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FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

A portfolio manager holds two assets with equal volatility of 10% and equal weights of 50%. The correlation is 0.20 under normal conditions, but is expected to rise to 0.80 in a crisis. What is the approximate change in portfolio volatility from the normal state to the crisis state?

Portfolio volatility rises from about 7.75% to about 9.49%. Variance is 0.25 times 0.01 times (2 plus 2 times correlation): 0.006 at correlation 0.2 and 0.009 at 0.8. Square roots give 7.75% and 9.49%, showing diversification erodes as correlation increases.

  1. AIt rises from 7.75% to 9.49%Correct
  2. BIt rises from 6.00% to 9.00%
  3. CIt rises from 7.75% to 8.00%
  4. DIt rises from 5.48% to 9.49%

Explanation

Portfolio variance = w²σ²(2 + 2ρ) with w=0.5, σ=0.10: 0.25×0.01×(2+0.4)=0.006 giving 7.75%; at ρ=0.8: 0.0025×3.6=0.009 giving 9.49%. Other options use wrong formulas, such as averaging or omitting terms.

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