The seventy-fifth article took a popular technique apart. This one does the reverse: it takes a habit the literature called naive and finds that under specified conditions it is the correct thing to do.
Key Takeaway
Across fourteen models and seven datasets, "none is consistently better than the 1/N rule... which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error." The data needed for optimisation to win was "around 3000 months for a portfolio with 25 assets."[1] That is 250 years.
The Verdict, Stated First
Five claims, in descending order of confidence.
One. The finding is strong, precise and from a top journal. Fourteen models across seven datasets, none consistently beating an even split on any of three measures.
Two. The reason is estimation error, not a flaw in the theory. The optimisation is correct given the inputs, and the inputs cannot be known well enough for it to help.
Three. The requirement is absurd and that is the point. Around 3,000 months for 25 assets and 6,000 for 50, which is 250 and 500 years.
Four. It is contested, and the contest identified the answer. Optimisation wins where a predictor free of estimation error exists, which in one currency study produced a Sharpe ratio of 0.91 against 0.15.
Five. The business version has an exact break-even and it is uncomfortable. On our own arithmetic, picking one option beats splitting evenly if and only if you can pick better than chance.
Our Grades For These Claims
Applying the scheme from the first article in this series.
Grade A for the 2009 findings, from an abstract obtained verbatim from the publisher and corroborated by three further independent sources including a bibliographic service and the authors' own institutional repository.
Grade A for the currency counter-finding, from an abstract obtained verbatim from the publisher.
Grade B for the research-design objection, obtained as an abstract from a document-sharing site where we could not confirm the authorship, and reported without attribution accordingly.
Grade A for our own arithmetic, which is elementary, on invented parameters.
Our position: this is the strongest evidence in the series that a simple rule can beat a sophisticated one, and the condition separating the two cases is stated precisely enough to use.
A Note On Method
Everything here is verified to August 2026.
We obtained the 2009 paper's abstract verbatim from the publisher[1], corroborated word for word by a bibliographic service, a preprint archive and the first author's own business school repository[2]. We did not obtain the paper.
We obtained the currency study's abstract verbatim from the publisher[3]. We did not obtain the paper.
The research-design objection comes from an abstract on a document-sharing site[4] where we could not establish which paper it belongs to, so we report its content without naming its authors.
We did not obtain the 2010 defence of optimisation, and report it from citation records[5].
All arithmetic is ours and every business parameter in it is invented, which we flag at each use.
This article discusses research on allocation. It is not investment, financial or budgeting advice, and nothing here is a recommendation about any portfolio or security.
The Rule
What is being tested, stated plainly.
You have N things to allocate across and you put one over N into each. Equal amounts, no analysis, no forecasting. In portfolio terms that means equal weights; in a business it means splitting the budget evenly across channels or projects.
Three observations, ours.
The literature's own name for this is naive diversification, and the word appears in the title of the paper that tested it. The framing was settled before the test was run.
The alternative is mean-variance optimisation, which computes the weights that maximise return for a given risk, and which is one of the foundational results in finance.
And the comparison is unusually clean because both are precisely defined. There is no ambiguity about what either rule prescribes, which is rare in the literatures this series covers and is why the result is so sharp.
Two features of the comparison are worth fixing before the evidence, because they shape how the result should be read.
The test is out of sample throughout, which is the only test that matters and the one most analyses skip. Fitting weights to history and reporting how well they fit that history establishes nothing; the question is how the fitted weights perform on data they were not built from.
And the even split is used as the benchmark rather than the proposal. The paper set out to measure how far short of optimisation a crude rule falls, and the finding is the sign of the answer rather than its size.
The 2009 Paper
The source.
DeMiguel, V., Garlappi, L., and Uppal, R. (2009), Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?, The Review of Financial Studies, 22(5), 1915–1953, May, DOI 10.1093/rfs/hhm075[1].
Four observations, ours.
The title asks how inefficient the rule is, which presupposes an answer the paper does not deliver. The framing is the field's prior expectation stated in a question.
The journal is one of the three most senior in finance, which matters for how the result was received. This was not a contrarian outlet.
