Lesson 5 of 14 · All lessons in this module

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 5 of 14 · 13 min

Scenario-based portfolio risk and the many-asset limit

Portfolio risk can be forecast directly from economic scenarios, and in a large portfolio it shrinks toward the average covariance, the part diversification cannot remove.

In short

With scenarios: compute the portfolio return in each scenario, then its probability-weighted mean and variance.
No covariance matrix is needed for the scenario method; co-movement is already built into each scenario's portfolio return.
Equal weights, common $\sigma^2$ and average correlation $\bar\rho$ : $\sigma_P^2 = \sigma^2/N + (1 - 1/N)\bar\rho\sigma^2$ .
As N grows, the first term vanishes and $\sigma_P^2 \to \bar\rho\sigma^2$ , the average covariance.
Most of the benefit arrives with roughly 20 to 30 holdings; what remains is systematic risk.

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