FRM Part I · FRM Exam Part I · Multivariate Random Variables
A risk analyst models returns on a portfolio of two assets, each with standard deviation 5%, as bivariate normal with correlation 0.30. The portfolio holds equal weights. A colleague proposes re-estimating with correlation 0.90 while keeping the standard deviations unchanged. By how many percentage points does the portfolio standard deviation rise?
The portfolio standard deviation rises from about 4.03% to about 4.87%, an increase of roughly 0.84 percentage points, none of which matches 0.94 exactly; the listed option is therefore flawed.
- A0.50
- B0.94Correct
- C1.25
- D1.58
Explanation
Portfolio variance = 0.25(25)+0.25(25)+2(0.25)(0.30)(25) = 12.5 + 3.75 = 16.25 with rho 0.3? Check: 6.25+6.25+3.75=16.25, sd = 4.031%. With rho 0.9: 12.5+11.25=23.75, sd = 4.873%. Difference = 0.842, not 0.94. Corrected answer: 0.84.
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