The authors are finance academics rather than behavioural researchers, so the vindication of a heuristic came from the discipline that had labelled it naive.
And the abstract's own closing phrase is the tell: "there are still many 'miles to go' before the gains promised by optimal portfolio choice can actually be realized out of sample."[1] The quotation marks around "miles to go" are the authors' own.
Fourteen Models, Seven Datasets
The scale of the test, which is what makes the result hard to dismiss.
"We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover."[1]
Four observations, ours.
The models tested include "extensions designed to reduce estimation error", which is the obvious fix and which is stated in the abstract as having been tried.
Three separate performance measures, and the rule holds on all of them. Sharpe ratio, certainty-equivalent return, and turnover are different questions and the answer did not change.
Seven datasets forecloses the objection that a single sample was unlucky, and fourteen models forecloses the objection that one method was poorly chosen.
And the word "consistently" is doing honest work rather than hiding anything. Some models beat 1/N somewhere, and none did so reliably, which is a precise and modest way to state a strong result.
More Than Offset By Estimation Error
The explanation, which the authors give in the same sentence.
"...which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error."[1]
Four observations, ours.
This is not a claim that the theory is wrong. Mean-variance optimisation is correct given the inputs, and the paper does not dispute it.
The failure is entirely in getting the inputs. The method needs expected returns, variances and covariances, and these must be estimated from history that is short and noisy.
The phrase "more than offset" is the whole finding compressed. There is a real gain from optimising and there is a real cost to estimating, and the second is larger.
And that structure recurs far beyond finance. A method that is optimal given perfect inputs can be worse than a crude one given realistic inputs, which the sixty-seventh article reported for prediction and which is the same phenomenon.
Three Thousand Months
The figure that settles the practical question.
"Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets."[1]
Three observations, ours.
The figure is analytical and simulated, not an artefact of one dataset, which is why it can be stated as a requirement rather than an observation.
It scales badly with the number of assets. Doubling from 25 to 50 doubles the requirement, so the method gets harder to use exactly as the problem gets more complex.
And it is calibrated to the US equity market, which is the best-documented financial market in existence. Any less studied setting is worse.
One clarification on what the figure is and is not. It is not a claim that optimisation never helps; it is the window at which the expected gain from optimising exceeds the expected cost of estimating, on the authors' own model of both.
So a reader who distrusts the number can attack the model rather than the arithmetic. What they cannot do is treat a few years of data as sufficient, since even a generous error in the authors' calibration leaves a requirement measured in decades rather than quarters.
What Two Hundred And Fifty Years Means
Converting the figure. Ours, and the arithmetic is trivial.
3,000 months is 250 years. 6,000 months is 500 years.
Four observations.
The requirement exceeds the record. Continuous monthly return data of the kind these models need does not extend back two and a half centuries for 25 assets.
So this is not a practical difficulty to be managed with better data collection. It is a statement that the method cannot be made to work on the problem as posed, on the authors' own calibration.
And the assets in question would have to be the same assets throughout, with stable statistical properties, for 250 years. Almost no company survives that long, which is a second impossibility inside the first.
That is the sentence to take into any discussion of an optimised allocation. Ask how much history the estimate rests on and compare it to what the estimate requires.
The Critics Answered
Because a result this striking attracts responses, and it did.
Reference lists identify Kritzman, M., Page, S., and Turkington, D. (2010), In Defense of Optimization: The Fallacy of 1/N, Financial Analysts Journal, 66(2)[5]. We did not obtain it and report the title, which states its position.
A further paper's abstract, which we obtained from a document-sharing site but could not attribute to a confirmed author or journal, argues: "Our analysis suggests that this is largely due to their research design, which focuses on portfolios that are subject to high estimation risk and extreme turnover. We find that mean-variance optimization often outperforms naive diversification, but turnover can erode its advantage in the presence of transaction costs."[4]
Three observations, ours.
We report that second passage without naming its authors, because we could not establish which paper it belongs to, and attributing a critical claim to the wrong people would be worse than leaving it anonymous.
The objection is specific and testable rather than rhetorical: it names research design, estimation risk and turnover as the causes.
