Money-weighted return (Money-Weighted Return)

Calculation and mechanics

What is wanted is one uniform yearly return that brings starting capital, deposits, withdrawals and ending value into line: the starting capital and every deposit, compounded to the end of the period, minus the withdrawals compounded the same way, give exactly the ending value. This return is usually found step by step with a numerical procedure. In this form it is called the internal rate of return (IRR).

An example: an account rises from 100,000 to 110,000 in the first half of the year. Then 100,000 are deposited. In the second half the account loses 5% and ends at 199,500. Because almost twice as much capital was invested during the losing phase, the money-weighted return is about -0.33% per year. The time-weighted return is +4.5% instead.

For some sequences of deposits and withdrawals the internal rate of return is not unique. If deposits and withdrawals alternate several times, the equation can have several solutions or none.

Starting value x (1 + r)^T + sum of deposits and withdrawals x (1 + r)^(remaining time) = ending value. Deposits count positive, withdrawals negative, each with its remaining time to the end of the period, T and remaining time in years.

Distinction

For a direct comparison with the usual index return the time-weighted return is better suited. The money-weighted return instead shows your personal result, taking your deposits and withdrawals into account. As it is a value per year, it is compared with the time-weighted return per year, not with the time-weighted return over the whole period.

Without deposits and withdrawals the yearly money-weighted return equals the CAGR. With cash flows the two can differ. If the money-weighted return is below the time-weighted return per year, this can indicate that more capital was invested during weaker phases. The Modified Dietz method is another money-weighted method that weights deposits and withdrawals by the share of the period they were in the account and needs no step-by-step calculation.

In Foliograph

In Analytics the money-weighted return appears in Account Performance below the time-weighted return and the CAGR, which it can be compared with. Foliograph calculates it as the internal rate of return (IRR) from the account value at the start and at the end of the period and the deposits and withdrawals in between, expressed per year. Foliograph shows the figure only for evaluation periods of at least one year. That way short-term results are not scaled up to a whole year. The search covers -99% to +1000% per year. If the calculation finds no solution there, the field stays empty.

Deposits and withdrawals come from the Flex Query or the statement. For a single account a position transfer counts at its market value, when all accounts are evaluated together the two sides of a transfer between your accounts cancel out. Missing or doubly recorded deposits and withdrawals distort both returns. Differences in the check of the time-weighted return against IBKR can point to such gaps.

More in the guide: Trading metrics: win rate, profit factor and drawdown · Try for free

Related terms

Time-weighted return (Time-Weighted Return, TWR)
CAGR (Compound annual growth rate)
Net Liquidation Value (NLV, account value, net liquidation)
Realized P&L and income (Realized profit, Realized incl. income)

All terms in the glossary

All market and analytical information is provided for educational and analytical purposes only and does not constitute investment advice or a trading recommendation.

Money-weighted return (Money-Weighted Return, MWR, internal rate of return)

Calculation and mechanics

Distinction

Related terms