TWR vs MWR — How to Measure Returns When You Deposit and Withdraw
Say you started the year with 10 million KRW, added another 5 million in June, and ended December with 18 million. What was your return? If you answer "(18 − 15) / 15 = 20%," you're only half right. There are two measurements, and they answer different questions — time-weighted return (TWR) and money-weighted return (MWR). This article lays out the difference and which one to use in practice.
1. The two measurements, defined
TWR (Time-Weighted Return)
Cut the timeline at every cash flow, then chain the sub-period returns together. The size and timing of deposits and withdrawals are ignored.
Where rᵢ is the return of the i-th sub-period (from the balance just after one cash flow to the balance just before the next).
MWR (Money-Weighted Return)
The single rate that makes all cash flows plus the final balance solve to the same IRR (internal rate of return). If a large sum arrived at a good time, MWR looks good; if it arrived at a bad time, MWR looks bad.
Where CFᵢ is the cash flow at time i (deposits negative; withdrawals and the final balance positive).
2. Same portfolio, different answers
Concrete example — start January with 10 million KRW, add 5 million in June, end December with 18 million (figures in millions):
| Date | Balance (before) | Deposit | Balance (after) | Period return |
|---|---|---|---|---|
| Jan 1 | 0 | +10 | 10 | — |
| Jun 1 | 8 | +5 | 13 | −20% |
| Dec 31 | 18 | 0 | 18 | +38.5% |
TWR: first half −20%, second half +38.5% → (1 − 0.20) × (1 + 0.385) − 1 = 0.80 × 1.385 − 1 = +10.8%
MWR: solve for the discount rate (IRR) that makes the cash flows −1,000 (Jan 1) · −500 (Jun 1) · +1,800 (Dec 31) net to zero. By day count, XIRR ≈ +23.5% (≈ +24.3% if you simplify the 5M to exactly half a year).
About a 13pp gap between the two (TWR +10.8% vs MWR +23.5%). Why?
The extra 5 million arrived just in time for the good second half (+38.5%), which pulled MWR up. TWR ignores the timing and size of deposits and looks only at per-period returns, so the −20% first half carries more weight in the average.
3. The question each one answers
TWR — "Did I trade well?" (manager skill)
Deposit timing is often outside the investor's control (contributions with every paycheck, a lump sum when a bonus lands, and so on). TWR strips that influence out and measures pure trading and stock-picking performance. It is the standard used to evaluate fund managers.
MWR — "How much did my account grow?" (actual balance)
MWR weights returns by how long the actual money was in the market. It gives the intuitive answer to "how much did I earn on the money I put in?" For an individual asking "how much did my wealth grow this year?", it's the more natural measurement.
| Measure | Question answered | Main use |
|---|---|---|
| TWR | How good was the trading itself? | Fund evaluation · manager performance |
| MWR (IRR) | How much did my balance grow? | Personal periodic investing · real-estate project finance |
4. When they agree — and when they diverge
With no cash flows, or very small ones, TWR ≈ MWR. They pull apart when:
- A large one-time deposit lands at a volatile moment — nail the bottom by luck and MWR ≫ TWR; buy the top and MWR ≪ TWR
- A withdrawal happens right before a big loss — the loss is dodged, and MWR rises
- Periodic contributions (DCA) — MWR and TWR generally stay close (entries are spread around the average point in time)
Someone brags "I made +30% last year" — but that may just be an MWR of +30% from a big lump sum dropped near the bottom, while the TWR (actual stock/market performance) was +5%. Don't expect the same result next year. To separate luck from skill, look at TWR.
5. What Multifolios shows
Multifolios uses purchase lots and valuations to show returns relative to average cost. Purchase lots are not a complete deposit-and-withdrawal ledger, so these records alone do not establish formal TWR or MWR.
- Return on each holding card — (current price − weighted-average cost) / weighted-average cost × 100. This is a simple return (vs average cost), not a proper MWR/IRR. MWR reflects both the timing and size of cash flows, whereas this figure ignores when the money went in (how long it stayed invested).
- buyLots weighted average — the weighted-average purchase price across multiple buy lots. Same as the usual average-cost display.
- Asset trend chart — cumulative portfolio value vs cumulative invested principal (sum of deposits) over time. Point-in-time comparison is possible, but a pure TWR breakout is not provided — a candidate for future expansion.
The current display is a simple return comparing value with invested principal, not formal TWR or MWR/XIRR. Those measures additionally require dated cash flows and appropriate period valuations; they are candidates for future expansion.
6. One-line summary
TWR separates period performance from external cash flows; MWR reflects the timing and size of invested money. The two can diverge when cash flows arrive at different times. Multifolios currently displays simple returns, not formal TWR or MWR/XIRR.