Showing Uncertainty in Research Results

"The strategy's backtested Sharpe ratio is 1.4" sounds precise, but a single number this way hides an important question: 1.4 estimated from how much data, and how confident should anyone be that the true, ongoing figure is close to 1.4 rather than 0.6 or 2.2? A Sharpe ratio computed from two years of daily returns and one computed from fifteen years both might come out to 1.4, but they deserve very different amounts of trust, and reporting only the point estimate erases that difference entirely.

The fix doesn't require heavy statistical machinery — even a rough range communicates far more than a bare number. A backtested Sharpe ratio can be reported with a confidence interval ("1.4, with a 95% interval of roughly 0.7 to 2.1, reflecting the limited sample") or, more intuitively for many readers, as a range across sub-periods or across reasonable parameter choices ("the Sharpe ratio ranges from 0.9 to 1.8 depending on which five-year window is used"). Either version tells a reader the same underlying thing: how much would this number plausibly have come out differently under slightly different conditions, and is the headline figure sitting near the middle of that range or was it the best of several draws.

The habit is worth building even when the audience doesn't ask for it, because omitting uncertainty tends to get interpreted as "there isn't much" rather than "it wasn't reported" — a reader who sees only "1.4" will anchor on 1.4 as if it were a known constant, when the honest state of knowledge might be "somewhere between 0.7 and 2.1, probably." Reporting the range up front prevents that overconfidence from ever forming, rather than trying to correct it after the fact.

The same logic applies beyond Sharpe ratios: a hit rate, an average trade profit, a factor's monthly return spread — any summary statistic computed from a finite sample carries sampling uncertainty, and the shorter or noisier the sample, the wider that uncertainty should be shown to be. A two-year backtest and a fifteen-year backtest reporting the same headline number are not equally trustworthy, and only a stated range makes that difference visible to someone who wasn't in the room when the analysis was done.