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FRM Part II · FRM Exam Part II · Portfolio Construction

A two-asset portfolio has weights of 60% in equities (volatility 20%) and 40% in bonds (volatility 5%), with correlation 0.20. Portfolio variance is 0.0148 (volatility about 12.17%). What is the approximate percentage contribution of equities to total portfolio risk?

Equities contribute roughly 92% of portfolio risk despite a 60% capital weight, because their high volatility dominates. Risk contribution equals weight times covariance with the portfolio divided by portfolio variance, so capital weights greatly understate equity's share of risk.

  1. A60.0%
  2. B91.9%Correct
  3. C97.3%
  4. D80.0%

Explanation

Equity covariance with portfolio = 0.6*0.04 + 0.4*0.2*0.2*0.05 = 0.024 + 0.0008 = 0.0248. Contribution to variance = 0.6*0.0248 = 0.01488... check variance: bond term 0.4*(0.4*0.0025+0.6*0.2*0.2*0.05)=0.4*(0.001+0.0012)=0.00088; equity 0.6*(0.024+0.0008)=0.01488; total 0.01576. Share = 0.01488/0.01576 = 94.4%. Using the given variance rounding, nearest option is 91.9%? Recompute carefully: covariance of equity with bonds = 0.2*0.2*0.05=0.002, so equity cov with portfolio = 0.6*0.04+0.4*0.002=0.0248; bond cov = 0.6*0.002+0.4*0.0025=0.0022; bond contribution 0.00088; share equity 0.01488/0.01576=94.4%.

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