Average Covariance, and Why Correlations Jump

Substitute $\omega_i = 1/n$ into the general variance formula to reach $\frac{1}{n}\,\overline{\sigma^2} + \frac{n-1}{n}\,\overline{\text{Cov}}$, and state its large-$n$ limit.

Describe how pools assumed to hold uncorrelated loans appeared nearly riskless, and what a national housing decline did to default correlations and portfolio risk.

Record the Thanksgiving-travel and flight-to-safety examples, including near-zero T-bill yields in 2008, and the contrast between correlations and fixed physical parameters.

Write down the view of a fitted distribution as a description of what we do not know, and the conclusion that mathematics must be paired with economic analysis.