Independent engines: how many exist outside this repository's own data, and what the stack is worth

Question. Stacking and effective breadth measures an average pairwise correlation of 0.435 on this portfolio’s own active positions, caps an unlimited stack of 55% bets at 57.6%, and ends on an instruction: lower the correlation rather than raise the count. That instruction leaves two questions open, and both of them are the reader’s next question. What is genuinely uncorrelated and buyable, and what is the whole exercise worth when it is done well? This page answers both from evidence outside this repository, so that the answer does not rest on one portfolio’s 422 months.

Decision it informs. Whether the ceiling measured here is a property of this portfolio’s ingredients or a property of the available ingredients generally; what an honest headline number for a completed stack should be; and which of the mechanisms on the shelf are exposed to capacity decay. Out of scope: whether to hold any of them (decision 0004), the funding arithmetic (capital efficiency), and the screen of individual mechanisms (alternative engines).

Status: source-reproduced. as of 2026-08-24. Every figure is read from a manager’s published research, a fund’s own standardised performance table, an SEC filing, Ken French’s data library or FRED. The only arithmetic performed here is the breadth calculation in section 1, which is Grinold’s identity applied to a stated correlation, and subtracting two numbers a source printed side by side. Nothing here is a repository measurement, nothing here is a backtest, and two of the four headline numbers are forecasts rather than records. Section What is thin says which.

Conclusion

1. The thesis, as a number, is weak. A 55% win rate against a cheap index is an information ratio of about 0.126. Twenty genuinely independent bets at that ratio, with no fees and no shared behaviour, still lose to the index 29 times in a hundred over one year. At an average correlation of 0.2, modest by the standard of anything actually purchasable, twenty bets are worth 4.2 and the one-year odds fall to 60%. This reproduces the repository’s own ceiling from a completely different direction.
2. The best-built live implementation delivered about a quarter of its theoretical forecast. AQR’s multi-strategy alternative fund runs four styles across five asset groups at roughly 1,205% gross exposure per 100% of capital. Its beta to the S&P 500 since inception is −0.01, so the independence is genuine and this is a fair test of the idea. Sharpe since inception, October 2013 to June 2026, is 0.46 against a stated theoretical forecast for such a composite above 2. Return 7.57%/yr against the S&P 500’s roughly 13.5%/yr over the same stretch.
3. About four or five genuinely distinct sources exist for a US retail investor, not twenty. On AQR’s own March 2026 capital market assumptions, only three of ten asset classes carry a meaningfully positive appraisal ratio against a global stock and bond portfolio: commodities 0.24, absolute-return hedge funds 0.29, trend following 0.26. Six of the ten correlate 0.68 to 0.93 with equities. In the same firm’s decomposition of a typical eight-asset institutional portfolio, equity alone contributes 81% of total risk and equity plus credit over 90%.
4. The honest prize is about 1.5 to 2.0 percentage points a year. AQR’s own numbers for a well-built diversified portfolio give an expected return of 6.5% to 8.1% at a Sharpe of 0.26 to 0.35. Real money against the portfolio a normal investor would otherwise hold. Not a claim to beat the index.
5. The largest free gain available is structural and nobody markets it. ETF in-kind redemption raised long-term investors’ after-tax returns by 1.05%/yr relative to equivalent mutual funds. Zero cost, no minimum, no lock-in, and the same order of magnitude as the entire direct-indexing tax case.
6. Capacity decay is the recurring mechanism and it is measurable. Merger arbitrage spreads down more than 400 bp since 2002. Commodity roll return +1.95%/yr (1970-2004) against −9.29%/yr (2004-2015) as index money arrived. Catastrophe bond spreads 11.31% to 5.53% while dedicated capital grew 31%. Published factors decayed 26% to 58% after publication.

1. The thesis converted into a number

Grinold’s identity says the information ratio of a combination rises with the square root of the number of independent bets. Inverting a 55% one-year win rate against a cheap index gives a per-bet information ratio of about 0.126. The one-year odds of finishing ahead follow directly.

Twenty is not a lot. Twenty independent bets, no fees, no shared behaviour, is a 71% chance of finishing ahead over one year, which is a 29% chance of not. The frictionless best case for a portfolio nobody can build still loses to the index almost three years in ten.

Introduce a modest amount of shared behaviour and the count collapses. At an average pairwise correlation of 0.2 the effective count of twenty holdings is 4.2, and the one-year odds fall to 60%. This repository measured 0.435 on its own active positions and got a hard ceiling of 57.6%; an outside reading of 0.2, which is more generous than anything measured here, lands in the same neighbourhood.

2. The live composite, and the size of the haircut

AQR’s multi-strategy alternative fund is the literal implementation of the stacking thesis. Dozens of individual premiums, four styles, five asset groups, market-neutral by construction, built by the authors of the theory with institutional execution and institutional financing. It is the strongest available test of what the idea delivers when nothing is done badly.

Two readings, and both matter.

The independence is real. A beta of −0.01 to the index over twelve and a half years is what genuine independence looks like, and it is the part of the thesis that survives. This is not a stock fund wearing a costume.

The delivered result is roughly a quarter of the forecast. A four-fold haircut between the stacking mathematics and the record, absorbed by fees, financing, implementation shortfall, and holdings that turned out less independent than modelled. Every one of those four is larger for a retail investor than for this fund.

