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CFA Level I Exam · The Return and Risk of a Financial Portfolio

Holding Period Return and Return Measures Explained

Updated 7 October 2026 · Fact-checked

Holding period return (HPR) is the total gain over one period: (end value − start value + income) ÷ start value. To summarise many periods, use the arithmetic mean for a single-period expectation, the geometric mean for compound growth, the time-weighted return to judge a manager, and the money-weighted return (IRR) to judge the investor's own timing.

Understand Holding Period Return and Return Measures

A holding period return measures what you earned on an investment over one stretch of time. It counts both price change and income such as dividends or interest. If you buy a share at $50, receive $2 in dividends and sell at $54, your gain is $6 on $50, so the HPR is 12%.

One period is easy. The trouble starts when you have several periods and want one number to describe them. Different questions need different averages. That is why the CFA curriculum gives you four tools.

The arithmetic mean adds the returns and divides by the count. It is the best estimate of the return in a single future period. The geometric mean compounds the returns, so it tells you the actual per-period growth rate over the whole span. The geometric mean is never larger than the arithmetic mean. They are equal only when every return is identical. The gap widens as returns become more volatile.

When cash is added or withdrawn, a further issue appears. The money-weighted return is the internal rate of return (IRR) of all cash flows, so it is affected by when and how much you invested. The time-weighted return chains the sub-period returns between cash flows, removing the effect of their size and timing. Because a manager usually does not control client deposits and withdrawals, the time-weighted return is the standard for judging manager skill. The money-weighted return shows what the investor actually earned.

If the manager times flows well, money-weighted beats time-weighted. If money is added before poor periods, money-weighted is lower.

Key formulas to remember

Holding period return
HPR = (P1 − P0 + D1) ÷ P0 = (P1 + D1) ÷ P0 − 1
P0 is the starting value, P1 the ending value, D1 income received in the period.
Multi-period HPR
HPR = (1 + R1)(1 + R2)…(1 + Rn) − 1
Link returns by multiplying growth factors. Never add them.
Arithmetic mean return
Arithmetic mean = (R1 + R2 + … + Rn) ÷ n
Use as a single-period expected return estimate.
Geometric mean return
Geometric mean = [(1 + R1)(1 + R2)…(1 + Rn)]^(1/n) − 1
Use for compound growth over time. Geometric ≤ arithmetic.
Money-weighted return
Σ CFt ÷ (1 + IRR)^t = 0
Solve for IRR using the calculator cash flow worksheet. Deposits are outflows from the investor's view at the start, and the ending value is an inflow.
Time-weighted return
TWR = [(1 + HPR1)(1 + HPR2)…(1 + HPRn)] − 1
Compute an HPR for each sub-period between cash flows, then compound. Annualise with the power 1/years.

How to solve Holding Period Return and Return Measures questions

Start by identifying what the question asks you to summarise and whether cash flows occur inside the period.

  1. 1Read the question to see which measure is named: HPR, arithmetic, geometric, money-weighted or time-weighted.
  2. 2List every period return as a decimal. Convert percentages and check whether income is included.
  3. 3For HPR, add income to the price change and divide by the starting value.
  4. 4For multi-period growth, convert each return to a growth factor (1 + R) and multiply them.
  5. 5For the geometric mean, take the nth root of the product of growth factors and subtract 1.
  6. 6For time-weighted return, split the timeline at each cash flow, find the HPR of each sub-period using values just before the flow, then chain them.
  7. 7For money-weighted return, write the dated cash flows, then solve for IRR with the cash flow worksheet.
  8. 8Check reasonableness: geometric must not exceed arithmetic, and a time-weighted result must ignore cash flow size.

Quickest way: Growth-factor shortcut with calculator

When to use it: Use for any multi-period return question where you need a geometric mean or a chained return.

  1. Convert each return to 1 + R and multiply on the calculator, keeping the running product.
  2. For the geometric mean, use the y^x key (BA II Plus) with 1/n as the exponent, or on the HP 12C enter the product, then n, 1/x, then y^x. Subtract 1.
  3. Estimate the arithmetic mean quickly by adding the returns and dividing by n. The geometric answer must be a little lower.
  4. Eliminate any option above the arithmetic mean when you are asked for a geometric mean. Options are listed smallest to largest, so this often leaves one or two choices.
  5. For money-weighted return, press CF, enter CF0, C01, F01 and so on, then IRR CPT. Treat the final value as a positive cash flow in the last period.

Common mistakes in Holding Period Return and Return Measures

  • Adding period returns to get a multi-period return

    Adding feels natural and works for the arithmetic mean.

