Five Hundred Years of Data

TL;DR

• Markowitz's 1952 paper deliberately begins after investors have formed beliefs about future returns. Portfolio choice is the second stage; estimating its inputs is the first.
• Rebuilding Robert Shiller's three-asset classroom example with two defensible US equity series moves the recommended equity weight from 38% to 26%, while estimated portfolio risk and return barely move.
• Repeating the same long-only calculation through time produces equity weights anywhere from 0% to 100%. A precise optimisation rule does not make its estimated inputs stable.
• DeMiguel, Garlappi and Uppal found that fourteen portfolio rules did not consistently beat equal weighting out of sample. Their famous “500 years” is a specific calibration, not a universal law.
• Equal weighting is a model too. Its advantage is low estimation variance; its weakness is the symmetry it imposes. The interesting question is which assumptions survive the environment in which a portfolio will actually be used.

In 1952, the year he published Portfolio Selection, Harry Markowitz also had to divide his own retirement contributions between stocks and bonds. He did not calculate an efficient frontier. He split the money fifty-fifty. His remembered reason was regret: he did not want either a rising market or a falling one to make him feel that he had chosen the only intolerable side.[1]

The anecdote is usually told as a joke about an economist ignoring his own theory. The joke edits out two useful facts. Markowitz described a decision made when his method was new, not a lifelong policy; in 2009 he said that he no longer invested that way.[1] More importantly, his theory had never promised to manufacture trustworthy beliefs. It told an investor what followed if expected returns, variances and covariances were supplied.

Faced with real money and uncertain inputs, the architect of the machinery used a rule that estimated neither expected returns nor covariances.

The lecture, and what happens after it ends

Robert Shiller's freely available Open Yale lecture on diversification makes the geometry unusually tangible.[2] He takes US equities, ten-year Treasuries and oil, estimates their historical means and covariances, draws an efficient frontier and finds the long-only portfolio with the largest estimated Sharpe ratio. Two slides in recordings of the course give nearby but different allocations: roughly 27% or 36% in equities, 64% or 52% in bonds, and the balance in oil.

I rebuilt the exercise on the January 1983 to December 2006 window used in the 2011 lecture. The Treasury leg is a constant-maturity par-bond approximation constructed from the Federal Reserve's ten-year yield. Oil is WTI spot. For equities, I ran the same calculation twice.

Shiller's published S&P series produces 37.6% equities, 55.8% bonds and 6.6% oil. The value-weighted US market from Kenneth French's data library produces 26.1%, 67.3% and 6.6%. These are close reproductions of the two classroom allocations, not exact reconstructions of every unpublished convention behind the slides.[2][3]

The equity series differ for defensible reasons. Shiller uses a broad historical S&P series whose monthly price is an average of daily closes. French reports a value-weighted portfolio return for a broader US universe and includes distributions. Those choices alter estimated means and covariances as well as volatility. With the optimiser held fixed, the recommended equity weight moves by 11.5 percentage points.

The weights make that change look consequential. In estimated risk–return space it is much smaller: both tangency portfolios are near 6% annualised volatility and 10% return. The optimiser has found two portfolios that look nearly interchangeable in objective space while differing visibly in composition. A shallow objective near the optimum can turn a defensible input change into a large change in the answer we notice.

Then I repeated the total-market calculation through time. Each month uses only the preceding 120 months. The common input panel begins in May 1953, so the first estimate is dated April 1963; the last is June 2026. The equity weight ranges from 0% to 100%, and the bond weight from 0% to 90%. In December 2006 the rule selected 21.2% equities and 67.8% bonds. In June 2026 it selected 92.1% equities and no bonds. The standard deviation of the equity weight across the full sequence is 35 percentage points.

Shiller states the modelling move plainly: take the historical moments as given.[2] That is an appropriate way to teach the frontier. It is also the precise point at which the problem solved on the board stops being the problem faced by an investor.

