Active vs Passive Investing Calculator

What the Fee Gap Has to Overcome

An actively managed fund and an index tracker holding similar assets end at different values for a reason that is arithmetic rather than a matter of skill: the charge comes off the return every year, whatever the return was. For the active side to finish level, its gross return has to exceed the passive gross return by the whole difference in charges. To finish ahead, it has to exceed it by more than that. The Break-Even Active Gross Return row states that threshold directly, and at the figures the tool opens with it reads 9.10% against a passive gross return of 8%.

How the Comparison Works

Each side compounds at its net rate, the gross return less the annual charge. Both sides receive the same starting amount and the same monthly contribution over the same horizon, so the only difference between them is the net rate. Two conventions are worth naming because they affect the figures. The charge is subtracted from the annual rate before that rate is divided by twelve, rather than being deducted from the balance at monthly rests, so the model states a nominal annual rate rather than an effective one. And contributions are treated as arriving at the end of each month, which is the ordinary-annuity convention.

Worked Example

On the sample figures used on this page, 10,000 at the start with 500 a month over thirty years, the passive side runs at an 8% gross return against a 0.1% charge and the active side at 8.5% against 1.2%. That leaves net rates of 7.9% and 7.3%. The passive side reaches 836,370.98, the active side 736,114.44, and the gap is 100,256.54, or about 12% of the passive final balance.

The active side starts with half a point more gross return and still finishes behind, because the charges differ by 1.1 points. That is the whole mechanism: half a point of extra return does not cover 1.1 points of extra cost.

How Much a Charge Gap Costs

The size of the drag depends on whether contributions are being added. Taking a lump sum on its own over thirty years at an 8% gross return, a one-point charge gap costs 25.8% of the final balance and a two-point gap 44.9%. Adding a monthly contribution changes those figures materially: on the sample figures the same one-point gap costs 19.1% and the two-point gap 34.2%.

Contributions reduce the proportional drag because money added late has spent less time exposed to the charge. Any figure quoted for fee drag therefore belongs to a particular contribution pattern, and a lump-sum number will overstate the effect on a portfolio that is still being paid into.

Where the Gap Narrows

The comparison turns on the charge difference rather than on the label either fund carries. An actively managed fund with a charge close to a tracker's faces a correspondingly small hurdle, and the break-even gross return moves down with it. Charges vary widely within both categories, so two funds carrying the same label can face very different hurdles.

Some markets and asset classes are harder to track cheaply than broad developed equity, which narrows the charge difference from the other direction. The tool does not model any of that: it takes two gross returns and two charges and compounds them.

What the Model Does Not Capture

Both gross returns are held constant for the whole horizon, which no fund delivers, and the order in which returns arrive changes the outcome for a portfolio receiving contributions throughout. Nothing here establishes what either gross return turns out to be, and the two differences do not rank in any fixed way. On the sample figures the charge difference on its own opens a gap of 173,454.82 toward the passive side, while the gross-return difference on its own runs the other way, 95,397.42 toward the active side. They do not simply add: applied together those same sample figures leave 100,256.54. Which of the two dominates depends on what is entered.

Tax sits outside the calculation entirely. Treatment varies by jurisdiction and by the type of account a fund is held in, and in some markets the two structures differ in how realised gains reach the holder, which can widen or narrow the after-tax gap relative to the pre-tax figure shown. Entry and exit charges, dealing costs, bid-ask spreads and any separate advice charge are all excluded as well.

The comparison is fund-level. An investor who moves between funds in response to past performance experiences neither of the two paths modelled here, and that behaviour is not something the arithmetic can represent.