Why stacking good ideas stops working
Your instinct that enough small advantages add up to a near-certainty is arithmetically correct; this page is about how many you would need and how few exist.
Start with the instinct, because it is sound. Suppose you own something that finishes ahead of a plain index fund 55% of the time. On its own that is barely better than a coin flip. Own several such things that have nothing to do with each other, and the odds that the collection finishes ahead climb, because their bad years do not land together.
So how many would you need?
| To be this likely to finish ahead | Unrelated 55% bets required |
|---|---|
| 60% | 5 |
| 70% | 18 |
| 80% | 45 |
| 90% | 105 |
| 95% | 172 |
| 99% | 343 |
That is the case for stacking and it is also the case against it. A hundred and seventy genuinely unrelated bets describes a market-making desk, not a portfolio of a few funds. Even about a hundred of them leaves you a shade under 90% likely to be ahead of the index, not certain.
Nothing you can buy is unrelated
The table above assumes your bets have nothing in common. Real holdings always do. Here is the same question when they move together, on a scale where zero means completely unrelated and one means identical.
| Number of bets | Unrelated | 0.1 | 0.2 | 0.3 | 0.5 |
|---|---|---|---|---|---|
| 5 | 61.1% | 59.4% | 58.3% | 57.5% | 56.4% |
| 20 | 71.3% | 62.9% | 60.1% | 58.6% | 56.9% |
| No limit | 100% | 65.4% | 61.1% | 59.1% | 57.1% |
The bottom row is what unlimited money, unlimited ideas and infinite patience buy you. At 0.3 an unlimited number of ideas is worth 3.3 unrelated ones, and gets you to 59%. The three funds in this portfolio that all buy cheap shares move together at 0.435, and at that reading an unlimited number of ideas tops out at 57.6%. Wherever the ceiling sits, five bets already takes you about two thirds of the way to it, ten takes you four fifths, and everything after that is decoration.
What we counted
Four funds that lean a particular way, plus one trend-following fund, measured over 422 months to the end of 2025: 3.71 independent bets out of five. Three of the four buy cheap shares, in the US, in other rich countries and in emerging markets. Those three are cousins, sitting at 0.435 against each other on that same scale, which is where the pessimistic 57.6% ceiling above comes from. Across all five positions the average is nearer a tenth, because the momentum fund and the trend fund often lean against the other three.
A second country is not a second idea
Take one idea, buying cheap shares, and spread it across three regions. Three holdings, about 1.55 independent bets. Do it with momentum instead and you get 1.35. Geography buys roughly half an extra bet.
Now take five different ideas inside one country: cheap shares, small companies, profitable companies, companies not expanding fast, and shares that have been rising. Those five come to 5.52 independent bets, more than five, because some of them lean against each other. Going abroad may be right for other reasons. As diversification it is nearly empty.
How you pay for it decides everything
If you sell stocks to buy the diversifier, your holdings still total 100%. Every dollar in the new idea came out of something you already owned, so your result is a weighted average of your ideas, and an average can never beat its best member. The most this route could deliver was 1.173% a year more than the same money in plain index funds, and only by putting everything into the single best idea. Spread across all four as actually held, it was 0.624% a year against that same comparison. Adding ideas raised the odds and shrank the prize at the same time.
Finance the diversifier on top instead. You keep the stocks, hold the new exposure with borrowed money, and nothing has to total 100%. The results add rather than average: 2.974% a year more than plain index funds. That is the one case where "stack more strategies" is literally correct. Borrowing has a price, and a fund that does it for you charges for it.
The portfolio published here is about 93% the first kind. Only one of its seven holdings is financed. Everything else was bought by selling something.
One more number, because it applies to everything above. Over the ten years to 2025 the average dollar invested earned 8.7% a year while the funds that dollar sat in earned 9.9%. That 1.2-point gap describes a population rather than a person: it compares the dated arrivals and departures of every dollar with the fund's own published return, and Morningstar disclaims the individual reading, because for every buyer there is a seller. Morningstar's own reading is that what drives it is neither cost nor management style but how jumpy the fund is: it runs from 0.4 points a year in the calmest fifth of funds to 2.1 in the jumpiest, which is exactly the sort of product this page is about.
What would change our mind
A holding whose good and bad years genuinely have nothing to do with the others, bought at a fee that leaves the advantage intact. Or an honest, cheap way for an ordinary investor to hold the diversifier on top rather than instead. The arithmetic is not in dispute; the inputs are.
Where these numbers come from
- The probability tables are computed directly from the assumption that each bet is 55% likely to finish ahead of the index, and are checkable with a spreadsheet.
- Monthly returns for regional stock market factors from the Kenneth French data library and AQR’s published trend series, 422 months, November 1990 through December 2025, used to count how independent the holdings really are.
- Fund filings for the exposures each fund actually delivers.
- Morningstar’s "Mind the Gap" study, ten years to 2025, for the population-average difference between what funds earned and what their investors earned.