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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return

Two assets, A and B, have a correlation coefficient of -1 between their returns. What is the effect of combining them in suitable proportions?

With a correlation of -1, the assets move in exactly opposite directions, so suitable weights can cancel all fluctuations and bring portfolio standard deviation to zero. The weighted-average risk outcome applies only when correlation is +1.

  1. APortfolio risk can be reduced to zeroCorrect
  2. BPortfolio risk is always the weighted average of the two standard deviations
  3. CPortfolio risk always exceeds that of the riskier asset
  4. DPortfolio return becomes zero

Explanation

With perfect negative correlation, movements offset completely, and a particular weighting makes portfolio variance zero. Weighted average risk occurs only at correlation +1. Portfolio risk cannot exceed that of the riskier asset when correlation is below +1, and expected return is still the weighted average of returns.

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