You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Quantitative Methods guide.
Holding period return
Holding period return (HPR) is everything you earned over the period, price change plus income, divided by what you paid. Over several periods, compound: multiply each (1 + R) together and subtract 1.
On the exam
- Calculate and interpret different approaches to return measurement over time and describe their appropriate uses
Calculate and interpret holding period returns, single and multi-period. Expect a one-step calculation with a dividend or coupon, and a multi-period chain where adding the returns gives the wrong option.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What is the holding period return?
HPR is the total gain over the time you held the asset, as a fraction of the amount you paid. The gain has two parts: the price change and any income received.
Split the numerator and you get two pieces. The capital gain yield is (P₁ − P₀) ÷ P₀. The income yield is I₁ ÷ P₀. Together they make the total return , and the holding period return is simply that total return measured over whatever period you held.
Questions do not always ask for the return. They give the return and ask for the price you can pay, the price you must sell at, or the dividend you need. It is the same formula, turned around.
An investor buys a share at 40.00, receives 0.80 of dividends and sells at 43.00. The holding period return is closest to:
(43.00 − 40.00 + 0.80) ÷ 40.00 = 9.50%
Holding period return, r9.50%
- 43−40+0.8=the dollar gain
- ÷40=as a decimal: × 100 for percent
- 43ENTER40−0.8+the dollar gain
- 40÷as a decimal
ENTER enter (on the HP, puts the number on the stack)
Returns can be written as decimals, fractions or percentages. They mean the same thing, so 0.095 and 9.5% are one answer.
The formula treats income as arriving at the end of the period. If it arrives earlier and is reinvested, the true return is a little higher.
Try this 0 of 2
- Let the price fall but still earn a positive return
- Hit a holding period return of exactly 10%
Show working
(43.00 − 40.00 + 0.80) ÷ 40.00 = 3.80 ÷ 40.00 = 9.50%
How do you chain several periods together?
Multiply the growth factors and subtract 1. Each period’s return applies to the balance at the start of that period, not to the original amount.
Exam tip If two options differ by a few tenths of a percent and one equals the plain sum, it is the trap.
Go deeper Why reinvested income changes the answer
The basic formula assumes all income arrives on the last day. In practice a share may pay a dividend halfway through the period. If you reinvest it, the reinvested money earns (or loses) the return for the remaining time, so ending wealth differs from the simple calculation. A single HPR number cannot capture that timing. This is the same problem you meet when an investor adds or withdraws money during a period, and it is exactly why lesson 4 separates the money-weighted return, which reflects timing, from the time-weighted return, which removes it. For exam questions, assume income arrives at the end unless the question tells you otherwise.
Go deeper Total return versus price return
A price return counts only the change in price. A total return adds the income. For a share that pays a meaningful dividend, or a bond whose coupon is most of its return, the difference is large. Many market indexes are published in both versions: a price index that ignores dividends, and a total return index that assumes they are reinvested. When a question gives you income, it expects you to include it. When you compare an index with a fund, make sure both are on the same basis, otherwise the comparison understates the index by the size of its yield.
Memorize this
MemorizeOne period and several
| Case | Formula |
|---|---|
| One period | |
| Several periods |
Memory hook "Gain plus income, over what you paid." Then: returns multiply, they never add.
Know it cold The base is always , and income counts.
Quick example
Buy at 40.00, receive 0.80 of dividends, sell at 43.00. (43.00 − 40.00 + 0.80) ÷ 40.00 = 9.5%.
- 43−40+0.8=÷40= 0.095
- 43ENTER40−0.8+40÷ 0.095
ENTER enter (on the HP, puts the number on the stack)
Quick example
Returns of 8%, −5% and 12%. 1.08 × 0.95 × 1.12 − 1 = 14.91%.
- 1.08×0.95×1.12−1= 0.1491
- 1.08ENTER0.95×1.12×1− 0.1491
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
HPR with a dividend
Buy at 450, dividend 6, sell at 468. HPR is closest to…
(468 − 450 + 6) ÷ 450 = 5.33%. The option without the dividend (4.00%) is the trap.
-
Chain several periods
+10%, −20%, +15%. Three-year return?
1.10 × 0.80 × 1.15 − 1 = 1.2%. The sum (5%) is the trap.
-
Work back to a price
Buy at 40, expect 0.80 of income. Sale price needed for 9.5%?
P₁ = 40 × 1.095 − 0.80 = 43.00.
Exam traps
- Forgetting the dividend or coupon. The return is price change plus income.
- Dividing by the ending price. The base is always what you paid, P₀.
- Adding period returns instead of compounding them.
Checkpoint
3 exam-style questions. About 90 seconds each.
1An investor buys shares at INR 450, receives a dividend of INR 6 per share at the end of the period and sells at INR 468. The holding period return is closest to:
2A fund returns 10%, −20% and 15% in three successive years. Its three-year holding period return is closest to:
3Compared with receiving it at the end of the period, a dividend received mid-period and reinvested at a positive return would make the holding period return:
Key takeaways
- HPR = (price change + income) ÷ starting price.
- Multi-period HPR compounds: multiply the (1 + R) terms, then subtract 1.
- HPR has no time unit by itself. Annualize before comparing returns over different lengths (lesson 5).
Quick example
Buy at 40.00, receive 0.80 of dividends, sell at 43.00. (43.00 − 40.00 + 0.80) ÷ 40.00 = 9.5%.
- 43−40+0.8=÷40= 0.095
- 43ENTER40−0.8+40÷ 0.095
ENTER enter (on the HP, puts the number on the stack)
Quick example
Returns of 8%, −5% and 12%. 1.08 × 0.95 × 1.12 − 1 = 14.91%.
- 1.08×0.95×1.12−1= 0.1491
- 1.08ENTER0.95×1.12×1− 0.1491
ENTER enter (on the HP, puts the number on the stack)
Questions about this lesson?
Where this comes back
- Time Value of Money in Finance Quantitative Methods
- Portfolio Risk and Return: Part I Portfolio Construction
Questions candidates ask
How do you calculate holding period return with dividends?
Add the dividend to the price change and divide by the purchase price: (P₁ − P₀ + dividend) ÷ P₀. Buying at USD 40.00, collecting USD 0.80 and selling at USD 43.00 gives 3.80 ÷ 40.00 = 9.5%.
What is the difference between holding period return and annualized return?
Holding period return covers whatever length of time you held the asset and carries no time unit. Annualized return restates it as a one-year equivalent by compounding, so that investments held for different lengths of time can be compared.
How do you calculate a multi-year holding period return?
Convert each year's return to a growth factor (1 + R), multiply the factors and subtract 1. Returns of 8%, −5% and 12% give 1.08 × 0.95 × 1.12 − 1 = 14.91%. Adding them would give 15%, which is wrong.
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