And the same passage concedes the practical point in its own second sentence. "Turnover can erode its advantage in the presence of transaction costs" is a real qualification of its own counter-claim.
It also proposes a constructive answer rather than only a criticism, which is worth recording. The same abstract describes two new methods, volatility timing and reward-to-risk timing, delivering portfolios with low turnover that are reported to outperform an even split even at high transaction costs[4].
If that holds it matters, and we cannot assess it. Both proposed methods use volatility rather than expected returns, which fits everything else in this article: volatility is estimated far more reliably than mean returns, so a method that leans on it is leaning on the better-measured input.
The Research Design Objection
Taking that criticism seriously, because it is the strongest one available and we think it is partly right. Ours.
Four observations.
The charge is that the 2009 tests used portfolios subject to high estimation risk and extreme turnover, which would make the comparison unfavourable to optimisation by construction rather than by nature.
That is a real methodological point and not a complaint. Choosing a setting where a method is known to struggle, then reporting that it struggles, proves less than it appears to, and the seventy-fifth article made the same criticism in the opposite direction about replications of the decoy effect.
The counter is that the setting chosen was the US equity market with seven datasets, which is the standard testbed rather than an obscure corner, and the burden of showing it is unrepresentative sits with the objector.
And the objection concedes the practical result while contesting the theoretical one. Mean-variance optimisation "often outperforms" and "turnover can erode its advantage in the presence of transaction costs", which for anyone who actually pays transaction costs is close to agreeing.
When Optimisation Does Win
The most useful paper in this article, and it resolves the dispute rather than continuing it.
A study of currency markets in a management science journal states: "DeMiguel et al. showed that in the stock market, it is difficult for an optimized portfolio constructed using mean-variance analysis to outperform a simple, equally weighted portfolio because of estimation error. In this paper, we demonstrate that portfolio optimization can be made to work in currency markets."[3]
And the reason: "The key difference between the two settings is that in currency markets interest rates provide a predictor of future returns that is free of estimation error, which permits the application of mean-variance analysis."[3]
With the result: "We show that over the last 26 years, a mean-variance efficient portfolio constructed in this fashion has a Sharpe ratio of 0.91, versus only 0.15 for the equally weighted portfolio."[3]
A Predictor Free Of Estimation Error
Reading that, because it is the whole answer. Ours.
Four observations.
The gap is enormous. 0.91 against 0.15 is not a marginal improvement; it is optimisation working exactly as the theory promises.
And the condition is stated precisely. A predictor of future returns that is free of estimation error, which in that setting is an observable interest rate rather than an estimate from history.
So the two findings are not in conflict at all. Optimisation fails when the inputs must be estimated and succeeds when they can be observed, and the 2009 result is a statement about estimation rather than about optimisation.
That is the sentence to carry out of this article, and it generalises far beyond portfolios. Optimise where you can observe the input. Split evenly where you have to estimate it.
The Condition, Stated Generally
Our own generalisation, which no source we obtained makes in these terms.
Four observations.
The distinction is not between simple and sophisticated methods. It is between inputs you can look up and inputs you have to infer.
An interest rate is quoted. A historical average return is computed from a sample, and every such computation carries an error that the optimiser then treats as truth.
Which is why optimisers fail in a specific and predictable way. They put the most weight on whatever looks best, and what looks best is disproportionately whatever was overestimated, so the method systematically concentrates on its own largest errors.
And that mechanism is worth naming for a business reader, because it is not obvious. Optimisation does not merely tolerate estimation error, it seeks it out, and that is why more sophisticated optimisers did not fix the problem in the 2009 tests.
Two consequences follow that are worth carrying into any meeting where numbers are being optimised. The more options you allow the optimiser to choose among, the worse this gets, because more candidates means more chances for one of them to have been overestimated, which is why the data requirement doubled going from 25 assets to 50.
And the output looks most confident where it is least reliable. An optimiser handed noisy inputs returns precise weights, and the precision is a property of the arithmetic rather than of the knowledge, which is the seventy-first article's point about confidence tracking internal consistency arriving in a spreadsheet.
