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FRM Part II · FRM Exam Part II · Hedge Fund Investment Strategies

A risk manager regresses a convertible arbitrage fund's monthly returns on equity market, credit spread and volatility factors. The R-squared is 0.80 and the intercept is 0.20% per month. The fund's total return variance is 25 (in %² per month). What is the residual (idiosyncratic) variance, and what does the intercept represent?

Residual variance is 5, because 20% of the total variance of 25 is unexplained by the factors. The intercept of 0.20% per month is the average return not attributable to the factor exposures, which is the estimated alpha.

  1. AResidual variance of 20; the intercept is the beta to the market
  2. BResidual variance of 5; the intercept is the return unexplained by the factors, the estimated alphaCorrect
  3. CResidual variance of 5; the intercept is the factor-explained return
  4. DResidual variance of 20; the intercept is the estimated alpha

Explanation

R-squared of 0.80 means 80% of variance is explained, leaving 20% unexplained: 0.20 x 25 = 5. The intercept is the average return not explained by factor exposures, the alpha. Option D uses 0.80 x 25 = 20, which is the explained variance instead.

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