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

In a single-index model for the return on security i, R_i = a_i + b_i R_M + e_i, which statement about the error term e_i is a standard assumption?

The error term in a single-index model is assumed to have zero mean and to be uncorrelated with the market return. It also is uncorrelated with other securities' errors, so the market is the only common factor driving the co-movement between securities.

  1. Ae_i has zero mean and is uncorrelated with the market return R_MCorrect
  2. Be_i has mean equal to the risk-free rate
  3. Ce_i is perfectly correlated with R_M
  4. De_i is perfectly correlated with the error terms of all other securities
  5. e_i has variance equal to the market variance

Explanation

The single-index model assumes the residual has zero expected value and is uncorrelated with the market return. Residuals of different securities are also assumed uncorrelated, so the only common influence is the market. Options with perfect correlation break this structure.

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