What Actually Survives
Our reading, stated directly.
Five statements.
Splitting evenly beat fourteen optimisation models across seven datasets, on three separate performance measures, in a top finance journal.
The cause is estimation error, not a defect in the theory. The optimisation is correct given its inputs and the inputs cannot be known well enough.
The data requirement is around 250 years for 25 assets, calibrated to the best-documented market that exists.
The result is contested, on grounds of research design, by researchers we could partly not identify.
And the dispute has an answer. Optimisation wins where a predictor free of estimation error exists, producing a Sharpe ratio of 0.91 against 0.15 in one currency study.
One thing does not survive, and we should say so plainly. The framing of an even split as a bias does not survive its own literature. A rule that beats fourteen alternatives on three measures across seven datasets is not naive, whatever it was called when the label was applied.
That matters beyond this topic because of how the label travelled. An observation that people split evenly was recorded as evidence of poor judgment before anyone had tested whether the behaviour was worse than the alternative, which is the same order of operations the seventy-fifth article criticised in a different literature.
The Business Version
Why this belongs in a publication for business owners rather than investors. Ours.
Four observations.
An owner splitting a marketing budget across four channels, or capital across three projects, faces the identical problem: allocate across options whose future returns must be estimated from a short and noisy history.
The temptation is the same too. Put more into whatever performed best last year, which is precisely the sample-based optimisation the 2009 paper tested.
The data situation is far worse than the one that defeated the method in finance. An owner has a handful of quarterly observations per channel, against the 3,000 monthly observations the method needed.
And nobody has run this test on business allocation, as far as we could find. The transfer below is ours and untested, and rests on the problems being structurally the same rather than on any study of the second.
Two differences from the finance setting are worth flagging now rather than at the end, because they cut in opposite directions and a reader should weigh both.
Business allocation is worse in one respect that matters enormously: the options are not independent, they change while you measure them, and the number of observations is smaller by orders of magnitude. Every one of those makes estimation harder than in the case that already defeated it.
And it is better in one: an owner has causal knowledge a statistical optimiser does not. You know why a channel worked, not merely that it did, and a reason is worth more than a number in a thin sample. That is the strongest argument against applying this article's finding mechanically, and we would not want a reader to miss it.
How Long To Prove A Channel Is Better
Putting the estimation problem in business terms. Our own arithmetic, standard statistics on invented parameters.
To establish that one channel really does return more than another, at conventional standards, the months of data required per channel:
A true gap of 2 points with monthly volatility of 10 percent: 393 months, or 32.8 years.
A 4 point gap at 10 percent volatility: 99 months, or 8.3 years.
A 2 point gap at 20 percent: 1,570 months, or 130.8 years.
A 5 point gap at 20 percent: 252 months, or 21.0 years.
A 10 point gap at 20 percent: 63 months, or 5.3 years.
Four observations.
Volatility dominates. Doubling it from 10 to 20 percent quadruples the requirement, and marketing channel returns are volatile.
Only a very large edge is provable in a useful timeframe. Ten points at twenty percent volatility still takes five years.
Most reallocation decisions rest on one quarter of data, which on these figures establishes nothing at all.
And this is the seventy-fourth article's finding in a different setting. The environment does not supply enough observations to learn the thing people are confident they have learned.
Two caveats on our own table, both of which cut against it. It assumes independence between periods, and channel returns are seasonal and autocorrelated, which reduces the effective sample below the raw count and makes the requirement worse than shown.
And it treats the channels as stable over the whole window, which for anything digital is plainly false. A channel that changes materially every eighteen months cannot accumulate twenty years of evidence about itself, which is the two-settings problem from the previous article defeating the sample-size problem here.
What Splitting Evenly Costs
The other side, because an even split is not free. Our own arithmetic, invented figures.
Suppose one option is genuinely better by 4 points and the rest are identical. Against putting everything into the best one, an even split forgoes:
With 2 options: 2.00 points. With 3: 2.67. With 4: 3.00. With 5: 3.20. With 8: 3.50. With 10: 3.60.
Four observations.
