Covariance and Why Raw Matrices Mislead

What does q = N ÷ T measure?

• How correlated the pairs are on average
• How many series there are per observation, which sets how noisy the sample matrix is
• The share of the matrix that is real structure

A sample matrix has an eigenvalue of exactly zero. What is an optimiser that inverts it likely to do?

• Ignore that direction, since it carries no risk
• Put heavy weight on that mix of pairs, because it looks riskless
• Refuse to trade any of the pairs involved