The optimizer is an error maximizer

A friend showed me his portfolio spreadsheet on Sunday. He had run Solver on five years of returns and it handed back weights to two decimal places. 47.32 pct in one stock. It looked like science.

I asked one question. What happens if a return forecast is off by one point.

We ran a clean demo. Three stocks, same volatility, correlation 0.8. Feed in forecasts of 12, 11 and 10 pct and the optimizer puts 91 pct in the first stock. Nudge the second forecast up by a single point and it splits 50/50. Swap two forecasts and the book flips to 9/91. One point of input error moved eighty points of portfolio.

Here's the part most people miss. Return forecasts are the noisiest number in finance. Ten years of history pins a 20-vol stock's true return no tighter than plus minus 6.3 points. The optimizer reads 12.00 as gospel and leans the whole book on the difference between 12 and 11. Richard Michaud named the bug back in 1989: the optimizer is an error maximizer. It loads up on exactly the assets whose returns were overestimated.

The test that settles it came in 2009. DeMiguel, Garlappi and Uppal ran 14 optimization models across 7 datasets against plain equal weight. None won out of sample consistently. For a 25-asset book the math needs roughly 3000 months of clean data, about 250 years, before it reliably earns its keep.

Equal weight makes zero forecasts, so it makes zero forecast errors. The work is done by the discipline of rebalancing back to equal. Selling what ran. Buying what lagged. On a calendar, not a feeling.

An optimizer answers to two decimal places a question nobody can answer to ten. Equal weight skips the question. That is the edge.

One point in, eighty points out

The demo in the opening, drawn as three outcomes. Same stocks, same risk, same correlation. Only the return forecasts change, by a point or two, and the weight in the first stock swings from almost all to almost nothing.

The reason is the high correlation. When three stocks move together, the optimizer sees them as near copies, and it piles into whichever copy has the slightly higher forecast. The tiny difference in forecasts is the only thing separating them, so the tiny difference decides everything.

How tight is a return estimate, really?

The error band on an average return shrinks with the square root of the years of data. The standard error is the volatility divided by the square root of the number of years. A stock with 20 percent volatility and ten years of history: 20 divided by the square root of 10, about 6.3 points. That is the figure in the opening.

To know a 20 percent volatility stock's average return to within one point, you need about 400 years of data. No stock has that. No market has that in a stable form. So the forecasts that feed the optimizer are guesses with a wide blur, and the optimizer treats the blur as precision.

Now apply it to a real index. The Nifty 50's daily returns had an annualised volatility of about 13.5 percent over the year to 30 Sep 2026, by NSE closing data. Even for the calmest broad index in India, one year of data pins its average return to within about plus or minus 13 points. The index fell 8.1 percent over that year. A forecast built on that year would be useless for next year.

What equal weight gives up and what it keeps

RupeeCase runs this idea on the Nifty 50 universe: all 50 names at equal weight, rebalanced every four weeks. In the model the Nifty 50 Equal Weight card compounded at 16.35 percent a year with a maximum drawdown of 15.71 percent and a Sharpe ratio of 1.13 (Model, back tested, as of 27 Apr 2026). It is the simplest card on the lineup, and the rule never asks anyone to forecast a return.

Equal weight is not free of judgment. It still needs a universe chosen with care, a rebalance cadence and an honest cost model. Those are decisions about process, not about which stock will earn 12 versus 11 next year. The Nifty 50 is 10 stocks plus 40 footnotes shows the same rule from the concentration side.

The free Learn module on modern portfolio theory covers the optimizer, the frontier and the estimation error that undoes both, with a quiz and a certificate. The Sharpe and volatility calculator shows risk adjusted return for any set of figures.