Holding Period Return (HPR)

HPR = \frac{P_1 - P_0 + D}{P_0}

$HPR$: holding period return — total gain per dollar invested, as a decimal
$P_0$: the subscript 0 means 'at the start': the price you paid
$P_1$: the subscript 1 means 'at the end': the price when you sold
$D$: any dividend or income collected along the way
$\frac{P_1 - P_0 + D}{P_0}$: everything you gained (price change plus income), divided by what you put in

Why it must be true

A return is just what you ended with, relative to what you put in. Over one holding period you gain (or lose) two ways: the price change $P_1 - P_0$ and any income $D$ received along the way. Divide the total gain by the starting price $P_0$ — the capital actually at risk — and you have the holding period return.

The classic slip is dividing by the ending price, or forgetting the dividend. Anchor on the question the ratio answers: "per dollar invested at the start, what came back?"

The derivation

Total wealth generated over the period, per dollar invested:

HPR = \frac{\text{ending value} + \text{income} - \text{starting value}}{\text{starting value}} = \frac{P_1 + D - P_0}{P_0}

Equivalently, split it into two familiar pieces:

HPR = \underbrace{\frac{P_1 - P_0}{P_0}}_{\text{capital gain yield}} + \underbrace{\frac{D}{P_0}}_{\text{dividend yield}}

When to reach for it

Performance of a single position over a single period, where income was received along the way.

Listen for

“bought at … sold at …”“received a dividend / coupon of …”“total return for the period”“beginning and ending price”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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Split it: price return + dividend yield. A stock up $4 on$ 50 (8%) with a pitfalls: [ dividend (2%) returned 10% — two easy fractions, added.
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Denominators of 25, 50, 100 are gifts: per-dollar moves are 4%, 2%, 1% respectively. Rescale awkward prices to the nearest one.

Traps in applying it

✗Forgetting the income term — return is price change PLUS distributions.
✗Dividing by the ending price instead of the beginning price.
✗Annualizing by multiplying instead of compounding when the holding period isn't a year.

Limits & criticisms

It is a single-period, pre-tax, pre-fee measure. It assumes the dividend arrives at period-end — mid-period income you could reinvest is worth slightly more. Chaining periods together requires compounding wealth relatives (the geometric mean), not adding HPRs.

Where it came from

Measuring return sounds obvious, but it was standardized surprisingly late. Early performance claims routinely ignored dividends until index pioneers — from Charles Dow's 1896 average to the Cowles Commission's 1930s studies of whether forecasters could actually beat the market — forced total-return accounting: price change plus income.

Today HPR is the atom of performance measurement: GIPS-compliant fund reporting, index total-return series, and every track record is built by chaining these single-period returns together.

One identity, 2 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

Total single-period return

HPR = \frac{P_1 - P_0 + D}{P_0}

Gain per dollar invested: price change plus income, over what you put in. It splits cleanly into capital-gain yield plus dividend yield.

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Price needed for a target return

P_1 = P_0(1 + HPR) - D

Read backwards: if part of the return arrives as income, the price doesn't have to climb as far to hit the target.

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Where it leads

Master this and the following come almost for free:

Geometric Mean Return Sharpe Ratio Margin Call Price Current Yield Hedge Fund Fees (2-and-20)

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