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Measuring What You Actually Earned

One measurement problem sits underneath all of the above and is almost universally muddled: your portfolio’s return and your return are different numbers, and the gap between them is sometimes enormous.

Time-weighted Return (TWR) strips out the effect of cash flowing in and out. It chains the returns of each sub-period between cash flows, so that a contribution or withdrawal neither helps nor hurts the figure:

1 + TWR = \prod_{i = 1}^{n} (1 + R_{i})

This is the right measure for judging a manager, who does not control when you deposit money, and it is what every fund is required to report.

Money-weighted Return (MWR) — equivalently the internal rate of return — is the discount rate that sets the net present value of every actual cash flow to zero:

\sum_{t = 0}^{T} \frac{C_{t}}{{(1 + MWR)}^{t}} = 0

This is the right measure for judging yourself , because it weights each period by how much money you actually had exposed.

Why the gap is not academic. Suppose a fund returns $- 20 %$ in year one and $+ 25 %$ in year two. Its time-weighted return is exactly $0 %$ — $0.80 \times 1.25 = 1.00$ — and it will advertise that it broke even. Now suppose you invested $100,000 at the start, watched it fall to $80,000, lost your nerve, and added nothing; a colleague invested $100,000 at the start and added another $100,000 at the bottom. You end at $100,000 having broken even. Your colleague ends at $225,000 on $200,000 invested. Same fund, same time-weighted return, materially different money-weighted returns — and the difference is entirely behavioral.

The effect runs in the unflattering direction far more often than the flattering one, because contributions tend to arrive after good performance and withdrawals after bad. That systematic gap between what funds earn and what their investors earn is real, and it is the strongest quantitative argument in this book for automatic contributions and a written rebalancing rule (section “Rebalancing Methods”): both remove the timing decision that produces the gap.

Track your own money-weighted return, not the returns your funds report. Most brokerages compute it — look for “personal rate of return” or “internal rate of return” rather than the fund performance figures. If the two diverge persistently, the problem is not your fund selection.

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