In Defence of Optimisation: the Fallacy of Equal Weighting
When does an optimized portfolio outperform a simple equal-weight allocation?
Compare optimized and equal-weight allocations under identical asset universes, constraints, costs and untouched test dates. Input quality determines the result; this study challenges a universal equal-weight rule without proving optimization wins across every market.
The empirical comparison challenges a universal one-over-N rule, without proving optimization always wins.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | The reply to the widely cited finding that naive equal weighting beats optimised portfolios out of sample. |
| Key result / formula | The original result compared optimisation using historical sample means as expected returns against equal weighting, and optimisation lost. |
| Why it matters for backtesting | An agent asked whether to optimise weights should present both sides, because the existing note on the naive benchmark states the other one. |
What it is
Kritzman, Page and Turkington argue the comparison was unfair to optimisation, and that with reasonable inputs the optimised portfolio wins.
Key result / formula
The authors' objection is that no competent practitioner uses historical sample means, because they are the noisiest input available and the one the optimiser is most sensitive to. Substituting more defensible expected returns, a risk-premium estimate, a long-run average across assets, or simply equal expected returns for all assets, and re-running the comparison over long histories and many data sets, optimisation outperforms equal weighting in the great majority of the cases they examine. Their further point concerns sample length: the estimation error in expected returns declines slowly, so the studies favouring equal weighting used windows too short for any method to work, and the conclusion drawn from them was about the window rather than about optimisation. The result they defend is modest: optimisation with sensible inputs beats a naive rule, which is not the same as optimisation with any inputs beating anything.
Why it matters for backtesting
The synthesis is that the decision depends on the quality of available inputs: with credible expected returns, optimise; without them, use a construction that does not need them; and do not feed an optimiser sample means from a short window. Stochastly can settle it empirically for the user's own instruments by running all three allocations out of sample on their data and comparing, which is a better answer than either side of the literature. The comparison must be at equal risk, since optimised portfolios often run at a different volatility than equal-weighted ones.
Source
Kritzman, Page & Turkington, "In Defense of Optimization: The Fallacy of 1/N", Financial Analysts Journal 66(2), 2010, 31-39. Primary source
Related in the library
Nothing Beats the Historical Mean Out of Sample, Except Under Constraints
Guide on this topic: In-sample vs out-of-sample testing
How the assistant cites the library · The checks behind a verdict