Write the dated cash flows
Use an invented account opened with $1,000 at Year 0. Exactly one year later, before any contribution, it is worth $1,200. Add $1,000 immediately after that valuation, giving $2,200. Exactly one further year later, the account is worth $1,760 and is hypothetically liquidated.
From the investor’s perspective the external flows are −$1,000 at Year 0, −$1,000 at Year 1, and +$1,760 at Year 2. Assume annual intervals, no additional fees or tax, and no other flows. CFA Institute explains that time- and money-weighted methods answer different cash-flow questions.
Calculate time-weighted performance
The first subperiod return is $1,200 ÷ $1,000 − 1 = +20%. The second is $1,760 ÷ $2,200 − 1 = −20%. The boundary around the Year 1 contribution prevents the new $1,000 from being counted as investment growth.
Link the subperiod factors: 1.20 × 0.80 − 1 = −4% cumulatively over two years. Annualize this equal-year result as √0.96 − 1 = approximately −2.0204% per year. The simple average of +20% and −20%, which is 0%, is not the linked time-weighted result.
Solve the annual money-weighted equation
For this cash-flow pattern, solve −1,000 − 1,000 ÷ (1 + r) + 1,760 ÷ (1 + r)² = 0. Equivalently, with x = 1 + r, solve 1,000x² + 1,000x − 1,760 = 0. Use the positive growth-factor root.
The root gives x ≈ 0.9177446879 and r ≈ −8.2255% per year. Substituting that factor back produces approximately $1,760 from the opening contribution grown for two years plus the second contribution grown for one. This is a numerical check of the fictional equation, not a reported account result.
Explain the difference before ranking anything
More money was exposed during the invented negative second year than during the positive first year. The money-weighted result reflects that timing. The time-weighted result describes the linked subperiod performance after separating the external contribution.
Compare annual with annual, or cumulative with cumulative, and keep the cash-flow record attached. A real account with irregular dates needs an actual-date convention. Different cash-flow patterns can also make an IRR difficult to interpret; this example establishes only the root for the stated simple pattern, not a universally unique solution.
A reconciliation note should therefore show both the portfolio valuations and the investor cash flows. Neither a bare ending balance nor a return percentage without its period is enough to reconstruct this example.
Method, sources, and limits
The subperiod factors, annualization, and IRR residual were checked using decimal arithmetic. The CFA Institute source was opened on 26 October 2026. No manager, customer, benchmark series, or future performance was evaluated. Neither return method alone answers whether the account took appropriate risk or whether the timing decisions were suitable.
Sources & checking dates
Primary references and the product release used for this guide. A source supports the claim attributed to it; it does not endorse Thesis Lab or validate an example's investment outcome.
Educational examples are hypothetical unless explicitly identified as a dated source observation. Product details can change after the update date.