Skip to content

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, where R_M is the return on a market index and e_i is the residual. Which assumption is standard for this model?

The standard assumption is that residuals are uncorrelated with the market index and with other securities' residuals. This means that all common movement between securities arises only through their dependence on the index, which greatly simplifies covariance estimation.

  1. AThe residuals e_i are uncorrelated with R_M and with the residuals of other securitiesCorrect
  2. BThe residuals e_i of different securities are perfectly positively correlated
  3. CThe beta b_i must equal 1 for every security
  4. DThe residual e_i has a mean equal to the market risk premium
  5. The index return R_M must be non-random

Explanation

The single-index model assumes the residual has zero mean, is uncorrelated with the index, and is uncorrelated with other securities' residuals. All co-movement between securities then arises through the index. The other options contradict this structure or are not required.

Did you get it right without looking?

One question tells you little. A timed set on Single and multifactor models for investment returns shows your real accuracy, how long you take and where you lose marks.

Practise Single and multifactor models for investment returnsFree diagnostic mock

More Single and multifactor models for investment returns questions