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

Consider an equally weighted index of 2 stocks, each with volatility 20%. The index implied volatility is 16%. What implied average correlation is consistent with these figures? (Index variance = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2.)

The implied correlation is 0.28. Index variance of 0.0256 equals 0.02 plus 0.02 times rho for two equally weighted stocks with 20% volatility, so rho equals 0.0056 divided by 0.02, which is 0.28.

  1. A0.28Correct
  2. B0.36
  3. C0.64
  4. D0.56

Explanation

Index variance = 0.0256. With w=0.5: 0.25(0.04)+0.25(0.04)+2(0.25)ρ(0.04)=0.02+0.02ρ. Setting 0.02+0.02ρ=0.0256 gives ρ=0.28. Check: 0.02+0.0056=0.0256. Option 0.64 is the variance ratio mistake, while 0.36 is one minus the correct ρ... actually it results from a wrong subtraction.

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