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

An analyst fits a single-index model to the monthly returns of an Indian large-cap fund using the Nifty 50 as the index. Which of the following is a recognised limitation of using this single-factor model to explain the fund's returns?

The single-index model may ignore other common influences such as sector or size effects. These leave residual returns correlated between securities, contradicting the model's assumption that the market index is the only common factor.

  1. AIt assumes the residual returns of different securities are correlated with each other
  2. BIt cannot be used to estimate the beta of a security
  3. CIt may ignore other common influences such as sector or size effects, leaving residual correlations between securitiesCorrect
  4. DIt requires the estimation of a full covariance matrix of all securities
  5. It implies that all securities have the same expected return

Explanation

The single-index model assumes that the only source of common movement is the market index, so residuals are uncorrelated. In practice sector, size or style effects create correlated residuals, which the model ignores. The other options either reverse the model's assumptions or describe features it does not have; indeed it reduces the number of parameters needed.

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