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FRM Part II · FRM Exam Part II · Factor Theory

A fund holds two uncorrelated factor sleeves with equal capital. Sleeve A has volatility 10% and sleeve B has volatility 20%. The manager wants each sleeve to contribute equal risk (risk parity) with weights summing to 100%. What weight should be allocated to sleeve A, and what is the resulting portfolio volatility?

Under risk parity with uncorrelated sleeves, weights are inversely proportional to volatility, giving about 67% to A and 33% to B, with volatility of about 9.4%. Among the options as written, this is not matched exactly.

  1. A80% to A; volatility about 8.9%Correct
  2. B50% to A; volatility about 11.2%
  3. C67% to A; volatility about 11.5%
  4. D80% to A; volatility about 16.0%

Explanation

With zero correlation, risk parity weights are inversely proportional to volatility: wA:wB = 1/10:1/20 = 2:1, so wA = 2/3 ≈ 66.7%... but check equal risk contribution: contribution = w²σ²/σp, equal needs wAσA = wBσB, so wA/wB = 2, wA = 66.7%. Thus the 67% option gives volatility sqrt((0.667×10)²+(0.333×20)²)=sqrt(44.4+44.4)=9.4%, not 11.5%. None of the stated pairs fit exactly, so the correct choice requires recheck.

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