CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return
Stocks X and Y have standard deviations of 20% and 30%. A portfolio holds 50% in each, and the correlation between them is -1. What is the portfolio standard deviation?
The portfolio standard deviation is 5%. With a correlation of -1, risk is the absolute difference of the weighted standard deviations: 0.5 x 30% minus 0.5 x 20% equals 5%. Risk could be eliminated only with weights of 60% and 40%, not equal weights.
- A25%
- B0%
- C5%Correct
- D50%
Explanation
With correlation -1, SD = |w1*s1 - w2*s2| = |0.5x20 - 0.5x30| = 5%. Zero is wrong because perfect hedging to zero needs weights inversely proportional to SDs (60:40), not 50:50. 25% is the +1 correlation answer.
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