Work out a holding period return and explain what it means
The idea
Holding period return is the total return over a single period, counting both the price change and any income received: HPR = (ending value - beginning value + income) / beginning value. It makes no assumption about how long the period is and no adjustment for reinvestment, which makes it the raw building block that other return measures are constructed from. Chaining several holding period returns geometrically gives the return over the whole span, which is how a multi-period record is built from its parts.
Formulas
Holding period return
HPR = (P₁ − P₀ + D₁) ÷ P₀
- P₀
- the price at the start
- P₁
- the price at the end
- D₁
- any cash received over the period
One period, any length. It is not annualised, and annualising a short one magnifies the noise in it.
A practice question
A share bought at $100 is sold a year later at $108 after paying a $3 dividend. What is the holding period return?
- 11.00% — correct
- 8.00%Why not: The price change alone, 8 ÷ 100. The $3 dividend was received and is part of the return.
- 3.00%Why not: The dividend alone, 3 ÷ 100. The $8 of price appreciation is missing.
(108 − 100 + 3) ÷ 100 = 11.00%. Counting only the price change ignores the dividend, which is part of what the investor actually received.
A harder one
An investment returns 10% in year one and −5% in year two. What is the holding period return over the two years?
- 5.00%Why not: 10 − 5, the returns added. Year two's −5% applies to the larger balance year one left, so the loss is bigger than the arithmetic suggests.
- 4.50% — correct
- 2.50%Why not: The arithmetic mean of the two years, (10 − 5) ÷ 2. That is an average annual figure, not the total over both years.
Returns compound rather than add: 1.10 × 0.95 − 1 = 4.50%. Adding them gives 5% and ignores that the second year applies to a larger base.
The hardest tier
Why can a holding period return not be compared directly across investments held for different lengths of time?
- Because it excludes income by constructionWhy not: It includes income — dividends and coupons are part of it. The obstacle is the period, not the components.
- Because it assumes reinvestment at the risk-free rateWhy not: It makes no reinvestment assumption at all: it covers a single period, inside which there is nothing to reinvest.
- Because it is a total return over its own period, not a rate per unit of time — correct
A 10% return over a month and a 10% return over a decade are very different propositions. Annualising puts them on a common footing before they can be compared.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →