Subtract what you supplied from outside
The monetary investment result is ending value − starting value − contributions + withdrawals. An account can grow while its investments lose money.
Reconcile growth, a deposit and a withdrawal
One invented year: €10,000 initially, €4,000 deposited, nothing withdrawn, €13,000 at the end. Values include investments and cash; fees or taxes deducted inside remain costs. Result: €13,000 − €10,000 − €4,000 = -€1,000. The balance grew €3,000 while investments lost €1,000.
Separately, €10,000 initially, €1,000 withdrawn and €9,000 left, with no other flows, gives €9,000 − €10,000 + €1,000 = €0. Adding back the withdrawal separates spending from investment performance.
These are money amounts. Dividing by the opening balance does not generally give a fair percentage when different amounts were invested for different lengths of time.
Draw the boundary before classifying a payment
Both moves stay within the boundary. The dividend is investment income; the purchase uses existing money.
Handle transfers, outside dividends and charges
A transfer between brokers leaves one account and enters another. Include investments transferred as well as cash. If both accounts are inside the measured portfolio, the transfer stays within it.
A dividend paid directly outside the portfolio counts once as value received outside. Omitting it understates the result; counting it twice overstates it. Fees or taxes paid from elsewhere may need adjustment for an after-cost personal result; the broker may not know them.
Ask when each contribution was exposed
Invented fund returns: +20%, then −10%. Each investor contributes €10,000 overall. All income reinvested; no withdrawals, costs or taxes.
- StartMoney enters before year 1↓ €10,000 contributed↓ €1,000 contributed
- Year 1 · +20%Only money already invested earns this return€12,000€1,200
- Between yearsImmediately after year 1, before year 2€12,000 stays invested↓ €9,000 added → €10,200
- Year 2 · −10%The loss acts on each new balance€10,800€9,180
Incoming arrows mark contributions; lane widths do not measure balances.
B could not necessarily have contributed earlier: the €9,000 may only then have become available. The favourable date is apparent in hindsight, not a rule for timing future savings.
Follow the two dated balances
A: €10,000 × 1.20 = €12,000; €12,000 × 0.90 = €10,800.
B: €1,000 × 1.20 = €1,200; add €9,000 to reach €10,200; multiply by 0.90 to reach €9,180.
The fund’s cumulative return is 1.20 × 0.90 − 1 = 8%. This links the two yearly rates without giving extra weight to B’s larger second-year balance.
Match the return method to your question
- Time-weighted return (TWR)
- Reads the two return periods above: +20%, then −10%. Compounding them gives both investors an 8% cumulative TWR, removing the effect of their different contributions. Use it to compare investment or strategy performance.
- Money-weighted return (MWR)
- Reads each investor’s incoming arrows and ending balance. It weights the periods by the money exposed: most of B’s contribution participated only in the losing year. The resulting rate describes the invested money’s experience.
For either method, check the period, currency, fees and whether the rate is cumulative or annualised.
Keep the records the method needs
Reports often use an internal rate of return, IRR or XIRR, for MWR. It is not gain divided by total contributions; dates matter. Check the method without needing to derive it.
Retain statements or exports with dated flows, starting and ending values, cash and investments transferred, and outside charges. TWR also needs valuations around cash flows or a suitable approximation; ending value and deposit history alone cannot reconstruct all intervening returns. Check a tool’s method and imports rather than collecting daily price records yourself.
Reconcile two independent records
Both hypothetical records run from 22 October 2026 to 22 October 2027 in euros. Internal investment expenses are already included; personal taxes and outside charges are omitted.
A starts with €6,000, has no contributions or withdrawals and earns +4% nominally. The price of its comparison basket rises 6%. B starts with €12,000, receives €3,000 from outside, pays €1,000 outside and ends at €15,000. B’s flow dates and intermediate valuations are missing.
For A, record the ending nominal balance, its value in opening-date prices and the real return. For B, reconcile the monetary investment result and state what additional records a percentage return would need.
Compare the reconciliation and missing records
€6,240 future euros ÷ 1.06 → €5,886.79 in 22 Oct 2026 prices
€14,000 supplied net + €1,000 investment result → €15,000 closing
A’s real change is €5,886.79 − €6,000 ≈ −€113.21, or 1.04 ÷ 1.06 − 1 ≈ −1.89%. The €240 nominal gain buys less than the opening balance did.
B’s monetary result is €15,000 − €12,000 − €3,000 + €1,000 = €1,000. Dividing by €12,000 would ignore when the other money participated. Obtain dated flows for MWR and suitable valuations around flows for TWR; these ending totals alone establish neither rate.
Check that A’s values share a price basis before comparison and that B’s external money is counted once. A clear statement of what cannot yet be calculated belongs in the reconciliation.
The next chapter asks who can produce the payments and value measured here: businesses, borrowers and the funds holding their claims.