Track 8 · Arithmetic · lesson 6

One percent, drawn to scale

11 min

One percent. Against a return of seven percent it is a seventh of the gain, and against a balance it is a rounding error. It is the smallest number anybody in this business quotes and it is the reason it gets quoted.

Over thirty years, on any balance, at any return, a one percent annual fee removes about a quarter of the final amount. Not a quarter of the gain. A quarter of the whole thing.

A percentage fee is charged on the balance, not on the gain. That is the first half of it.

The second half is that every unit taken in fees is a unit that then fails to grow for all the remaining years. The fee itself is small; the compounding it prevents is not, and the gap between the two grows with every year that passes.

Which is why the damage from a fee is not proportional to the fee, and is not proportional to time either.

A property worth predicting

Before running anything, decide what the answer should be.

Predict

Does the share of the final balance lost to a fixed percentage fee depend on the rate of return?

Yes — a higher return means more is lost, because the fee is charged on a bigger balanceNo — the share depends only on the fee and the number of yearsOnly above a certain balanceYes, but only slightly, and in the other direction

Find the fee that costs a quarter

The model runs two balances side by side at the same gross return, one charged an annual fee and one charged nothing. Drag the return around first and watch the share stay put.

Fee drag

Hypothetical model, not a forecast

Compares a balance charged an annual percentage fee against the same balance charged nothing.

It assumes

The fee is a percentage of the whole balance, taken once at each year end.
Growth is applied first and the fee is then taken from the grown balance.
The gross return before fees is identical in every one of the thirty years.
The fee percentage never changes over the whole period.

It ignores

Transaction costs, spreads and the cost of holding cash
Tax, which can interact with fees in either direction
Any fee charged as a flat amount rather than a percentage
Whether the fee buys anything of value in return

Find the annual fee that removes a quarter of the final balance over the thirty years. Move the return around afterwards and watch what the share does.

Return before fees700%

Annual fee25%

Charged on the whole balance each year, not on the gain.

Final balance, after fees: 706,156
Final balance, no fee: 761,226
Fees handed over: 24,084
How much smaller the balance ended up: 55,070
Growth lost on top of the fees: 30,986
Share of the no-fee balance given up: 0.072

No fee
After the fee

Two curves rising together and separating slowly at first, with the gap between them widening sharply in the later years.
Year	No fee	After the fee
0	100k	100k
1	107k	107k
2	114k	114k
3	123k	122k
4	131k	130k
5	140k	139k
6	150k	148k
7	161k	158k
8	172k	168k
9	184k	180k
10	197k	192k
11	210k	205k
12	225k	219k
13	241k	233k
14	258k	249k
15	276k	266k
16	295k	284k
17	316k	303k
18	338k	323k
19	362k	345k
20	387k	368k
21	414k	393k
22	443k	419k
23	474k	448k
24	507k	478k
25	543k	510k
26	581k	544k
27	621k	581k
28	665k	620k
29	711k	662k
30	761k	706k

Not there yet — keep moving the controls.

At a 7% gross return the no-fee balance ends near 761,000 and the one percent balance ends near 563,000. The gap is about 198,000, and only a part of it was ever handed over as a fee. The rest is growth that never happened on money that was no longer there.

That second component is the one the readout calls growth lost on top of the fees, and it is the reason the damage is nonlinear in time.

A fee paid in year one is small. What it costs is that amount plus twenty-nine years of growth on it. A fee paid in year thirty costs the amount and nothing else. Add up thirty of those and most of the total is the early ones, which are also the ones that looked the most harmless.

Check

The same one percent fee, over ten years instead of thirty. What share of the final balance goes?

About a third of the thirty-year figure, so around 9%The same 26%, because the fee has not changedAbout 1%, one year's feeAround 20%, because most of the damage happens early

Where this model stops being fair to feesOptional

Three things are missing, and two of them favour the fee.

The model says nothing about what the fee buys. A charge that prevents one panicked sale in a career may pay for itself several times over, and nothing in this arithmetic can see that.

It also treats percentage fees only. A flat annual charge behaves completely differently: it is punishing on a small balance and negligible on a large one, which is the reverse of the pattern here.

And it ignores transaction costs, spreads and the cost of holding cash, all of which are real, none of which appear on a fee schedule, and all of which push the same way as the fee.

Worth remembering

A percentage fee is charged on the whole balance every year, not on the gain.
The share of the final balance lost to a fee depends only on the fee and the number of years — the return and the starting amount cancel out.
Roughly: one percent a year for thirty years removes about a quarter of the ending balance.
Roughly: the same one percent over ten years removes about a tenth, so the damage grows faster than the time does.
Most of the loss is not the fees themselves but the growth those fees would have earned in the years that followed.