Your portfolio was 100,000 at the start of the year and 130,000 at the end. Did you make thirty per cent? If you added nothing during the year, yes. If you did, that number tells you nothing.
What the change in balance measures
The most common calculation is the most misleading one: end-of-period balance minus start-of-period balance.
If you paid in 20,000 during the year, 20,000 of that 30,000 increase came out of your own pocket. The portfolio produced 10,000, and that is not ten per cent on the opening capital either, because the money you added was not working for the whole year.
The problem is more than a correction. Someone paying in regularly watches their balance rise even if the portfolio earns nothing, and that view produces a feeling of performance.
Two questions, two measures
There are two standard ways to measure return and they answer different questions.
Time-weighted return measures the portfolio’s own performance. The effect of money moving in and out is stripped out. The question it answers: how did this strategy do, independent of when and how much I paid in?
Money-weighted return measures your performance. When you added money is part of the result. The question: what did my money actually return?
The two can differ substantially on the same portfolio. Someone adding at the bottom of a drawdown looks better on the money-weighted measure, someone adding at the top looks worse. The portfolio itself is unchanged in both.
How time-weighted return is worked out
The method is to cut the period at every cash flow.
Each sub-period gets its own return: value at the end divided by value at the start. Those sub-period returns are then multiplied together. Money you pay in is added to the starting value of the next sub-period, so it never enters that day’s return.
Concretely: in the first half the portfolio went from 100,000 to 110,000, ten per cent. At the midpoint you paid in 20,000 and the balance became 130,000. In the second half it went from 130,000 to 139,000, about seven per cent. The time-weighted return for the year is 1.10 times 1.07, about seventeen per cent.
On the same portfolio, the raw change in balance reads thirty-nine per cent, and a simple calculation that subtracts the deposit reads nineteen. Neither of those is the portfolio’s performance.
Which one to look at
Both, for different purposes.
Judging a strategy or a bot, time-weighted return is the right measure. The same holds for comparison: measuring against an index or another strategy is only meaningful once cash flows have been removed.
Judging your own decisions, money-weighted return is the more honest mirror. The gap between the two shows what your timing decisions earned you or cost you, and for most people that gap is larger than expected.
The prerequisite is a record
None of these calculations is possible unless the dates and amounts of your cash flows are recorded.
If your portfolio spans several exchanges or accounts, that record does not appear on its own. A transfer from one exchange to another looks like a withdrawal on one side and a deposit on the other; at portfolio level it is neither. A record that does not draw that distinction produces a wrong return on both sides.
The smallest useful record is three columns: date, amount, and whether it was an external flow or an internal transfer. Without the third column, every calculation after it is a guess.
