This argument is usually settled by waving a study at people. You do not need one. The core of it is arithmetic, and the rest can be modelled from first principles — which is more convincing than any league table, because arithmetic does not have a survivorship problem.
The Part That Is Not Up For Debate
All investors together hold the entire market. That is a definition, not an observation. So before costs, the average actively managed franc earns exactly the market return — it cannot do otherwise, because the active managers are trading with each other and their collective holding is the market.
After costs, the average active franc must therefore earn the market return minus its costs. Necessarily. If active funds cost 1.3 percent more than an index fund, the average active franc trails by exactly 1.3 percent a year. Not usually. Always.
This is the part people argue with and cannot win. Whether skill exists is an open question. Whether the average active investor can beat the average passive one after costs is closed by identity.
Why The Odds Get Worse The Longer You Wait
Now model the interesting question: what fraction of individual funds beat the index net of costs?
Assume gross alpha is randomly distributed with a 3 percent annual dispersion and no real skill anywhere — every manager's true edge is zero. Charge active funds 1.3 percent a year more. Then:
— After 1 year: about 33 percent beat the index — After 3 years: about 23 percent — After 5 years: about 17 percent — After 10 years: about 8.5 percent — After 20 years: about 2.6 percent — After 30 years: about 0.9 percent
The mechanism is the whole lesson: costs scale with time, luck scales with the square root of time. Over one year, the cumulative cost is 1.3 percent against 3 percent of luck — luck dominates, and a third of funds get lucky enough. Over thirty years, the cumulative cost is 39 percent against 16.4 percent of luck. Costs win, and almost nobody escapes.
That single asymmetry explains every league table you have ever seen, without needing the league table.
Every Winner Above Is Luck
Read the assumption again: in that model, no manager has any skill at all. True alpha is zero for everyone. And still, 8.5 percent of them beat the index over ten years.
So "some funds beat the index" is fully consistent with skill not existing. The existence of winners is not evidence of anything. Any large group of coin-flippers produces a champion, and that champion will have a compelling explanation for their process.
Can You Identify Skill In Advance
This is the question that actually matters, and the arithmetic is brutal. To distinguish real alpha from luck at conventional confidence, you need the t-statistic to reach about 2, which means roughly (2 x tracking error / alpha) squared years of data:
— Alpha 3 percent a year, tracking error 4 percent: about 7 years — Alpha 2 percent, tracking error 4 percent: about 16 years — Alpha 2 percent, tracking error 6 percent: about 36 years — Alpha 1 percent, tracking error 4 percent: about 64 years — Alpha 1 percent, tracking error 6 percent: about 144 years
A genuinely good manager with a real 2 percent edge needs sixteen years before you can say so with any confidence. Most funds do not exist for sixteen years. Most managers do not stay that long. And a three-year track record — the thing every factsheet leads with — carries almost no information about skill whatsoever.
The Swiss Wrinkle
One local point that cuts against the usual index sermon: in Switzerland, "index" does not mean "diversified".
The Swiss market is dominated by a handful of very large names, to a degree that has no parallel in the US or UK. A Swiss blue-chip index tracker is a concentrated position in a few companies wearing the costume of a diversified fund. This is not a fringe observation — it is precisely why capped index variants exist at all, and why UCITS concentration rules (which limit single-issuer exposure, with specific exemptions for index trackers) make a pure Swiss blue-chip tracker awkward to construct.
So the honest version here is not "buy the index". It is: know what the index actually holds. A globally diversified tracker and a Swiss blue-chip tracker are different animals, and only one of them is doing the diversification you think you bought.
The Catch
The model assumes zero true skill everywhere. That is an assumption, not a finding — it is a way of showing that the observed pattern of winners needs no skill to explain, not proof that skill is absent. Real markets may contain real edges, particularly in less liquid or less covered corners.
The dispersion figure does the work. At 3 percent dispersion, 8.5 percent beat over ten years; at 5 percent, about 20 percent do. Segments with wider dispersion — small caps, emerging markets — produce more winners by luck alone, which is exactly why active management markets itself hardest there.
And index funds are not free. They have costs, tracking error, securities lending policies and, as the previous lesson showed, withholding leakage that never appears on any factsheet. The comparison is cheap-versus-expensive, not free-versus-expensive.
Do This
— Find the total cost of every active fund you own and subtract the cost of a comparable index fund. That difference is what the manager must beat every year, forever, just to draw level. — Ignore any track record shorter than about a decade. The arithmetic above says it cannot distinguish skill from luck, whatever the factsheet implies. — Look up the top five holdings of any index fund you own and their combined weight. If you own a Swiss tracker, that number will probably surprise you.
This is education, not financial advice. It's general information, not a recommendation for your situation, and it doesn't account for your circumstances. Rules and figures change — verify before you act, and speak to a qualified professional for decisions that matter.