    Fix: For total return over several periods, always multiply growth factors (1 + R) and subtract 1.

  • Forgetting income in the holding period return

    Students focus on the price change shown in the stem.

    Fix: Add dividends or interest to the numerator: (P1 − P0 + D1) ÷ P0.

  • Using the arithmetic mean to describe compound growth

    It is quicker to compute.

    Fix: Use the geometric mean when asked about growth of an investment over multiple periods. The arithmetic mean overstates it when returns vary.

  • Mixing up which return suits a manager

    Both measures look similar and both use cash flows.

    Fix: Time-weighted return judges the manager because it removes timing and size of client flows. Money-weighted return reflects the investor's experience.

  • Computing sub-period HPRs with the wrong ending value for time-weighted return

    Students forget the cash flow arrives at the end of the sub-period.

    Fix: Use the value just before the cash flow as the end of the sub-period, and the value just after it (including the flow) as the start of the next.

  • Taking the root with the wrong exponent

    Confusing n periods with number of returns plus one, or using years when returns are quarterly.

    Fix: Use 1/n where n is the count of returns being compounded. Convert to annual only after you know the period length.

Worked examples

Example 1

A fund returns +20%, −10% and +15% in three consecutive years. What is the geometric mean annual return? Options: A) 7.0% B) 7.5% C) 8.3%

Show the solution
  1. Convert to growth factors: 1.20, 0.90, 1.15.
  2. Multiply: 1.20 × 0.90 = 1.08; 1.08 × 1.15 = 1.242.
  3. Take the cube root: 1.242^(1/3) ≈ 1.0752.
  4. Subtract 1: about 7.5%.
  5. Check: arithmetic mean = (20 − 10 + 15) ÷ 3 = 8.33%, so geometric must be below it. Also 1.075^3 = 1.2423, which confirms 7.5%.

Answer: Geometric mean ≈ 7.5% (option B).

Example 2

An investor buys one share at $40. After one year she receives a $2 dividend and buys a second share at $44. At the end of year two she receives $2 per share on two shares ($4) and sells both shares at $46 each. Find the money-weighted return.

Show the solution
  1. Time 0: buy one share, cash flow −40.
  2. Time 1: dividend +2, then buy another share at 44 for −44. Net cash flow = 2 − 44 = −42.
  3. Time 2: dividends 4 plus sale proceeds 92 = +96.
  4. Set NPV = 0: −40 − 42 ÷ (1 + r) + 96 ÷ (1 + r)² = 0.
  5. Calculator: CF0 = −40, C01 = −42, F01 = 1, C02 = 96, F02 = 1, then IRR CPT.
  6. Test r = 0.1: −40 − 38.18 + 79.34 = 1.16. Test r = 0.11: −40 − 37.84 + 77.92 = 0.08. Test r = 0.111: −40 − 37.80 + 77.78 ≈ −0.02. So r is just above 11%, about 11.1%.

Answer: Money-weighted return ≈ 11.1% per year.

Exam tips

  • Read for cash flows in the stem. If there are deposits or withdrawals, the question is probably testing time-weighted versus money-weighted.
  • Use the rule geometric ≤ arithmetic to knock out options fast. Equality needs identical returns.
  • If a question asks which measure evaluates a manager, answer time-weighted. If it asks about the investor's actual experience, answer money-weighted.
  • Compute with growth factors, not percentages, to avoid rounding slips. Keep at least four decimals until the final step.
  • Watch the period length. Quarterly returns need annualising with the power 4 if compounding, not multiplying by 4.

Practice questions from The Return and Risk of a Financial Portfolio

Holding Period Return and Return Measures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Holding Period Return and Return Measures: frequently asked questions

What is the holding period return formula for CFA Level I?

HPR = (ending value − beginning value + income) ÷ beginning value. It captures price change and any dividends or interest received during the period. For several periods, multiply the growth factors (1 + R) and subtract 1.

What is the difference between arithmetic mean and geometric mean return?

The arithmetic mean is the simple average of period returns and estimates a single-period expected return. The geometric mean compounds returns and measures the actual growth rate over the whole span. The geometric mean is lower unless all returns are equal.

When should I use time-weighted vs money-weighted return?

Use time-weighted return to evaluate a manager, because it removes the effect of the size and timing of client cash flows. Use money-weighted return to see the investor's own result, since it is the IRR of all cash flows and reflects timing decisions.

How do I calculate the geometric mean return for a portfolio?

Convert each period return to 1 + R, multiply them, raise the product to the power 1/n, then subtract 1. On the BA II Plus use the y^x key with 1/n as the exponent.