One afternoon in 1950

Markowitz's path to the problem began while he waited outside Jacob Marschak's office at the University of Chicago. Another visitor, a stockbroker, suggested applying mathematical statistics to the market. Marschak referred him to Marshall Ketchum at the business school; Ketchum supplied a reading list.[4]

The basic idea came later, in the library, while he was reading John Burr Williams. Williams argued that a security was worth the discounted value of its future dividends. Markowitz noticed that an investor who cared only about expected value should put everything into whichever security had the largest expected return. Because investors diversify, expected return alone could not describe the choice he wanted to model. He reached for variance, looked up the variance of a weighted sum in J. V. Uspensky's probability text, and found the covariances that make diversification a mathematical object.[4]

The 1952 paper is only fifteen pages. It contains seven diagrams and no dataset. The computational algorithm followed in 1956; the fuller behavioural justification for mean and variance followed in the 1959 book.[5][6][7] The achievement was a frame: beliefs about assets enter on one side, a set of efficient choices leaves on the other.

The idea also arrived more than once. A. D. Roy independently published his safety-first rule four months later, selecting the portfolio with the greatest expected excess over a disaster threshold per unit of risk.[8] Bruno de Finetti had formulated a mean–variance problem for correlated insurance risks in 1940, although he solved only a particular uncorrelated case. Markowitz later credited him with posing the correlated problem while reserving credit for its solution.[9]

This is less a contest over priority than evidence that related questions had become visible from several fields at once. Probability theory, investment trusts and statistical decision-making had converged enough that multiple researchers could see neighbouring problems. A founding contribution need not contain every component first; it can be the formulation that makes a research programme legible.

The first stage

Markowitz drew the boundary in the opening paragraph of the paper. Portfolio selection, he wrote, has two stages. Observation and experience first become beliefs about securities' future performance; those beliefs then become a portfolio. His paper addresses the second stage.[5]

That bracket is not hidden. Later pages call belief formation difficult, suggest combining statistical methods with expert judgement, and leave it as “another story.”[5] The frontier is conditional reasoning: given a vector of expected returns and a covariance matrix, these portfolios are efficient. It does not say that the estimated vector and matrix are true, or even stable enough to support a real decision.

The input count grows quickly. For N assets, an unrestricted mean–variance model needs N expected returns, N variances and N(N − 1)/2 pairwise covariances: N(N + 3)/2 numbers. Fifty assets require 1,325 inputs; one hundred require 5,150; five hundred require 125,750. A thirty-year monthly record contains 360 observations per asset. Computing more sample moments does not create more history.

The mean is the fragile part. In a continuous-time diffusion model, Robert Merton showed that sampling more frequently improves estimation of variance but does not increase the information available about expected return when the calendar span is fixed.[10] Daily observations can make volatility precise while leaving the drift “almost useless.” The scope matters: this is not a theorem about every possible return process. It explains why an apparently long price series can still contain little information about its mean.

Optimising Against a Guess showed why optimisation selects attractive errors.[11] DeMiguel, Garlappi and Uppal gave a finance-specific two-asset illustration. If two almost perfectly correlated assets truly share an 8% mean and 20% volatility, the symmetric solution is 50/50. Change one estimated mean to 9% and an unconstrained plug-in solution can jump to +635% and −535%.[12]

This is not a numerical failure. It is the requested optimum for a table whose least reliable entries have been treated as facts.

Five hundred years

Gerd Gigerenzer supplied the line that became the title of this article. Reporting DeMiguel, Garlappi and Uppal's analysis, he wrote that an optimiser allocating among fifty assets could require a 500-year window before outperforming 1/N.[13]

The underlying study compared fourteen allocation rules with equal weighting over seven datasets. Portfolios were estimated on rolling 120-month windows and judged out of sample by Sharpe ratio, certainty-equivalent return and turnover. None of the fourteen rules beat 1/N consistently across those criteria and datasets.[12]

Their analytical question was narrower than “How many years does Markowitz need?” Given a number of assets, an assumed Sharpe advantage for the population tangency portfolio over 1/N, and a risk-aversion calibration, how long must an estimation window be before the expected utility cost of estimating parameters falls below the cost of imposing equal weights? In one fifty-asset calibration, the answer exceeded 6,000 months, or 500 years. Another fifty-asset calibration gave 530 months, about 44 years. The headline is real; it is also conditional.

