CS Executive · Corporate Accounting and Financial Management · Security Analysis
A portfolio has 60% invested in Share X (expected return 15%) and 40% in Share Y (expected return 10%). The two shares have perfectly negative correlation (−1). Standard deviations are X = 10% and Y = 15%. What is the portfolio standard deviation?
The portfolio standard deviation is 0%. With perfect negative correlation, risk equals the absolute difference of the weighted standard deviations: 0.6×10 equals 6 and 0.4×15 equals 6, so the difference is zero. The risks cancel completely, giving a risk-free portfolio.
- A0%Correct
- B12%
- C3%
- D6%
Explanation
With correlation −1, portfolio SD = |wX·σX − wY·σY| = |0.6×10 − 0.4×15| = |6 − 6| = 0%. Option 12% is the weighted average of SDs (6+6), valid only for correlation +1. Option 3% and 6% do not follow from the formula.
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