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

In a multifactor model of security returns, R_i = a_i + b_i1 F1 + b_i2 F2 + e_i, which statement about the term e_i is correct under the standard assumptions?

The term e_i is the specific or idiosyncratic return. It has zero mean and is assumed uncorrelated with the factors and with other securities' residuals, so it is diversifiable in large portfolios, unlike the systematic part driven by the factors.

  1. AIt is the systematic component and is perfectly correlated across securities
  2. BIt is the specific (idiosyncratic) return, uncorrelated with the factors and with other securities' specific returnsCorrect
  3. CIt equals the risk-free rate of return
  4. DIt must be identical for all securities in the same sector
  5. It is the factor sensitivity of the security to F1

Explanation

In a multifactor model the residual e_i captures the security-specific return. It is assumed to have zero mean and be uncorrelated with the factors and with the residuals of other securities. This is why specific risk can be diversified away in a large portfolio.

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