The paper's industry dataset is public, so I reproduced the 1/N leg using the current Kenneth French vintage. Ten industry portfolios plus the US market, a 120-month window, and the paper's July 1963 to November 2004 sample span produce 377 evaluated monthly returns after the first 120 months are reserved as the common estimation window. The resulting monthly Sharpe ratio is 0.13533, against 0.1353 in the published table.

I also ran four portfolio rules on the same current-vintage panel. These runs are a sensitivity study, not an exact reproduction of every published rule: the public pipeline uses French's one-month risk-free series, whereas the original study used a 90-day Treasury-bill rate. The unconstrained sample mean–variance rule has a monthly Sharpe ratio of −0.0166 and annualised volatility of 88.4%. Its mean month-to-month sum of absolute changes in target weights is 41.3; because the calculation compares targets directly, this is an instability diagnostic rather than a transaction-cost turnover measure. At the most extreme dates, one target weight reaches −2,134 times capital (−213,445%) and another +519 times (+51,883%). The long-only rule produces much smaller swings. The unconstrained minimum-variance rule has a slightly higher Sharpe than 1/N on this period, but it too permits short positions and leverage. No single row supports the slogan that optimisation always loses.

Figure 3 uses the six mean–variance results reported in the paper's Table 3, rendered independently rather than copied from its figure. In-sample Sharpe falls out of sample in all six panels. Equal weighting is better in some and worse in others. That is the more durable result: estimation error can consume a large in-sample advantage before the portfolio reaches the future it was meant to serve.

Why a simple rule can win

Gigerenzer's useful idea is not that heuristics are secretly optimal. It is ecological rationality: the quality of a decision rule depends on the structure of its environment.[13][14] A flexible rule can approximate more relationships, but it must estimate more things. A simple rule accepts bias in exchange for lower estimation variance.

Equal weighting imposes symmetry. It ignores differences in expected return, risk and correlation, so calling it unbiased would be wrong. Conditional on the chosen asset universe, however, its weights have no sampling variance because no return parameter is estimated. That can be valuable when samples are short, signals weak and correlations unstable. It can be costly when persistent differences are large and measurable.

Gigerenzer says this explicitly on the same page as the 500-year result: both heuristics and optimisation can produce good or bad outcomes depending on the environment.[13] The claim is not 1/N over Markowitz. It is that model complexity must earn its estimation cost.

Many later repairs share a regularising effect. Long-only and norm constraints remove degrees of freedom; covariance shrinkage and Bayesian priors add structure; robust uncertainty sets change the errors a portfolio must survive. These methods are not equivalent, but each limits how directly a noisy sample can become a leveraged bet.

Even the theoretical case for 1/N has boundaries. Pflug, Pichler and Wozabal show that, for a broad class of convex risk functionals and Kantorovich-distance ambiguity sets, optimal portfolios converge towards uniform weights as the ambiguity radius grows.[15] This is an asymptotic result under a specified ambiguity model, not proof that equal weighting is universally, or at every finite ambiguity level, optimal. Its value is its precision: it identifies a stated regime in which refusing to distinguish assets is rational.

Where the simplification leaks

Equal weighting is not costless ignorance. It assumes every chosen asset deserves the same capital, and the asset universe itself was selected using information. Add or split a category and the portfolio changes. A rule with no estimated return parameters can still encode a strong prior.

