Time-weighted vs money-weighted

Once you can handle flows, you can ask two different questions. How well did the manager invest? And how did the investor's money actually do? They sound identical. They aren't.

Time-weighted return (TWR): Chains together each period's return, so the size of the account in each period doesn't matter. It judges the manager, who doesn't control when clients add or withdraw money.
Money-weighted return (MWR): The internal rate of return. Periods with more money in them count for more. It describes the investor's own experience, including their timing.

In plain termsTwo friends invest in the same fund. One puts money in at the start. The other adds a big lump sum just before a crash. Same fund, same manager, very different outcomes. TWR describes the fund; MWR describes each friend.

Two years, one cash flow

Start with 100. Set each year's market return, and how much the investor adds (or withdraws) between them.

Year 1 return

Flow after year 1

Year 2 return

TWR, per year

The manager's result

MWR, per year

The investor's result

Investor's money gain

End value minus all money put in

For practitionersMWR solves for the single rate that makes the value of all flows, compounded to the end date, equal the ending value. It's standard for private equity, real estate funds and other strategies where the manager controls capital calls. GIPS requires TWR for most strategies and permits MWR when the firm controls external cash flows and the portfolio is closed-end, fixed life or illiquid.

All numbers are illustrative. The models are simplified for teaching: annual coupons, Black-Scholes options, simplified fee mechanics and no intra-period trading. Real systems add transaction-based returns, daily valuation, tax and corporate action processing, and reconciliation to the official TWR.