Calculation and mechanics
A deposit raises the account value without being a return. The time-weighted return therefore removes it: for every sub-period between two deposits or withdrawals the return is calculated from the value at its start and at its end, then the sub-period returns are linked. Changes in the value of open positions count as well, as do the income and costs contained in the account value.
An exact calculation needs the account value at the moment of every deposit or withdrawal. A daily calculation links the daily returns instead. Deposits and withdrawals are assigned to the start or the end of the day by a fixed rule. With larger amounts on days with strong price moves, this assumption can noticeably change the calculated return.
An example: an account rises from 100,000 to 110,000 in the first half of the year, a gain of 10%. Then 100,000 are deposited and the account falls from 210,000 to 199,500 in the second half, a loss of 5%. The time-weighted return is 1.10 x 0.95 - 1 = 4.5%. A calculation from starting and ending value that ignores the deposit would arrive at almost 100%.
Daily return = account value today / (account value yesterday + deposits and withdrawals today) - 1, deposits positive and withdrawals negative (assigned to the start of the day). Time-weighted return = (1 + r1) x (1 + r2) x ... x (1 + rn) - 1
Distinction
The money-weighted return gives phases with a lot of capital more weight and so describes the result of the money invested. The time-weighted return instead describes the development of one franc or dollar that stayed in the account for the whole period. It is therefore suited for a comparison with a matching index. Period, currency and the treatment of dividends should match, as described under return relative to a benchmark.
Realized P&L with income contains no unrealized gains of open positions and is not a return on capital. CAGR converts a return over several years into a yearly rate. It can be based on a time-weighted return or on starting and ending value.
Related terms
- Money-weighted return (Money-Weighted Return, MWR, internal rate of return)
- CAGR (Compound annual growth rate)
- Return Relative to a Benchmark (Relative performance, vs SPY, vs ACWI)
- Net Liquidation Value (NLV, account value, net liquidation)
All market and analytical information is provided for educational and analytical purposes only and does not constitute investment advice or a trading recommendation.