Its apparent performance can also come from rebalancing. Plyakha, Uppal and Vilkov show that the advantage of equal weighting over value weighting depends materially on the rebalancing mechanism.[16] Kirby and Ostdiek construct simple timing strategies that outperform naïve diversification in their tests.[17] DeMiguel and co-authors show that modest norm constraints can improve plug-in portfolios by controlling extreme weights.[18] The correct comparison is therefore not “mathematics versus common sense.” It is one explicit rule against another, under the same information and trading-cost protocol.

Our three-asset example makes the same point on a smaller scale. Apply the total-market tangency weights estimated through December 2006 to every monthly return from January 2007 through June 2026, rebalancing back to those fixed target weights each month. The realised annualised Sharpe ratio is 0.705, below the in-sample estimate of 0.788 but hardly a collapse. Three assets, long-only constraints and fixed target weights already impose substantial regularisation. An unconstrained eleven-asset problem has much more room to turn noise into leverage.

There is a deeper objection too. Time-average and ensemble-average growth need not answer the same question for multiplicative wealth with absorbing ruin. Ole Peters and collaborators argue that the realised path should therefore be central to economic evaluation; other economists dispute what this adds to expected-utility theory.[19] Taleb gives the practical version: a strategy ruined on day 28 has no day 29.[20]

Heavy tails add a different problem. If extreme observations are more common than a Gaussian model allows, sample means and covariances can be unstable in feasible samples. For the daily and intraday equity returns studied by Gopikrishnan, Plerou and co-authors, estimated tail exponents were near three, compatible with finite variance but not a finite fourth moment.[21] Thus “variance exists” and “variance can be estimated reliably from this sample” are separate claims. The tail exponent, dependence structure, horizon and loss function have to be stated; no single tail result invalidates every mean–variance use.

What came next

Markowitz later reported surprise when Michaud's resampled-frontier method outperformed the approach he and Nilufer Usmen tested: “Much to our surprise, the Michaud methodology did better than ours.”[22] That reaction is a better bridge to modern portfolio research than either reverence or dismissal. The frontier solved a durable second-stage problem. The first stage kept moving.

Those responses do not form a single family. Some repair estimates; some change the objective; some change the economic question altogether. CAPM, in particular, is not simply a newer optimiser: it adds market equilibrium and asks why assets should have particular expected returns.

That distinction gives this series its route. The next article moves from the efficient frontier to the market portfolio and asks what one beta can explain when the market itself is only observed through a proxy. Later pieces will compare estimation repairs, conditional and asymmetric CAPM extensions, factor-model alternatives and recent predictive methods without pretending that there is one official “latest CAPM.”

Five hundred years is not the verdict. It is the bill for treating uncertain beliefs as if they had already become data.

Data and code

The Beyond Markowitz foundation study contains the data manifest, tested portfolio and CAPM foundations, numerical outputs and the three generated figures. It records source URLs, retrieval time and SHA-256 digests for the Kenneth French, Shiller and FRED inputs; third-party raw files are downloaded rather than redistributed. One command rebuilds the results, and an independent verification pass reproduces every committed artifact in a temporary directory.

The replication is intentionally explicit about approximation. The bond leg is reconstructed from a constant-maturity yield rather than a held Treasury security, and WTI spot omits futures roll and collateral returns. Current French data use CRSP's CIZ format; older published results may use the previous FIZ construction.[3] A data refresh is therefore a new vintage, not a promise that mutable upstream files will remain byte-identical forever.