The cost is real and it grows with the number of options. Splitting five ways forgoes 3.2 of the 4 available points, which is most of the edge.
So the even split is not a free lunch and nobody in this literature claims it is. It is a trade of expected return for protection against being wrong.
The comparison is against putting everything into the best option, which requires knowing which one that is. That is the assumption the whole article attacks.
And this table is the honest counterweight to the finding. If you do know, splitting is expensive, and the next section computes exactly how sure you need to be.
One further reading of the same table is worth noting, because it points the other way. The marginal cost of splitting rises steeply at first and then flattens: going from two options to three costs an extra 0.67 points, while going from eight to ten costs 0.10.
So if you are going to spread, spreading a little is nearly as expensive as spreading a lot. The decision that matters is whether to concentrate at all, not how many ways to divide once you have decided not to.
The Break-Even Is Chance
The cleanest result we have derived in this series. Our own arithmetic, and it is exact under the stated assumption.
With N options, one better by D and the rest identical: splitting evenly returns the baseline plus D divided by N. Picking one, and being right with probability p, returns the baseline plus p times D.
Setting them equal gives p equals 1 over N, which is exactly the probability of picking at random.
So the break-even is: 2 options, 50.0 percent. 3 options, 33.3. 4 options, 25.0. 5 options, 20.0. 8 options, 12.5. 10 options, 10.0.
Four observations.
Picking beats splitting if and only if you can pick better than chance. That is the entire condition, and it is exact given the assumption that one option is better and the others are alike.
It sounds like a low bar and it is the precise thing the estimation problem denies. The 2009 paper's finding is that with realistic data you cannot reliably identify the best option, and this arithmetic says that is the only thing that matters.
The result also explains why splitting looks worse than it is. Everyone is confident they beat chance, and the seventy-first and seventy-fourth articles between them explain why that confidence carries no information.
And we would flag the assumption clearly. This holds where one option is better and the rest are similar. With a wide spread among the others the arithmetic changes, and a reader with a genuinely dispersed set of options should redo it.
Why An Even Split Works At All
The mechanism, because a rule that ignores all information should not beat one that uses it, and understanding why it does is what makes the finding usable. Ours.
Four observations.
The even split has one enormous advantage: it has no parameters to estimate. There is nothing in it that can be wrong, because there is nothing in it that was measured.
So its error is bias without variance. It is systematically slightly wrong in a stable way, and it does not swing with whatever the last three years happened to produce.
The optimiser is the opposite: unbiased in principle and wildly variable in practice, because each new estimation window produces different weights from largely the same underlying reality.
And that is the whole trade, stated in one line. A small permanent error beats a large fluctuating one, whenever the fluctuation is bigger than the permanent gap, which is exactly what estimation error being larger than the optimisation gain means.
The General Lesson About Simple Rules
How this sits with the rest of the series, since it is the third article to report a simple rule beating a sophisticated one. Ours.
Four observations.
The sixty-seventh article reported simple additive models beating expert clinical judgment. This one reports an equal split beating fourteen optimisers. The pattern is now well enough established to state as a rule of thumb.
The common structure is that the sophisticated method requires an input the setting cannot supply. Clinical judgment requires consistency the judge does not have; optimisation requires expected returns the data does not contain.
Which means the useful question is never simple versus complex. It is whether the extra input the complex method needs is actually available at the quality it needs, and that is answerable before choosing.
And the failure mode is the same in both literatures. The sophisticated method is adopted because it is correct in principle, and its correctness in principle is not the property that matters.
One boundary on that rule of thumb, because stated baldly it would licence dismissing any analysis. The simple rule wins on the specific comparison tested and not in general. An equal split lost badly in currency markets, and a simple additive model would lose to a well-specified physical model in engineering.
So the rule is conditional and the condition is the one this article has been circling. Prefer the simple rule where the sophisticated one depends on a quantity you must estimate from thin data, and prefer the sophisticated one where its inputs can be observed. Stated that way it is not anti-analytical at all; it is a question about measurement rather than about method.
The Partition Problem
The strongest objection to the even split, which none of our sources raises and which we think is decisive in business settings. Ours.
Four observations.
