You will be able to explain why your account return differs from your fund's return and calculate both.
Two years ago Marcus put S$70,000 into his account, which was mostly a world equity ETF. In the first year it rose 14%. Then he received a bonus and some money from his late father's estate, and on the first working day of year two he added another S$70,000. That year the portfolio fell 18%. These are the made-up figures we'll use throughout the course for his account.
His ETF's factsheet for the two years shows a loss of about 3.3% a year. Marcus's own sum feels much worse. He put in S$140,000 and has S$122,836. Both are correct. They answer different questions, and an analyst needs both.
The fund manager controls what the fund holds. The manager doesn't control when you add or take out money. So a fund's reported return has to strip out the effect of investors' deposits and withdrawals, or managers would look good or bad because of their clients' timing.
A time-weighted return does that. You split the period at every cash flow, work out the return for each sub-period, and chain them together by multiplying. For Marcus, the sub-periods are the two years: 1.14 times 0.82 is 0.935, so the two-year time-weighted return is about minus 6.5%, or about minus 3.3% a year. It doesn't matter whether Marcus added S$70,000 or S$7 million at the start of year two. The answer is the same, because it measures what one dollar left in the portfolio the whole time would have done.
Funds report this way as a rule, and the Global Investment Performance Standards, the GIPS code that many managers follow, are built around time-weighted returns. It's the right number for judging the manager, or for judging the investments you chose.
A money-weighted return answers your other question: what rate did my actual money earn, given when I added it? It is the single yearly rate that turns all your deposits and withdrawals into your ending value, which is the internal rate of return of your cash flows. For Marcus it is about minus 8.4% a year, five points a year worse than the fund. Most of his money arrived just before the bad year, so most of his money had the bad year.
Run the same fund returns the other way round. Suppose year one had been the fall of 18% and year two the gain of 14%. The time-weighted return is identical, because multiplication doesn't care about order. But now Marcus's big second deposit would have arrived after the fall and caught the recovery, and his money-weighted return would have been well above the fund's.
That is why the gap between the two numbers is information. If your money-weighted return trails the time-weighted return of your own portfolio year after year, your timing of deposits and withdrawals is costing you. Some of that is luck, such as a bonus that happens to arrive before a fall. Some of it is behaviour, such as adding after good years and holding back after bad ones, which Behavioural Finance: why you make the money mistakes you make covers in lesson 1.3, The behaviour gap between fund returns and investor returns.
You don't solve for an internal rate of return by hand. Excel and Google Sheets both have XIRR, which takes a column of dated cash flows and returns the yearly rate.
Lesson 7.2 of Investing in US and global markets from Singapore, Track your real return in Singapore dollars, set up the basic method: money going in is negative, money coming out is positive, and the current value goes in as a final positive row on today's date, as if you sold. For Marcus's two years, the rows are minus S$70,000 on the first day of year one, minus S$70,000 on the first day of year two, and plus S$122,836 on the last day of year two.
Three refinements make it analyst grade.
Withdrawals count, including dividends you took as cash. If a payout went to your bank account and was spent, it left the portfolio, so it is a positive row on its pay date. Dividends that stayed in the account and were reinvested need no row. Use account-level flows, not trades. Buying one ETF with cash already in the account is not a cash flow. Only money crossing the border of the account counts: transfers in, transfers out and payouts taken. Keep a time-weighted series beside it. Record the account value just before each deposit, so you can work out each sub-period's return and chain them. Without those values you can't tell how much of your result came from your picks and how much from your timing.
The time-weighted series needs one more piece of discipline. If you can't get the value on the exact day of a deposit, use the closest month-end, and note that you did. A small dating error matters much less than a missing deposit.
So for every account you run, you'll carry two numbers. The time-weighted return tells you how good your choices were, and you'll compare it with a benchmark in lesson 1.6. The money-weighted return tells you what you earned, and the gap between them tells you what your timing cost or added. Start with the second one: gather every deposit and withdrawal for one account, with dates, from your bank and broker statements.
List every deposit and withdrawal with dates for one account and calculate its money-weighted return with XIRR.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).