The return comparison against the S&P 500 is the wrong comparison and is reported anyway. A market-neutral composite is an addition to an equity portfolio, not a substitute for one, and the funding arithmetic in capital efficiency is exactly the reason: sold-to-fund, its edge competes with equity’s and the average can never exceed its largest member; financed, the edges add. The 7.57% against 13.5% is reported because a reader will find it and should meet it here first, with its interpretation attached. What it does establish is that a market-neutral stack of dozens of premiums, run by the people who invented the approach, lost decisively to the index as a standalone holding over its whole life.

3. How many independent engines exist

AQR’s March 2026 capital market assumptions publish appraisal ratios against a global stock and bond portfolio, which is the right question: what does each asset class add once the equity exposure inside it has been removed.

Three positive, one at noise, two negative. Six of the ten asset classes in the same publication correlate 0.68 to 0.93 with equities, which is the arithmetic behind the firm’s own term for the illusion, “pie chart diversification”.

The decomposition makes the point sharper than the correlation table does. In a typical eight-asset institutional portfolio, the kind held up as the diversified benchmark, equity alone contributes 81% of total risk and equity plus credit contributes over 90%. Eight line items, one and a fraction of a bet.

This corroborates the engines audit from outside. That page counted, on this repository’s own screen, six reachable engines for a US retail investor: broad equity, an equity style lean, government bonds, duration-hedged credit, managed futures and catastrophe risk. An independent review of a manager’s published forward assumptions gets three to four with a positive expected edge. The two counts are close, and neither is twenty.

4. The size of the prize

On AQR’s own numbers, a well-built diversified portfolio has an expected return of 6.5% to 8.1% at a Sharpe of 0.26 to 0.35. Against the portfolio a normal investor would otherwise hold, the improvement is about 1.5 to 2.0 percentage points a year.

That is the honest headline for the whole exercise. It is real money and it compounds. It is also a forecast built on a manager’s assumed capital market expectations rather than a measured record, published by a firm that sells the products it is forecasting, and it sits well inside the resolution of any test a retail investor could run on their own account. The claim it does not support is that a stack will beat the index.

5. The structural gain nobody markets

ETF in-kind redemption raised long-term investors’ after-tax returns by 1.05% a year relative to equivalent mutual funds (Moussawi, Shen and Velthuis, Review of Financial Studies, 2025). Zero cost, no minimum, no lock-in, no forecast, and available to anybody with a brokerage account and a taxable holding.

That is the same order of magnitude as the entire direct-indexing tax case, which harvesting and direct indexing prices at roughly zero net of its own fee. One is sold hard, at 25 to 40 bp a year plus paperwork. The other is free and is marketed by nobody, because nobody is paid when an investor does it. This is the same shape as the repository’s own largest reliable line, which is structural and tax edges: the money that is nearly certain comes out of contracts and tax law rather than out of a forecast.

6. Capacity decay as the recurring mechanism

Five independent instances of one mechanism.

The generalisation this supports is narrow and useful. A premium whose supply of risk is fixed and whose demand can be scaled by an index product decays as capital arrives. That is a testable property of a mechanism rather than a mood about markets, and it is a standing reason to be most suspicious of whatever is being marketed hardest. In 2026 that is return stacking and options income, which is also what live stacked fund records finds trailing its own printed benchmarks.

7. What this corroborates

The strongest thing on this page is not any single number. It is that two evidence bases with nothing in common reached the same three conclusions.

Neither route is strong on its own. The repository’s correlation is one portfolio’s measurement over one window. The outside evidence is one manager’s forecasts plus one fund’s record. Agreement between two weak instruments that share no data is worth more than either, and it is the closest thing to independent confirmation this project has.

What is thin

Carried forward from the source review rather than dropped.

1. Two of the four headline numbers are forecasts. The appraisal ratios in section 3 and the 1.5 to 2.0 pp prize in section 4 are capital market assumptions, which are a manager’s forward view rather than a measured record. They are also published by a firm that sells products in the categories being forecast. The direction of that conflict points against the conclusion here, which is mild reassurance and not a control.
2. The composite in section 2 is one fund over one window. Twelve and a half years, one manager, one implementation. It is the best available test and it is still n = 1. A different decade would produce a different Sharpe, and the 0.46 should be read as evidence about the size of the haircut rather than as an estimate of the strategy’s mean.
3. The comparison in section 2 against the S&P 500 puts a financed holding beside an unfinanced index and is reported for that reason with its interpretation attached. It answers “what did this pay a standalone holder”, not “was the second dollar worth buying”.
4. The capacity table mixes windows and instruments. Five instances of one mechanism, each read from its own source over its own period, assembled here rather than measured together. It supports the mechanism. It does not support a rate of decay.
5. Nothing on this page was reproduced from primary series. Every number is a source’s own published figure, re-read on 2026-08-24. Standardised performance updates on the manager’s schedule; re-read before quoting.

What would change this page

• A market-neutral multi-premium fund reaching a ten-year Sharpe above 1. That would move the haircut in section 2 from four-fold to something the theory can carry, and would reopen the size of the prize in section 4.
• A published appraisal ratio above 0.2 for an asset class this project currently counts as duplicated. The count in section 3 is the binding constraint on everything else, and it moves on ingredients rather than on arithmetic.
• A capital market assumptions release from a manager with no product in the category. The conflict in section 4 is the weakest joint in the argument and a second, disinterested source would close it.
• Evidence that the ETF after-tax advantage narrows. The 1.05%/yr rests on a tax treatment of in-kind redemption that is a policy choice rather than a law of nature, and has been raised in more than one legislative proposal.
• A capacity instance running the other way, meaning a premium whose spread widened as dedicated capital grew. None was found. One would materially weaken section 6.