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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

Returns on two assets have equal variances and a correlation of -1. Which weights produce a portfolio with zero variance?

Equal weights of 50% and 50% give zero variance. With correlation of -1 and identical volatilities, portfolio volatility equals the absolute difference of the weighted volatilities, which vanishes only when the weights are equal.

  1. AWeights of 50% and 50%Correct
  2. BWeights of 70% and 30%
  3. CWeights of 100% and 0%
  4. DWeights of 150% and -50%

Explanation

With correlation -1 and equal volatility s, portfolio volatility is |w1 s - w2 s|. This is zero only when w1 = w2, so 50/50 with weights summing to one. Other options leave a nonzero difference.

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