Skip to content

FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio has two positions with weights 60% in A and 40% in B. Volatilities are 10% for A and 20% for B, with correlation 0.25. Portfolio volatility is approximately 10.8%. What is the percentage contribution of B to portfolio variance (component share)?

B contributes about 61% of portfolio risk. Portfolio variance is 0.0124, and B's component is its weight times its covariance with the portfolio, 0.4 times 0.019, or 0.0076. Dividing gives roughly 61%, far above its 40% weight because of its higher volatility.

  1. AAbout 61%Correct
  2. BAbout 39%
  3. CAbout 48%
  4. DAbout 74%

Explanation

Variance = 0.36(0.01)+0.16(0.04)+2(0.6)(0.4)(0.25)(0.1)(0.2)=0.0036+0.0064+0.0024=0.0124 (vol 11.14%, so the stated approximate 10.8% is only rough). B's contribution = wB x cov(B,P) = 0.4 x [0.6(0.25)(0.1)(0.2)+0.4(0.04)] = 0.4 x (0.003+0.016)=0.0076. Share = 0.0076/0.0124 = 61.3%. Using B's weight 40% ignores its higher volatility and correlation.

Did you get it right without looking?

One question tells you little. A timed set on Portfolio Risk: Analytical Methods shows your real accuracy, how long you take and where you lose marks.

Practise Portfolio Risk: Analytical MethodsFree diagnostic mock

More Portfolio Risk: Analytical Methods questions