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IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns

In a single-factor model of returns, R_i = a_i + b_i*I + e_i, where I is a common index and the e_i are specific terms. Which assumption is made about the specific terms e_i?

The specific (residual) terms are assumed uncorrelated with the common index and with each other across securities. All co-movement between securities therefore comes only through the common factor, which keeps the covariance structure simple and limits the number of parameters needed.

  1. AThey are uncorrelated with I and with each other across securitiesCorrect
  2. BThey are perfectly correlated across all securities
  3. CThey have the same variance for every security
  4. DThey are equal to the market risk premium
  5. They are perfectly negatively correlated with I

Explanation

The single-index model assumes the specific returns have zero mean, are uncorrelated with the common factor, and are uncorrelated with the specific returns of other securities. This is why all covariance between securities arises through the common factor. Equal variances or perfect correlations are not assumed.

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