FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology
Two assets each have volatility of 20%. A manager forms an equally weighted portfolio (50/50) and the portfolio volatility is 15%. What is the correlation between the assets?
Portfolio variance is 0.0225. For equal weights it equals 0.02 plus 0.02 times rho, so rho is 0.125. Weak positive correlation explains why volatility falls from 20% to 15%; a correlation of 0.5 would give about 17.3%.
- A0.125Correct
- B0.250
- C0.500
- D-0.125
Explanation
Portfolio variance = 0.25(0.04)+0.25(0.04)+2(0.25)(rho)(0.04) = 0.02+0.02rho. Set equal to 0.0225: rho = 0.125. Check: 0.02+0.0025=0.0225. Correct is 0.125.
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