Add money to a portfolio halfway through the year and it will start reporting two different returns for the same twelve months — sometimes several points apart, occasionally with opposite signs. Neither is wrong. They answer two different questions: how well did the holdings do, and how well did your money do. This guide works through both with numbers, shows why they split, and says which one to read for which decision.
A return is a gain divided by the money that earned it. With a single lump sum and no further deposits that is unambiguous: you put in $10,000, it is worth $11,000 a year later, you made 10%. The trouble starts when money moves in or out during the period. The gain is still a single number, but “the money that earned it” is no longer one amount — part of it was there all year, part of it for a month.
The two standard answers differ in what they do with that timing. A time-weighted return removes it on purpose; a money-weighted return keeps it on purpose. Everything else follows from that one choice.
The time-weighted return cuts the period at every deposit or withdrawal, measures the return of each slice on its own, and chains the slices together:
TWR = (1 + r₁) × (1 + r₂) × … × (1 + rₙ) − 1
Because each slice starts fresh after a cash flow, the size of the cash flow drops out entirely. What is left is the growth of one dollar left in the portfolio for the whole period. That is why funds report it, why performance standards require it, and why it is the right figure to put beside an index: the S&P 500 never received your August deposit either.
The money-weighted return is the single rate that makes every cash flow — the starting value, each deposit and withdrawal, the ending value — balance out. It is the internal rate of return (IRR) of your account. A dollar that was invested for the whole year counts for a whole year; a dollar added in December counts for a month.
Solving for an IRR needs iteration, so a common shortcut is the Modified Dietz method: the gain divided by the starting value plus each cash flow weighted by the share of the period it was invested.
Modified Dietz = gain ÷ (start value + Σ cash flowᵢ × time investedᵢ)
Either way, the result reflects what you actually did — when you added money and how much — not only what the holdings did.
Start the year with $10,000. The holdings rise 20% in the first half, to $12,000. On 1 July you add another $10,000, making $22,000. The holdings then fall 10% in the second half, ending the year at $19,800.
| Step | Value |
|---|---|
| 1 January | $10,000 |
| 30 June, after +20% | $12,000 |
| 1 July, after a $10,000 deposit | $22,000 |
| 31 December, after −10% | $19,800 |
Time-weighted: 1.20 × 0.90 − 1 = +8.0%. The holdings made money over the year.
Money-weighted: you put in $20,000 and have $19,800, a $200 loss. The IRR that balances $10,000 invested for a year and $10,000 for half a year against $19,800 at the end is about −1.3%, and Modified Dietz gives the same: −$200 ÷ ($10,000 + $10,000 × 0.5) = −1.33%.
Both numbers are correct. The holdings returned 8%; your money lost a little, because twice as much of it was invested during the bad half as during the good one.
Swap the two halves: the holdings fall 10% first, to $9,000; you add $10,000 on 1 July, making $19,000; the holdings then rise 20%, to $22,800.
| Measure | Bad timing | Good timing |
|---|---|---|
| Time-weighted return | +8.0% | +8.0% |
| Money-weighted (Modified Dietz) | −1.3% | +18.7% |
| Gain in dollars | −$200 | +$2,800 |
The time-weighted return does not move — the holdings did exactly the same thing in both years, only in a different order. The money-weighted return swings by twenty points, because it is measuring the deposit decision as well: $2,800 ÷ ($10,000 + $5,000) = +18.7%.
A large gap between the two is information rather than an error: it says your deposits and withdrawals landed at unusually good or bad moments. A gap that persists year after year is worth looking at — it is a pattern in your timing, not in your stock picks.
The portfolio analytics board prints one of each, labelled. The percentage in the performance chart’s title is a return on capital: the profit for the window divided by the capital at work — the value at the start of the window plus everything added during it. It is a simple money-based measure, a close cousin of the money-weighted return, and it counts late money in full rather than by the time it was invested, so it sits between the two in the example above (−$200 ÷ $20,000 = −1.0%).
The yearly column of the monthly returns heatmap is time-weighted: the months chained together with deposits and withdrawals taken out, which is the figure to hold against an index. On a year with a large deposit the two will disagree, and now you know which question each one answers.
The analytics board is part of Ultimate; tracking a portfolio is free. Every new account gets Ultimate for seven days once the email address is confirmed.
Lemma Analysis gives independent investors both lenses in one terminal — a stock screener and an intrinsic value tool for the fundamentals, alongside price history and charts for timing.