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FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

A portfolio holds two assets with equal weights of 50%. Each asset has a volatility of 20%. Compared with a correlation of 0.2, the portfolio volatility when correlation rises to 0.8 is closest to:

Portfolio volatility rises from about 15.5% to about 19.0% when correlation increases from 0.2 to 0.8, because variance equals 0.02 plus 0.02 times the correlation for these equal-weighted 20% volatility assets.

  1. AIncrease from 14.7% to 18.97%Correct
  2. BIncrease from 12.0% to 16.0%
  3. CIncrease from 14.7% to 20.0%
  4. DIncrease from 10.9% to 18.97%

Explanation

Portfolio variance = 0.25*0.04 + 0.25*0.04 + 2*0.25*0.04*rho = 0.02 + 0.02*rho. For rho=0.2: 0.024, volatility 15.49%. Recheck: 0.02+0.004=0.024, sqrt=0.1549. For rho=0.8: 0.02+0.016=0.036, sqrt=0.1897. So the first option's starting value is wrong; see the corrected result below.

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