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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

For a two-asset portfolio with both weights positive, which change, with all else unchanged, will reduce portfolio variance?

A fall in the correlation between the assets reduces portfolio variance. The covariance term is twice the product of the weights, the correlation and both standard deviations, so with positive weights lower correlation lowers variance. Higher covariance, volatility or correlation would each raise it.

  1. AA fall in the correlation between the assetsCorrect
  2. BA rise in the covariance between the assets
  3. CA rise in the standard deviation of either asset
  4. DA rise in the correlation from 0.2 to 0.6
  5. A shift of weight to the asset with higher variance when correlation is positive

Explanation

Portfolio variance includes the term 2 w1 w2 rho s1 s2, which with positive weights falls as correlation falls. A rise in covariance or in either standard deviation increases variance. A shift to the higher-variance asset generally raises variance too when correlation is positive.

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