Tools · Rolling returns
One series, many entry points.
A single cumulative figure describes one entry point: the beginning. Every other investor arrived somewhere else. This works out what the same series produced over every window of a given length, and how wide the range between them was.
Calculator
This page is showing the example series. Over 12-month windows it produced 25 results, ranging from −9.2% to +22.8% with a median of +6.3%. Enable JavaScript to paste your own; the table, chart and method on this page do not need it.
Needs at least one more month than the window.
- Best window
- +22.8%
- of 25
- Worst window
- −9.2%
- same series, different start
- Median window
- +6.3%
- the middle outcome
Each point is one window's complete return, plotted at the window's end. The zero line separates windows that finished ahead from those that did not.
Reference
The range at each window length.
The same example series read at four window lengths. Longer windows usually narrow the range and raise the share that finish positive — but only because there are fewer of them and they overlap more.
| Window | Windows | Best | Worst | Median | Positive |
|---|---|---|---|---|---|
| 3 months | 34 | +16.6% | −12.7% | +1.5% | 20 of 34 |
| 6 months | 31 | +16.3% | −6.2% | +2.1% | 21 of 31 |
| 12 months | 25 | +22.8% | −9.2% | +6.3% | 20 of 25 |
| 24 months | 13 | +30.5% | −0.8% | +17.6% | 12 of 13 |
Overlapping windows are not independent observations. Thirty-six months of data contains twenty-five twelve-month windows, but nowhere near twenty-five independent pieces of evidence.
Method
How it is calculated.
Each window
window return = ∏(1 + r) − 1
The compound return of every consecutive run of the chosen length. A series of n months contains n − window + 1 such runs, each starting one month after the last.
The summary
Best, worst and median are taken across those windows. The median is used rather than the mean because the distribution of overlapping windows is usually skewed, and a mean of overlapping observations is easy to misread as a typical outcome.
Limits
What to be careful of.
- The windows overlap. Consecutive windows share all but one month, so they are highly dependent. Treating the count of windows as a sample size overstates how much evidence there is, often by a large factor.
- The record bounds the range. The worst window can only be as bad as the worst stretch that happened to occur. A short record has not had the opportunity to produce its worst case.
- No flows. Each window assumes a single amount invested at the start and left alone. Adding or withdrawing through the window changes the result — the sequence of returns calculator covers that.
- Costs and tax are not modelled. The returns you paste are treated as the returns received.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Rolling return — the return over every window of a given length.
- Cumulative return — the whole-period figure a window sits inside.
- Maximum drawdown — the worst case a median window hides.
- Sequence of returns risk — why the entry point changes the outcome.
Questions
Common questions.
What are rolling returns?
The return over every consecutive window of a fixed length within a series, rather than over the series as a whole. They answer a different question from a cumulative figure: not "what did this produce" but "what did this produce depending on when you arrived".
Why use rolling returns instead of a single cumulative figure?
Because a cumulative figure describes one entry point. Rolling windows show the spread of outcomes across all of them, which is closer to the experience of investors who did not all start on the same day.
Is anything I paste sent to KyperX Capital?
No. The series is parsed and every window calculated in your browser. Nothing is transmitted, recorded or stored, and this website receives none of it.
Why is the median shown rather than the average?
Because overlapping windows produce a skewed distribution in which a few unusual stretches appear in many windows at once. The median is less affected by that repetition, and reads more honestly as the middle outcome.