medium · Quantitative Finance
A portfolio manager is diversifying a portfolio. If she adds a new asset that is completely 'uncorrelated' (ρ=0) with the existing portfolio, what is the impact on the portfolio's total variance?
- The variance will only decrease if the new asset has a lower volatility than the portfolio.
- The variance will always decrease if the weights are optimized.
- The variance will increase due to the addition of more risk sources.
- The variance remains the same because the assets do not co-move.
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