FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A two-asset portfolio under a normal model has weights of 60% in Asset A and 40% in Asset B. Volatilities are 10% for A and 20% for B, and the correlation is 0.5. Portfolio value is $100 million. Using a z-value of 2.0 for the confidence level, what is the component VaR of Asset B (in $ millions, over the same horizon as the volatilities)?
The computed component VaR of Asset B is about $14.5 million, so none of the listed values is right.
- AAbout 6.4Correct
- BAbout 4.3
- CAbout 10.6
- DAbout 8.0
Explanation
Variance = 0.36(0.01)+0.16(0.04)+2(0.6)(0.4)(0.5)(0.1)(0.2)=0.0036+0.0064+0.0048=0.0148; sigma=12.166%. Cov(B,P)=0.6(0.5)(0.1)(0.2)+0.4(0.04)=0.006+0.016=0.022. Component = w_B*z*Cov/sigma*V = 0.4*2*0.022/0.12166*100=14.47... recompute: Cov/sigma=0.18083; times z 2 =0.3617; times 0.4 =0.1447; times 100 = 14.5. Check: component A = 0.6*2*(0.006+... ) so the stated key needs to match 14.5.
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