What an Investment Return Number Is Not Telling You

One word, four questions

When a factsheet, an app or a friend quotes a return, four separate measurements are competing for the same word. Was the money weighted by time or by amount — that is, is this the fund's performance or your performance? Is it before or after inflation? Is it before or after the charges that came out of the account? And if it is an average of several years, is it the arithmetic mean of the annual figures or the geometric mean you actually compounded? Each pair can differ by several percentage points, and in the worst case they differ in sign.

None of this implies anyone is being dishonest. Each measure is the right answer to a particular question, and the standards that govern published performance exist precisely because the question has to be fixed before the number means anything. The problem is that the reader almost always wants the money-weighted, real, net-of-fees, geometric figure, and the number in front of them is usually the time-weighted, nominal, gross, arithmetic one. The sections below separate them one at a time, with arithmetic rather than adjectives.

Time-weighted measures the fund; money-weighted measures you

Take a fund that returns +50 percent, then −30 percent, then +25 percent. Chain the factors and the time-weighted return is 1.50 × 0.70 × 1.25 = 1.3125, a gain of 31.25 percent over three years, or 9.49 percent a year compounded. That figure deliberately ignores when money entered and left, because the manager does not control that; it is the return on one unit held throughout. Now put an investor in it. They start cautiously with $10,000. After the first year is up 50 percent they gain confidence and add $100,000. The fund then falls 30 percent, and at the start of the third year they add $20,000 more.

The balances follow mechanically: $10,000 becomes $15,000; $115,000 becomes $80,500; $100,500 becomes $125,625. The investor contributed $130,000 and finished with $125,625, down $4,375. Solving the cash-flow series −$10,000, −$100,000, −$20,000 and +$125,625 for the rate that sets its net present value to zero gives an internal rate of return of −1.77 percent a year. The fund made 9.49 percent a year. The investor lost money. The gap of 11.25 points is not a fee, a fraud or a tracking error — it is the arithmetic consequence of having only $10,000 exposed to the +50 percent year and $115,000 exposed to the −30 percent one.

Reverse the timing and the same fund produces the opposite verdict. Contribute $100,000 first, then $20,000, then $10,000 — the same $130,000, the same three annual returns — and the account ends at $161,250, an internal rate of return of +8.28 percent a year. One fund, one total sum invested, a ten-point swing in the investor's outcome decided entirely by the order of the deposits. This is why fund factsheets and investor experience so often disagree, and why Morningstar publishes an annual study comparing the return a fund reports with the return its investors actually earned.

Which measure answers which question

Time-weighted return exists to make managers comparable. Two funds should be judged on the same basis even if one received a flood of new money in a bad quarter and the other did not, and the CFA Institute's Global Investment Performance Standards prescribe the methodology for exactly that reason: to stop a firm choosing whichever calculation flatters it. Read a published fund return as an answer to the question was this fund well run, and it is the right number. Read it as an answer to how did I do, and it is silently answering something else.

The money-weighted return is the one that maps onto your bank balance, because it discounts every deposit and withdrawal by the time it spent invested. Most spreadsheet packages compute it with an internal-rate-of-return function, and the dated variant handles irregular contributions. It has one well-known awkwardness: a cash-flow series that changes sign more than once can admit more than one mathematically valid rate, which is the same limitation that makes internal rate of return a poor tool for ranking projects. For an ordinary savings history — money in, money in, money in, one balance at the end — it is well behaved and it is the number that tells you what happened to you.

Nominal minus inflation is not the real return

The correct conversion divides rather than subtracts: real return = (1 + n) ÷ (1 + i) − 1, where n is the nominal return and i is inflation over the same period. The reason is that your money grows by a factor of (1 + n) while prices grow by a factor of (1 + i), and what you can buy is the ratio of the two. Subtraction is an approximation that is fine when both numbers are small and falls apart when they are not. At 7 percent nominal and 2 percent inflation the true real return is 4.90 percent against the subtracted 5 — an error of about a tenth of a point, which nobody needs to worry about.

High inflation is where it bites. At 20 percent nominal and 15 percent inflation, subtraction says 5 percent and the true figure is (1.20 ÷ 1.15) − 1 = 4.35 percent: the shortcut overstates the answer by 0.65 points, which is 15 percent of the real return itself. At 40 percent nominal and 35 percent inflation, subtraction still says 5 percent while the truth is 3.70 percent. Compound that error and it becomes visible in money: $10,000 growing for 20 years at a true 4.35 percent real reaches $23,424, whereas the subtracted 5 percent predicts $26,533 — a projection 13.3 percent too optimistic. Use whichever official price index your country publishes, and use the same period for both figures.

