FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management
Two assets each have a standard deviation of 20%. A portfolio holds them 50/50. Which pair correlation gives a portfolio standard deviation of exactly 17.32%?
The correlation is 0.50. With equal 50% weights and 20% volatilities, portfolio variance equals 0.02 plus 0.02 times the correlation. At 0.5 this is 0.03, and its square root is 17.32%. Other correlations give different volatilities.
- A0.25
- B0.50Correct
- C0.75
- D0.00
Explanation
Portfolio variance = 0.25(0.04) + 0.25(0.04) + 2(0.25)(0.04)ρ = 0.02 + 0.02ρ. With ρ=0.5: 0.03, whose square root is 17.32%. With ρ=0 the variance is 0.02, giving 14.14%. With ρ=0.25 it gives 0.025 (15.81%), and with ρ=0.75 it gives 0.035 (18.71%).
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