable. Wide intervals, concentrated coverage, or unstable estimates justify an inconclusive result even when the point estimate looks attractive.
Inspect distributions and influential episodes
Pair the mean with the median, spread, adverse outcomes, and an episode-level view. A favorable mean can coexist with frequent small losses or a small number of influential gains. Compare the full sample with a clearly labeled leave-one-episode-out sensitivity analysis, without selecting whichever version looks strongest. Do not annualize a short conditional average as though the state occupied every period. Comparisons across many states, assets, and horizons also create selection opportunities; the search history belongs beside the selected result.
A fictional comparison with unequal coverage
The table uses entirely invented, nonoverlapping one-session returns. State A has four observations spread across two episodes; State B has four observations from one episode. A's returns sum to 2%, giving a 0.5% arithmetic mean. B's returns sum to 8%, giving a 2.0% arithmetic mean. These sums are arithmetic inputs, not compounded portfolio gains. The larger mean does not establish that B is more repeatable: its entire sample describes one episode, and no uncertainty estimate or independent test has been supplied.
Keep the label archive and the conclusion narrow
A decision-oriented table should use labels constructed from information available before each measured outcome. A table rebuilt with revised inputs or full-sample smoothed states is retrospective and must be identified separately. The Philadelphia Fed's vintage-data documentation makes this information-set distinction concrete. Preserve both views when studying revision sensitivity, but do not combine their labels opportunistically. A useful conclusion names the horizon, coverage, uncertainty, and unresolved weaknesses. This is an educational framework for reading evidence, not investment advice or evidence that any state will deliver a particular future return.
Inspect the comparison
| Invented state | Invented one-session returns | Rows | Episodes | Arithmetic mean |
|---|---|---|---|---|
| A | +3%, -1%, +2%, -2% | 4 | 2 | +0.5% |
| B | +4%, 0%, -2%, +6% | 4 | 1 | +2.0% |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.