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VIWhy quants never trust their covariance matrix ?
Most portfolio optimization models rely on the covariance matrix.
500 stocks = 125,000 parameters to estimate from only 252 trading days. More relationships than data points. Most of what you estimate is noise.
Marchenko and Pastur (1967) showed that pure random data produces a predictable eigenvalue distribution. Overlay it on real data and you can separate signal from noise.
On S&P 500 data, only a handful of eigenvalues sit above the noise band. The rest is random fluctuation.
That’s why quants clean the matrix before optimizing, using eigenvalue clipping, shrinkage (Ledoit-Wolf), or other regularization methods. Factor models and Bayesian approaches also address the same problem.
The core idea: if you don’t question your inputs, no optimizer will save you
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