APT Induced Efficient Insurance Indices for Sharpe Mean-Varian

The purpose of this study is two-fold. First, it is to invert an insurance industry index(s) from a linearly independent factor structure derived from the application of the Ross (1976) arbitrage-pricing model (APT) on a sample of insurance industry returns. The second objective is to identify the effect this index has on the performance of the Sharpe multi-index model in the formation of the mean-variance (M-V) efficient set. These questions are examined by employing a multivariate comparison of M-V portfolios. We compare portfolios inverted from the Sharpe multi-index model with the inclusion of the APT latent factor industry index to portfolios produced by the Markowitz full covariance model. The analysis is complimented by a comparison of these results to M-V portfolios extracted from a model with linearly dependent factors. Our results show that M-V portfolios produced by the inclusion of the efficient industry index dominate M-V portfolios produced by a model that incorporates a naively specified insurance industry index. The results also provide clear evidence that within the insurance industry there is statistical equivalence between efficient portfolios extracted from the Markowitz full covariance model and the Sharpe multi-index model when the latter includes the APT induced efficient insurance industry index.