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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

A portfolio holds 50 equally weighted stocks. Each stock has beta 1.0 and residual variance of 0.0400. The market variance is 0.0225. Residuals are uncorrelated with each other and with the market. What is the portfolio's total standard deviation (nearest 0.1%)?

The portfolio standard deviation is about 15.3%, from systematic variance of 0.0225 plus diversified residual variance of 0.0008.

  1. A15.0%
  2. B16.3%Correct
  3. C17.0%
  4. D20.0%

Explanation

Portfolio beta = 1.0, so systematic variance = 1 x 0.0225 = 0.0225. Residual variance of the portfolio = 0.04/50 = 0.0008. Total variance = 0.0233, and the square root is about 15.3%. Check: sqrt(0.0233)=0.1526, so the correct value is 15.3%, which is not listed under the intended key; recomputed key must match 15.3%.

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