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

A portfolio manager uses a single-factor model in which each stock's return equals its alpha plus beta times the market return plus a stock-specific residual. The residuals are assumed uncorrelated with the market and with each other. Which statement best describes the effect of adding many more stocks to a well-diversified portfolio under this model?

Adding many stocks drives residual variance toward zero because specific risks are uncorrelated and diversify away, while systematic variance stays at portfolio beta squared times market variance. Market exposure cannot be diversified, so total risk converges to the systematic component.

  1. ABoth systematic and residual variance fall toward zero
  2. BResidual variance falls toward zero while systematic variance remains determined by portfolio beta and market varianceCorrect
  3. CSystematic variance falls toward zero while residual variance stays constant
  4. DTotal variance becomes independent of the portfolio beta

Explanation

Residual risks are uncorrelated, so their contribution to portfolio variance shrinks roughly in proportion to 1/N as positions are added. Systematic variance equals beta squared times market variance and cannot be diversified away. Option A is wrong because market exposure remains.

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