Lesson 5 of 7 · 14 min

Correlation and the power of diversification

Combining assets that are less than perfectly correlated cuts risk without cutting expected return, and in large portfolios average covariance is what remains.

In short

  • At ρ\rho = +1, σp\sigma_p is the weighted average of σ\sigmas: no diversification benefit.
  • At ρ\rho < +1, σp\sigma_p is below the weighted average; at ρ\rho = −1 a portfolio can be made riskless.
  • Expected return does not depend on correlation; only risk does.
  • Equal-weighted portfolio of N assets: σp2=σˉ2/N+N−1NCov‾\sigma_p^2 = \bar\sigma^2/N + \frac{N-1}{N}\overline{\text{Cov}}. As N grows, average covariance dominates.
  • Correlations above about 0.90 offer little diversification; below about 0.50 are attractive.
  • Add a new asset if its Sharpe ratio exceeds the portfolio's Sharpe ratio times their correlation.

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Correlation and the power of diversification · Portfolio Risk and Return: Part I