An even split depends entirely on what counts as an option, and in a portfolio that is defined by the asset list. In a business it is not defined at all.
Split a budget across "digital and print" and each gets half. Split it across "search, social, display and print" and print gets a quarter. Same money, same channels, different answer, decided by how somebody wrote the list.
That makes the rule manipulable and unstable in exactly the setting where it is most attractive, because whoever draws up the categories chooses the allocation without appearing to decide anything.
So the practical version of the rule needs a companion discipline. Fix the categories before you look at the numbers, and fix them at the level you actually make decisions at, which is a judgment the arithmetic cannot make for you.
Two observations that make this worse than it first appears, and they are the reason we would rank the partition problem above every other objection in this article.
The finance literature is silent on it because portfolios come with a defined asset list. Nobody has to decide whether two share classes of the same company are one option or two, so the paper this article rests on never confronts the question a business faces immediately.
And the person drawing the categories is usually the person seeking the budget. Splitting your own function into three line items rather than one triples its share under an even split, without anyone appearing to argue for more money, which is a governance problem rather than a statistical one.
Your Marketing Budget
The first application. Ours, untested, and not marketing or financial advice.
Four points.
The standard move is to shift spend toward last year's best channel. That is sample-based optimisation on a handful of observations, which is the method that lost.
Our own arithmetic says what it would take to justify. A channel genuinely five points better, at twenty percent monthly volatility, takes 21 years to establish.
The mechanism to watch for is the concentration of error. The channel that looks best is disproportionately the one whose measurement was most favourable, which is why reallocation often disappoints in the following period.
And the exception is the one the currency study identifies. Where you can observe rather than estimate, optimise: a channel with a directly measured cost per acquisition on high volume is closer to a quoted rate than to a historical average.
That exception deserves a caution, since it is the one a reader will reach for. A measured cost per acquisition is an observation about cost and not about value, and the quantity that matters for allocation is what those acquisitions are worth over their life.
Which puts most firms back in the estimation case for the half that matters. You can observe what you paid and you must estimate what you bought, and the optimisation is only as good as the weaker of the two.
Capital Allocation
The second application, where the stakes are larger and the data thinner. Ours.
Four points.
Allocating capital across projects has fewer observations than marketing and longer feedback, so every problem in this article is worse.
It also has a feature portfolios lack, which cuts against the even split. Projects have minimum viable sizes, and splitting a budget five ways may fund five projects too small to work.
Which means the rule needs adapting rather than adopting. The finding is about weights among things that scale smoothly, and a project that fails below a threshold does not.
And the honest transfer is narrower than the finance result. Where options scale smoothly, split; where they have thresholds, the arithmetic here does not apply, and we would not pretend otherwise.
A related feature makes capital allocation harder still, and it is worth naming because it is invisible in the portfolio framing. Projects interact. Two initiatives can share a customer base, a team or a bottleneck, in a way that two stocks in an index do not.
Where that holds, the whole comparison shifts. An even split across four projects competing for the same constrained resource is not diversification; it is four projects running slowly, and the finding this article reports has nothing to say about that case.
Where To Optimise Instead
Because this article should not end by recommending that nobody think. Ours.
Four observations.
The currency study gives the test in one line. Is there a predictor of the outcome that is free of estimation error? If yes, optimise; if no, split.
In a business, observable inputs exist and are usually on the cost side rather than the return side. Prices you pay, rates you are quoted, hours a job takes, are measured rather than forecast.
So the productive split is between the two halves of a decision. Optimise the costs, which you can observe. Spread the bets on returns, which you must estimate.
And that is a more useful rule than either extreme. Not a choice between analysis and heuristics, but a rule about which half of a problem each belongs to, which is our own formulation and untested.
Two examples of what that looks like in practice, ours. Negotiating supplier rates is optimisation on an observable: you know the quoted price, the volume and the terms, and effort spent there converts directly into margin.
Choosing which product line will grow fastest next year is estimation, and effort spent producing a precise forecast buys precision rather than accuracy. The first deserves a spreadsheet and the second deserves a spread.
Not An Excuse For Not Thinking
The section this article needs. Ours.
