The question
Your stacking instinct is right
Say you find a strategy that beats a cheap index fund 55 times out of a hundred. On its own that is nearly nothing. So find another one, and another, and keep going. Each is a slightly loaded coin, and the more of them you flip the tighter the average has to get.
That instinct is correct, and it is a theorem rather than folk wisdom. Richard Grinold wrote it down in 1989 and whole firms have been built on it since. How good your record gets rises with the square root of the number of independent bets you place. A hundred unrelated 55% bets finish ahead of a cheap index fund 89.6% of the time, and you would need about 104 bets to be 90% sure.
The arithmetic is on your side. Everything now depends on one word in that sentence, which is independent.
The catch
Most strategies are one bet in several costumes
Cheap US stocks and cheap Japanese stocks are one idea in two postcodes, and they had their bad decade together. A fund that buys stocks which have been going up, and a managed-futures fund that buys bonds which have been going up, are one instruction pointed at two markets. Neither pair hands you two bets.
We measured this on the active positions inside one real portfolio: three funds buying cheap stocks, one buying recent winners, and a trend fund, month by month over 422 months to December 2025. The average pair moves together at 0.435. At that level an unlimited stack of 55% strategies reaches 57.6% and stops. The whole portfolio is worth 3.71 independent bets, and several of its tickers hold no active position at all. They are the benchmark.
Read that correlation as a fact about that portfolio and about nothing else. It is a measurement rather than a constant of investing, and four cheap-and-rising stock funds plus a trend fund are close relatives. A genuinely wider stack, one holding stock styles and trend and credit and catastrophe risk, would come in lower and reach higher. What travels between portfolios is the shape. Noise in a stack falls, then flattens, then settles on a floor made of whatever the holdings have in common, and that floor is the correlation.
More bets raise the odds. Correlation decides how far, and it is not far.
Chance of finishing ahead of a cheap index, against how many 55% strategies you stack. Log scale.
Correlation is measured between the modelled returns of the earlier eight-fund proposal's four long-only leaning funds plus its trend fund, over 422 months to 2025-12. How long you hold drops out of the arithmetic, so one curve holds at every holding period at once.
Each curve flattens because the part your holdings share cannot be averaged away. It is in every one of them. Add more and the unshared part gets quieter while the shared part does not, so the line runs into a ceiling set by how alike they are.
The arithmetic treats the edge as known. A real edge is estimated, and that error never diversifies away — it caps the answer again, lower, at the probability that the edge is positive at all. Every curve here is a best case, including the dashed one.
The same curves as a table
| Correlation | 1 | 2 | 3 | 5 | 10 | 25 | 50 | 100 | Limit |
|---|---|---|---|---|---|---|---|---|---|
| 0 — independent, hypothetical | 55.0% | 57.1% | 58.6% | 61.1% | 65.4% | 73.5% | 81.3% | 89.6% | certainty, never reached |
| 0.20 | 55.0% | 56.4% | 57.3% | 58.3% | 59.4% | 60.3% | 60.7% | 60.9% | 61.1% |
| 0.435, measured on the eight-fund proposal | 55.0% | 55.9% | 56.3% | 56.7% | 57.1% | 57.4% | 57.5% | 57.5% | 57.6% |
| 0.70 | 55.0% | 55.4% | 55.6% | 55.7% | 55.8% | 55.9% | 55.9% | 56.0% | 56.0% |
Open the table under that chart. Its top row is your mental model, and your mental model is right. Now read the row underneath. A fifth of a point of shared behaviour costs you the entire top half of the grid.
Where breadth is
Geography is nearly free. Style is the real thing.
This is the most useful thing on the page, and it runs against the way most portfolios are built. Spreading a single strategy across the US, developed markets and emerging markets buys about half an extra bet: 1.35 to 1.55 of three. Putting five different styles inside one region buys 5.52 of five, which is more than the number of things you bought, because cheap stocks and rising stocks are frequently opposites and one tends to be working while the other is not.
A second country is worth much less than it looks. A second idea is worth more than it looks. An international allocation may still be right for you on currency or valuation grounds, and it should not be defended as diversification.
The same effect is visible inside the portfolio measured above. Its international momentum fund moves with its managed-futures fund at +0.331, because a trend fund is momentum wearing a different coat. That fund still earns its place. It earns it on its own edge rather than on any breadth it adds.
One more limit is worth knowing, because nobody mentions it. Hand an optimiser twelve stated candidates of differing quality and let it do as it likes, and it goes long the best few and sells the rest short. Almost all of the extra value lives in that short leg. Take short selling away, because you buy funds in a brokerage account, and the best long-only portfolio holds three strategies, however many candidates you offer it. Most of the benefit of breadth lives in positions an ordinary investor cannot take.
How you pay
How you pay for an addition matters more than what you add
Here is the largest number this project has found, and it says nothing at all about which strategy you pick.
Sell to buy. You have $100. You sell $20 of stocks and buy $20 of a trend fund. Your weights still add to 100. Your portfolio's edge is now the weighted average of the edges of its parts, and an average can never be larger than its largest member. You cannot stack your way past your own best idea. Every addition raises your breadth and lowers your average edge in the same motion.
Finance it. You have $100 and you buy a fund that packs $100 of stocks and $50 of managed futures into one share, using borrowing you never see. Your money is still $100. Your exposure is $150. Now the edges add rather than average, a sum has no ceiling, and "stack a ton" becomes exactly the right instruction.
Same four leaning stock funds, three ways of paying for them, priced on the portfolio in question under the most generous assumption about what the leaning earns:
| How it is paid for | Portfolio edge, a year |
|---|---|
| The whole budget into the single best of the four, funded by selling | 117.3 basis points |
| All four as actually weighted, funded by selling | 62.4 basis points |
| All four financed on top of what you already own | 297.4 basis points |
The portfolio in question is almost entirely the first kind. The gap between the two ways of paying is worth about 2.44 percentage points a year against an all-stock starting portfolio, and it contains nothing whatever about the strategy being added. It is larger than any extra return this project has managed to measure, which was a slightly embarrassing thing to discover after a year spent measuring them.
What to do
Lower the correlation rather than raise the count
That is the whole instruction, and it is a usable one. A twelfth fund that behaves like your first eleven buys almost nothing and charges you for the privilege. One holding that genuinely marches to a different drum buys more than its share of the count. So stop counting tickers and start counting engines, where an engine is a distinct way of making money with its own distinct way of failing. Two funds that lose money in the same crisis are one engine.
On our count an ordinary investor can reach six, and four worth the trouble. They are broad stocks, a lean toward one kind of stock, government bonds, corporate credit with the interest-rate risk stripped out, managed futures, and catastrophe risk. Everything else we tested duplicated something you already own, or came in a retail version costing more than the mechanism pays.
Stacking works. It runs out at about four good ideas, and the route past that wall is a cheaper correlation rather than a longer list. Which leaves the question of what is genuinely uncorrelated and what the finished job pays. Outside evidence answers both, and it is worth about two points a year: how many different bets you can buy.
Sources
Where this comes from
Correlations, the ceiling and the count of separate bets come from the stacking measurements, over 422 months to December 2025, on modelled returns rather than on the funds' own. The twelve-candidate ladder is a stated example rather than twelve funds we priced, so its answer is a property of that ladder. Everything here treats an edge as known, so read every probability as a best case. The funding arithmetic comes from capital efficiency and breadth, and how sure we are lists every error this project has caught in itself.