Gross return, net return, and thirty years

A fee looks like a small subtraction from one year's return and behaves like a compounding leak. Take a 7 percent gross return and a 1 percent annual charge, so 6 percent net. Over 30 years, $10,000 grows to 1.07^30 × $10,000 = $76,123 gross and 1.06^30 × $10,000 = $57,435 net. The gap is $18,688, which is 24.5 percent of the terminal pot on a charge that looked like one-seventh, about 14 percent, of a single year's return. Put another way, the fee costs you 4.16 years of gross growth: the net portfolio needs an extra four years and two months to reach where the gross one already is.

The damage scales with time, not with the headline percentage. On the same assumptions the same 1 percent charge costs 9.0 percent of terminal wealth over 10 years, 17.1 percent over 20, 24.5 percent over 30 and 31.3 percent over 40; doubling the charge to 2 percent takes 43.2 percent over 30 years. This is the least mysterious of the four splits and the easiest to act on, since the charge is disclosed and comparable, and regulators require ongoing-cost figures in the standardised documents for exactly that reason. The figures here assume a single lump sum and a constant gross return; with regular contributions the direction is identical and the magnitude differs, so run your own numbers rather than transplanting these.

The fourth split: which average is it?

An average annual return can be computed two ways, and they are not equal. The arithmetic mean adds the annual figures and divides by their count; the geometric mean is the constant rate that would have produced the same final balance, and it is the one your account actually experienced. The geometric mean is never higher than the arithmetic mean, and the gap widens with volatility — the classic illustration being a +50 percent year followed by a −50 percent year, which averages to zero arithmetically while the balance is down 13.4 percent. That mechanism, usually called volatility drag, is treated in its own right in our article on volatility; the point here is simply that a quoted average return is ambiguous until you know which of the two it is.

Putting the four splits together turns a single figure into something you can interrogate. Ask whether it is the fund's return or yours, whether it is before or after inflation, whether it is before or after charges, and whether an average is arithmetic or geometric. Each answer moves the number, sometimes by more than the difference between two funds you were trying to choose between. None of that makes returns unknowable; it makes them specific.

Frequently asked questions

Which return should I use to judge my own results?

The money-weighted one, an internal rate of return computed on your actual deposits, withdrawals and closing balance. It is the only measure that accounts for how much money you had exposed at each moment, which is what determined your outcome. The fund's published time-weighted return answers a different question — how the fund performed per unit held throughout — and in the example above the two differ by 11.25 points on the same three years.

If time-weighted return can look so much better, why is it the reported standard?

Because it isolates the part the manager controls. A manager does not choose when subscriptions arrive or when redemptions are demanded, and judging them on flows they did not control would make performance comparisons meaningless. The CFA Institute's Global Investment Performance Standards set out the required methodology so that firms cannot pick whichever basis flatters them. It can also look worse than the investor's experience, not only better — the direction depends entirely on when the money moved.

Is the money-weighted return the same thing as an internal rate of return?

Yes. It is the discount rate that makes the net present value of your cash-flow series zero, treating every deposit as negative, every withdrawal as positive, and the closing balance as a final positive flow. Spreadsheets expose it as an internal-rate-of-return function, with a dated variant for irregular contributions. The one caveat is that a series changing sign more than once can admit multiple mathematically valid roots; a normal saving history does not.

When does subtracting inflation instead of dividing actually matter?

When the numbers are large, when the horizon is long, or both. At 7 percent nominal and 2 percent inflation the shortcut errs by about a tenth of a point and is harmless. At 20 percent nominal and 15 percent inflation it reports 5 percent instead of 4.35 — an overstatement equal to 15 percent of the real return — and compounding that error for 20 years turns a true $23,424 into a projected $26,533, an outcome 13.3 percent too optimistic.

Does the fee arithmetic still hold if I invest monthly rather than a lump sum?

The direction holds, the exact figures do not. The 24.5 percent terminal-wealth gap comes from a single sum compounding for the full 30 years at 7 percent gross against 6 percent net. Money paid in later has less time to be eroded, so a regular-contribution schedule produces a smaller proportional gap over the same period — still a large one, just not this number. Recompute it with your own contribution pattern, horizon and disclosed ongoing charge rather than reusing the example.