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IAI Actuarial Core Principles · Business Finance · Key principles of finance

A portfolio manager at an Indian mutual fund holds two shares with returns that have a correlation coefficient of 0.2. Compared with the weighted average of the two shares' standard deviations, the portfolio standard deviation (with positive weights in both) will be:

The portfolio standard deviation will be lower than the weighted average. Unless correlation equals +1, combining the shares reduces risk because their returns do not move perfectly together, so some of the variability offsets.

  1. ALower, because correlation is less than 1Correct
  2. BEqual, because correlation is positive
  3. CHigher, because correlation is positive
  4. DEqual to zero, because correlation is low
  5. Equal to the lower of the two standard deviations

Explanation

Portfolio variance includes 2wAwBρσAσB. Only when ρ = 1 does the portfolio standard deviation equal the weighted average. With ρ = 0.2 it is strictly less, so diversification benefit arises. It is not zero, as that needs perfect negative correlation with suitable weights.

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