Skip to content

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

A two-asset portfolio holds equal amounts in assets A and B. Each asset has a 10-day 99% standalone VaR of USD 4 million. The model assumes a correlation of 0.20, but in a crisis the realized correlation rises to 0.80. Using the normal-based formula for portfolio VaR, what is the approximate increase in portfolio VaR caused by the correlation change?

Portfolio VaR rises from about USD 6.20 million at correlation 0.20 to about USD 7.59 million at correlation 0.80, an increase of roughly USD 1.4 million, so USD 1.35 million is the closest choice. It follows from VaR equals 4 times the square root of 2 plus 2 rho.

  1. AUSD 0.70 million
  2. BUSD 1.35 millionCorrect
  3. CUSD 1.90 million
  4. DUSD 3.20 million

Explanation

Portfolio VaR = sqrt(4^2+4^2+2*rho*4*4) = 4*sqrt(2+2rho). At rho=0.2: 4*sqrt(2.4)=6.197. At rho=0.8: 4*sqrt(3.6)=7.589. Difference is 1.39, about 1.35-1.4 million, closest to USD 1.35 million. The USD 3.20 million figure confuses the undiversified sum change with the actual rise.

Did you get it right without looking?

One question tells you little. A timed set on Empirical Properties of Correlation: How Do Correlations Behave in the Real World? shows your real accuracy, how long you take and where you lose marks.

Practise Empirical Properties of Correlation: How Do Correlations Behave in the Real World?Free diagnostic mock

More Empirical Properties of Correlation: How Do Correlations Behave in the Real World? questions