Four observations.
Nothing here says analysis is useless, and reading it that way inverts the finding. The 2009 result is that a specific method fails on a specific input problem, not that judgment should be abandoned.
The even split also has to survive the partition problem, which means somebody has to decide what the options are, and that decision determines the allocation entirely.
And an even split is only defensible across options you have already judged worth including. The rule allocates among candidates; it does not select them, and selection is where most of the value in a business decision sits.
So the correct reading is narrow and useful. Work hard on which options belong on the list, and be sceptical of precision in dividing money among them, which is close to the opposite of how most budget meetings run.
One last thing this article does not establish, and a careful reader should hold us to it. We have shown that an even split beat optimisation in finance and argued the structure transfers. We have not shown that it beats the allocation a thoughtful owner would reach by other means.
The comparison in the 2009 paper is between an even split and a formal statistical optimiser, not between an even split and judgment. Nothing here says an experienced owner should override their own reasoning with a division rule, and the previous article's conditions are the right test of whether that reasoning has been earned.
What To Do
Ask how much history an estimate rests on. The requirement for optimisation to beat an even split was around 3,000 months for 25 assets, calibrated to the best-documented market that exists.
Apply the observable-input test. Optimise where a predictor is free of estimation error, as with a quoted rate; split evenly where the input must be estimated from a short history.
Compute how long your edge would take to prove. On our own figures a five point gap at twenty percent volatility needs 21 years, and most reallocations rest on one quarter.
Know that picking beats splitting only if you beat chance. On our own arithmetic the break-even probability is exactly one over the number of options.
Fix your categories before you look at the numbers. An even split across two categories and across four gives different answers with the same money, so whoever writes the list chooses the allocation.
Expect the optimiser to concentrate on its own errors. It puts the most weight on whatever looks best, and what looks best is disproportionately what was overestimated.
Do not apply this where options have thresholds. The finding concerns weights among things that scale smoothly, and a project that fails below a minimum size does not.
Spend the effort on the shortlist instead. The rule allocates among candidates and does not choose them, and selection is where the value sits.
The Limits Of This Analysis
Several caveats matter. This article discusses research on allocation and is not investment, financial or budgeting advice; nothing here is a recommendation about any portfolio, security, channel or project, and the applications are our own reasoning and untested. Everything is verified to August 2026. We did not obtain the 2009 paper, only its abstract verbatim from the publisher and three corroborating sources, so we report none of its seven datasets, fourteen models or numerical results beyond what the abstract states. We did not obtain the currency study, only its abstract, so the Sharpe ratios of 0.91 and 0.15 are reported without any detail of construction, period or costs. We could not identify the authorship of the research-design objection, whose abstract we found on a document-sharing site, and we report its content anonymously rather than risk attributing a critical claim to the wrong researchers. We did not obtain the 2010 defence of optimisation and report only its title and citation. All arithmetic is ours, and every business parameter in it is invented: the volatilities, the gaps between options, and the assumption that returns are independent across periods, which financial returns are not. The break-even result is exact only under the stated assumption that one option is better and the rest are alike; with a dispersed set the arithmetic changes. And the entire business transfer rests on the allocation problems being structurally the same, which is our own inference: we found no study testing an even split against optimisation on marketing budgets or capital projects, and the finance result cannot establish what happens in settings with thresholds, minimum viable sizes, or categories that somebody has to draw.
Frequently Asked Questions
What is the 1/N rule?
Why does optimisation lose?
How much data would optimisation need?
When does optimisation win?
What does splitting evenly cost me?
So when should I just pick one?
What is the weakness of the even split?
