Lesson 5 of 8 · All lessons in this module
  1. Asset classes: return, risk and other characteristics
  2. Risk aversion and utilityVideo lesson
  3. Indifference curves and the capital allocation lineVideo lesson
  4. Measuring asset and portfolio riskVideo lesson
  5. Correlation and the power of diversificationVideo lesson
  6. Integrated cases: a foreign bond with currency, and pairs from a scenario table
  7. Minimum-variance and efficient frontiersVideo lesson
  8. Optimal risky portfolio and the optimal investor portfolioVideo lesson

Lesson 5 of 8 · 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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