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FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

An analyst estimates factor betas for a fund by regressing its excess returns on the excess returns of the market, a value factor and a momentum factor. The estimated coefficient on the momentum factor is 0.30 with a standard error of 0.10. Which interpretation is most appropriate?

The coefficient means that, holding the other factors constant, a 1% rise in the momentum factor return is associated with a 0.30% rise in the fund's excess return. The t-statistic of 3 (0.30 divided by 0.10) indicates statistical significance.

  1. AHolding the other factors constant, a 1% rise in the momentum factor return is associated with a 0.30% rise in the fund's excess return, and the t-statistic of 3 suggests the loading is statistically significantCorrect
  2. BA 1% rise in the momentum factor return raises the fund's total return by 30%, and the t-statistic of 3 is not significant
  3. CThe fund holds 30% of its assets in momentum stocks and the t-statistic of 3 indicates the beta is zero
  4. DThe coefficient is the fund's alpha, and a t-statistic of 3 means alpha is insignificant

Explanation

A multifactor beta is the partial sensitivity of the fund's return to a factor, holding other factors fixed. A t-statistic of 0.30/0.10 = 3 exceeds conventional critical values, so the loading is significant. It is not a portfolio weight nor the alpha (the intercept).

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