What a return actually measures

Learning goals

• Separate an asset’s realized return from an investor’s required return.
• Build a nominal hurdle rate from inflation and compensation for risk.

Draft · approximately 60 minutes, excluding further revision.

Choose the owner, dates and cash flows

A return is a change in economic wealth relative to the capital committed. For one asset held between two dates with no additional investment, holding-period return is (ending price − beginning price + cash income)/beginning price. Include distributions even when the quoted price falls on the ex-dividend date. State whether costs are included.

A 6% return over six months is not automatically 12% a year. The investment horizon is part of the measurement. Neither an average market return nor a historical winning period is a promised future return.

Required versus realized

The required return is an opportunity-cost benchmark set before the outcome is known. The realized return is observed afterwards. An investment can exceed its requirement through luck; one favorable outcome does not validate the forecast model. Compare like currencies, horizons and risk exposures.

A nominal risk-free rate can be related to a real risk-free rate and expected inflation through (1 + nominal) = (1 + real)(1 + inflation). Credit, liquidity, maturity and other risks may justify additional compensation; simply adding premia is an approximation whose components can overlap. A required rate is not a guarantee that risk will be rewarded.

Reconstruct the investment before choosing a return

A fictional share costs 80 at the beginning of the year, pays a cash dividend of 3 at year-end and closes at 85. Separate price appreciation, 5/80=6.25%, from income yield, 3/80=3.75%. The holding-period return is (85−80+3)/80=10%. The calculation assumes ownership for the full period and ignores tax, transaction costs and dividend reinvestment. A quote of 6.25% describes price change only.

If inflation over the same year is 4%, real purchasing-power return is 1.10/1.04−1=5.7692%, not exactly 6%. The subtraction shortcut is only an approximation. Keep period, currency, gross/net treatment and nominal/real basis consistent before comparing investments. Write those four labels next to every return used in a recommendation.

Formula and assumptions

HPR = (P₁ − P₀ + D)/P₀; 1 + r_nominal = (1 + r_real)(1 + π)

A distribution and an inflation hurdle

1. Buy at 80, receive 3 in cash, and sell at 83: HPR = (83 − 80 + 3)/80 = 7.5%.
2. A 2% real risk-free requirement and 3% expected inflation imply nominal risk-free = 1.02 × 1.03 − 1 = 5.06%.
3. A separate assumed risk premium of 4 percentage points gives an approximate risky hurdle of 9.06%. The 7.5% outcome falls below it; this comparison alone is not a suitability decision.

Errors to catch

• Ignoring distributions when computing total return.
• Adding overlapping premia or comparing annual requirements with a shorter-period return.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org