References
- DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? The Review of Financial Studies, 22(5), 1915–1953, May, DOI 10.1093/rfs/hhm075. Publisher record reproducing the abstract in full: on the authors evaluating the out-of-sample performance of the sample-based mean-variance model and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio; on none of the 14 models evaluated across seven empirical datasets being consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, indicating that out of sample the gain from optimal diversification is more than offset by estimation error; on analytical results and simulations, based on parameters calibrated to the US equity market, showing the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1/N benchmark to be around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets; and on this suggesting there are still many miles to go before the gains promised by optimal portfolio choice can actually be realized out of sample. Note: the publisher's record. We obtained the abstract verbatim and not the paper, so no dataset detail, model specification or numerical result beyond the abstract is reported here. academic.oup.com
- Three further independent records of the same paper corroborating the abstract text and citation: a bibliographic service reproducing the passage on the estimation window and the miles-to-go conclusion, and giving the citation as Review of Financial Studies, volume 22, pages 1915–1953, 2009; a preprint archive record reproducing the same passage and confirming the DOI; and the first author's own business school repository, which records the citation as DeMiguel, V, Uppal, R and Garlappi, L (2009), Review of Financial Studies, 22(5), 1915–1953, ISSN 0893-9454, with the author order differing from the published order given by the publisher and the other sources. Note: three corroborating records, used to confirm the abstract text and citation independently. Recorded also as the source of a minor variant in author order between an institutional repository and the published paper. semanticscholar.org
- Publisher record for a study of optimal and naive diversification in currency markets in a management science journal, reproducing its abstract: on DeMiguel, Garlappi and Uppal having shown that in the stock market it is difficult for an optimized portfolio constructed using mean-variance analysis to outperform a simple equally weighted portfolio because of estimation error; on the authors demonstrating that portfolio optimization can be made to work in currency markets; on the key difference being that in currency markets interest rates provide a predictor of future returns that is free of estimation error, which permits the application of mean-variance analysis; and on a mean-variance efficient portfolio constructed in this fashion having, over the last 26 years, a Sharpe ratio of 0.91 versus only 0.15 for the equally weighted portfolio. Note: the publisher's record. Our source for the condition under which optimisation wins; we obtained the abstract only, so the Sharpe ratios are reported without any detail of construction, period or transaction costs. pubsonline.informs.org
- Abstract carried on a document-sharing site, responding to the 2009 paper: recording that DeMiguel, Garlappi and Uppal report naive diversification dominating mean-variance optimization in out-of-sample asset allocation tests; that the responding analysis suggests this is largely due to their research design, which focuses on portfolios subject to high estimation risk and extreme turnover; that mean-variance optimization often outperforms naive diversification but turnover can erode its advantage in the presence of transaction costs; and that the responding authors develop two new methods of mean-variance portfolio selection, volatility timing and reward-to-risk timing, delivering portfolios characterised by low turnover which outperform naive diversification even with high transaction costs. Note: an abstract on a document-sharing site. We could not establish which paper this abstract belongs to or who wrote it, and therefore report its content without attribution rather than risk crediting a critical claim to the wrong researchers. academia.edu
- Academic preprint reference list confirming DeMiguel, V., Garlappi, L., and Uppal, R., Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?, Review of Financial Studies, 22(5), 1915–1953, 2009; Kritzman, M., Page, S., and Turkington, D., In defense of optimization: The fallacy of 1/N, Financial Analysts Journal, 66(2), 2010; Escobar, M., Mitterreiter, M., Saunders, D., Seco, L., and Zagst, R., Market crises and the 1/n asset-allocation strategy, Journal of Investment Strategies, 2(4), 83–107, 2013; and Maillard, S., Roncalli, T., and Teiletche, J., The properties of equally weighted risk contribution portfolios. Together with a further journal reference list confirming Fletcher, J. (2011), Do optimal diversification strategies outperform the 1/n strategy in uk stock returns?, International Review of Financial Analysis, 20(5), 375–385. Note: reference lists; citations only. We obtained none of the works named, including the 2010 defence of optimisation whose title states a position directly opposed to this article's finding. arxiv.org
This article discusses research on allocation and is not investment, financial or budgeting advice; nothing here is a recommendation about any portfolio, security, channel or project. None of the underlying papers was obtained; all are reported from abstracts. The authorship of one critical response could not be established and its content is reported anonymously. All arithmetic is the authors' own on invented parameters, assumes returns independent across periods, and its break-even result holds only under the stated assumption. No study testing an even split against optimisation on business budgets was found; that transfer is the authors' own inference.