Holding-period yield, annualised

The holding-period return is bare arithmetic on three observed amounts: the ending value, plus whatever income arrived along the way, less the beginning value, all divided by the beginning value. Nothing is assumed and nothing is forecast — it is a record of a finished stretch of ownership, which is precisely why it is trustworthy and precisely why it cannot be quoted as a rate without further work.

That further work is annualisation: the period’s growth factor is raised to the power of a year-count over the elapsed days, compounding the observed pace across a full year. It answers a hypothetical — what would a year at this pace deliver — and the shorter the period, the more violently the hypothetical extrapolates. A strong month annualises into a spectacular figure that no honest reader treats as a forecast.

Income is counted once, at face value. A coupon or interim interest payment joins the gain the day it is received, but nothing here reinvests it — reinvestment would need a rate of its own and would quietly turn a measurement into a model. Keeping the income term plain is what lets two holdings be audited on identical terms.

The two outputs answer different questions, and swapping them is the classic error. The period figure says what this stretch of ownership delivered; the annualised figure says how fast it was delivered. Comparing a raw part-year return against an annual quote flatters whichever ran shorter, and the entire point of annualising is to take that flattery away.

The first output of this calculation is almost embarrassingly simple: everything the position gained, divided by what it cost to hold. The gain has two sources — the change in the value itself and any income collected along the way — and both are observed amounts on real dates rather than expectations. Nothing is estimated, nothing is projected, and there is no rate hiding anywhere in it.

That simplicity is what makes the figure trustworthy, and it is also what makes it incomparable. A return of a given size means something entirely different depending on whether it took a month or a decade, and the raw figure does not carry the duration with it. Quoted alone it is honest but useless for ranking; quoted against a yearly rate it is actively misleading.

Counting income separately from the change in value is worth pausing on, because leaving it out is the most common way this measurement goes wrong. A holding that paid coupons and ended where it began did not deliver nothing; it delivered the coupons. Any audit that reads only the beginning and ending values will systematically understate exactly those instruments whose whole purpose is to pay income.

Annualising takes the growth factor the period achieved and compounds it across a whole year — asking, in effect, what would happen if this pace simply continued. That is a genuinely useful question, because it is the only way a part-year result can be laid beside a yearly quote without one of them flattering the other. It is also a hypothetical, and it borrows its entire credibility from an assumption the period itself cannot support.

The borrowing gets more expensive the shorter the period. A strong month, compounded twelve times over, becomes a spectacular annual figure that no honest reader treats as a forecast — and the same arithmetic turns a weak month into a catastrophe that will probably never arrive either. Annualisation amplifies whatever it is handed, in both directions, and short periods hand it the noisiest input available.

Note also that compounding a pace is not the same as scaling it. Doubling the length of a period does not halve the annualised figure, because each notional repetition builds on the one before it. This is why annualised results from short holdings sit so much further above the raw return than intuition expects, and why the try-it below is worth running twice: once shortening the period at a fixed gain, once stretching it.

The practical use of the second output is comparison. Two positions held for different lengths of time cannot be ranked on their raw returns — the longer one has had more time to accumulate and will usually look better regardless of how it performed. Annualising both removes that advantage and leaves only pace, which is the property a ranking actually wants to know about.

The same move rescues an equally common error in the other direction: comparing a raw part-year result against an annual quote. Left unannualised, a part-year return is being judged against a full year’s worth of a rate, and it will lose a contest it never entered. Whether the correction flatters or deflates a particular holding is not something to decide in advance — it is what the calculation is for.

The elapsed-day count deserves as much care as the values themselves, because it is the denominator of the pace. A holding period entered a few days wrong barely moves the raw return and moves the annualised figure noticeably, and on short holdings the sensitivity is at its sharpest. Where a statement gives dates, count them; where it gives a rounded month, note that the annualised figure inherits the rounding.

This calculation measures one holding, in one currency, between two dates. It does not reinvest the income, which means it neither rewards nor punishes what was done with the coupons after they arrived. It does not know about tax, dealing costs or spreads — those are inside the answer only if the reader put them inside the inputs, and being consistent about that across two holdings is what keeps a comparison fair.

Nor is it a performance attribution. The figure says what happened, not why: a strong result may be skill, market direction, an accident of the dates chosen, or a currency movement that the single-currency assumption has quietly folded in. And a negative result is a legitimate answer rather than an error — stating the size of a bad stretch precisely is one of the most useful things this measurement does, and remembering it vaguely instead is one of the least.

The engine below arrives pre-filled with the pack’s own declared example: a position held for roughly half a year that ends modestly above where it began, with one small income payment collected along the way. Read the two outputs against each other first. Then hold the values still and shorten the holding period — the raw return will not move at all, and the annualised figure will leap. Stretch the period instead and watch the same gain sink below the yearly rates it was being compared against.

Read the period figure as what this stretch of ownership delivered, and the annualised figure as how fast it was delivered — a hypothetical year at the observed pace, not a forecast of the next one. Both are computed live by the verified engine from your inputs; this page stores neither.