why the optimized portfolio loses to the boring one

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.

The construction math, decoded module by module: