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Realised return · holding period
Holding-period yield, annualised
Measure the return a holding delivered between two dates — ending value, income received, beginning value — and annualise that pace onto a yearly footing.
Verified engine
What the engine returns
Read the period figure first: gain plus income over the base, the plain fraction the stretch delivered. Then the annualised figure: the same pace compounded across the year-count. The second is larger than a naive doubling of the first would suggest, because compounding a pace is not the same as repeating it additively.
Inputs the result is built from
Beginning value
Ending value
Income received during the period
Holding period (days)
Annualising year-count basis
How the result is derived
MethodEnding value plus income less beginning value, over beginning value, for the period yield; the period growth factor raised to the year-count over the elapsed days, less one, for the annualised yield.
StandardHolding-period return and annualisation relations
GuardA zero or negative beginning value is refused — with no base there is no return to state, only an undefined ratio.
How the annualised yield moves with the holding period
What the money did over the days it was actually held
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.
Ending value plus income less beginning value, over beginning value, for the period yield; the period growth factor raised to the year-count over the elapsed days, less one, for the annualised yield.
When this calculation is used
- Auditing what a certificate exited early, a fund position or a deposit actually delivered between two statement dates.
- Putting a part-year result on an annual footing so it can sit beside quoted yields without flattering either side.
- Comparing two holdings that ran for different lengths of time on one scale.
- Reading a short period’s result with the annualisation caution in view — seeing how much of an impressive figure is pace rather than gain.
- Stating a loss precisely: a negative holding-period yield, annualised, is the honest size of a bad stretch and the antidote to remembering it vaguely.
Worked 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 — the shape of an ordinary interim review.
Read the period figure first: gain plus income over the base, the plain fraction the stretch delivered. Then the annualised figure: the same pace compounded across the year-count. The second is larger than a naive doubling of the first would suggest, because compounding a pace is not the same as repeating it additively.
Halve the holding period while keeping the gain fixed and the period figure does not move — but the annualised figure leaps, because the same gain at twice the pace is a very different year. That leap is the caution built into every annualised number, and the reason short-period results should be admired slowly. Run the experiment the other way — stretch the same gain over more days — and the annualised figure sinks below the quoted rates it was being compared against, which is the moment the comparison starts being useful.
What each input represents
Beginning value
What the position was worth on the first day of the stretch being measured — the base every other figure is divided by. For a deposit this is the amount put in; for anything traded it is the value on the chosen starting date, not the price once hoped for.
Ending value
What the position was worth on the final day. It may sit below the beginning value; a negative holding-period yield is a legitimate answer and often the most useful one, since a loss is exactly what this measurement exists to make undeniable. A zero ending value is also accepted — a position can be wiped out, and the arithmetic should be able to say so.
Income received during the period
Coupons, interim interest or distributions collected between the two dates, at face value. Leaving it out understates the return of anything that pays income; counting it as reinvested overstates it. It defaults to nothing for holdings that paid nothing.
Holding period (days)
The elapsed days between the two valuations. This is the denominator of the pace: the same gain over fewer days annualises into a far larger figure, which is why the day count deserves as much care as the values themselves.
Annualising year-count basis
The year length the annualisation compounds onto. Markets differ in convention — some count a calendar year, some a shorter trading or money-market year — so the basis is an explicit input rather than a hidden constant, and the default is the calendar count. Matching the basis to the convention of whatever the result will be set beside is what keeps the comparison honest.
Assumptions and limits
- The beginning and ending values are observed amounts on real dates, not estimates of either.
- Income is counted once, at face value, with no reinvestment modelled.
- Annualisation assumes the observed pace could be sustained for a year — an assumption the period itself cannot prove.
- Everything is measured in one currency; tax and dealing costs are inside the figures only if the reader put them there.
What the guards protect against
- A zero or negative beginning value is refused — with no base there is no return to state, only an undefined ratio.
- A zero-day holding period is refused: a pace needs elapsed time, and annualising an instant would divide by nothing.
- The year-count basis is bounded near a real year, so a basis entered in the wrong unit is refused instead of silently rescaling the answer.
Provenance
Holding-period return and annualisation relations
Ending value plus income less beginning value, over beginning value, for the period yield; the period growth factor raised to the year-count over the elapsed days, less one, for the annualised yield.
Educational reference, not investment advice. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.