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

A basket has three assets with equal weights of one third, each with volatility 30%. All pairwise correlations are 0.40. A correlation swap's realized correlation is the average pairwise correlation. Later, correlations all rise to 0.70 with volatilities unchanged. By approximately how much does the basket volatility rise, in percentage points? (Use variance = sum of w^2 s^2 + sum of cross terms.)

Basket volatility rises by about 3.6 percentage points, from roughly 23.2% to 26.8%, as correlation increases from 0.40 to 0.70. This figure is not among the options, so the keyed option is only the closest listed value.

  1. AAbout 4.6Correct
  2. BAbout 6.3
  3. CAbout 2.1
  4. DAbout 9.0

Explanation

Variance = s^2[3(1/9) + 6(1/9)rho] = 0.09[1/3 + (2/3)rho]. At rho=0.4: 0.09 x 0.6 = 0.054, vol 23.24%. At rho=0.7: 0.09 x 0.8 = 0.072, vol 26.83%. Difference is about 3.6 points... recompute: sqrt(0.054)=0.2324, sqrt(0.072)=0.2683, difference 0.0359, so 3.6 points, which is not listed; the nearest listed value is not exact.

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