References

1. Harry Markowitz, quoted in Jason Zweig, “What Harry Markowitz Meant”, 2 October 2017; includes Markowitz's 2009 clarification.
2. Robert J. Shiller, “Portfolio Diversification and Supporting Financial Institutions”, ECON 252, Lecture 4, Open Yale Courses, 2011, with the corresponding 2008 course recording.
3. Robert J. Shiller, “Online Data”; Kenneth R. French, “Data Library”; Federal Reserve Bank of St. Louis, GS10 and WTISPLC, data retrieved 21 August 2026.
4. Jeffrey R. Yost, “An Interview with Harry M. Markowitz”, Charles Babbage Institute oral history OH 333, 18 March 2002.
5. Harry Markowitz, “Portfolio Selection”, Journal of Finance 7, no. 1 (1952): 77–91.
6. Harry Markowitz, “The Optimization of a Quadratic Function Subject to Linear Constraints”, Naval Research Logistics Quarterly 3, nos. 1–2 (1956): 111–133.
7. Harry M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Cowles Foundation Monograph 16 (Wiley, 1959).
8. A. D. Roy, “Safety First and the Holding of Assets”, Econometrica 20, no. 3 (1952): 431–449.
9. Harry M. Markowitz, “The Early History of Portfolio Theory: 1600–1960”, Financial Analysts Journal 55, no. 4 (1999): 5–16; Harry M. Markowitz, “de Finetti Scoops Markowitz,” Journal of Investment Management 4, no. 3 (2006): 5–18; Paul D. Kaplan, “What Does Harry Markowitz Think?”, Morningstar Advisor, 15 June 2010.
10. Robert C. Merton, “On Estimating the Expected Return on the Market”, Journal of Financial Economics 8, no. 4 (1980): 323–361.
11. Richard O. Michaud, “The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?”, Financial Analysts Journal 45, no. 1 (1989): 31–42.
12. Victor DeMiguel, Lorenzo Garlappi and Raman Uppal, “Optimal Versus Naive Diversification”, Review of Financial Studies 22, no. 5 (2009): 1915–1953.
13. Gerd Gigerenzer, “Why Heuristics Work”, Perspectives on Psychological Science 3, no. 1 (2008): 20–29.
14. Gerd Gigerenzer and Henry Brighton, “Homo Heuristicus”, Topics in Cognitive Science 1, no. 1 (2009): 107–143.
15. Georg Ch. Pflug, Alois Pichler and David Wozabal, “The 1/N Investment Strategy Is Optimal Under High Model Ambiguity”, Journal of Banking & Finance 36, no. 2 (2012): 410–417.
16. Yuliya Plyakha, Raman Uppal and Grigory Vilkov, “Equal or Value Weighting? Implications for Asset-Pricing Tests”, in Financial Risk Management and Modeling (Springer, 2021): 295–347.
17. Chris Kirby and Barbara Ostdiek, “It's All in the Timing”, Journal of Financial and Quantitative Analysis 47, no. 2 (2012): 437–467.
18. Victor DeMiguel, Lorenzo Garlappi, Francisco J. Nogales and Raman Uppal, “A Generalized Approach to Portfolio Optimization”, Management Science 55, no. 5 (2009): 798–812.
19. Ole Peters and Murray Gell-Mann, “Evaluating Gambles Using Dynamics”, Chaos 26 (2016): 023103; Ole Peters, “The Ergodicity Problem in Economics”, Nature Physics 15 (2019): 1216–1221; Jason N. Doctor, Peter P. Wakker and Tong V. Wang, “Economists' Views on the Ergodicity Problem”, Nature Physics 16 (2020): 1168.
20. Nassim Nicholas Taleb, Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications, STEM Academic Press, 2020.
21. Parameswaran Gopikrishnan et al., “Inverse Cubic Law for the Distribution of Stock Price Variations”, European Physical Journal B 3 (1998): 139–140; Vasiliki Plerou et al., “Scaling of the Distribution of Price Fluctuations of Individual Companies”, Physical Review E 60 (1999): 6519–6529.
22. Harry Markowitz and Nilufer Usmen, “Resampled Frontiers Versus Diffuse Bayes: An Experiment,” Journal of Investment Management 1, no. 4 (2003): 9–25; Markowitz's reaction is reported in “Optimizing Harry Markowitz”, Institutional Investor, 14 June 2006.