Comment on the following: The single model in relation to the multi index model.

The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model was developed by William Sharpe in 1963. The major assumption of Sharpe's single-index model is that all the co-variation of security returns can be explained by a single factor. This factor is called the index, hence the name 'single-index model.' Multi-index model is an extension of Single Index Model. The multi-index model assumes a return-generating process that is a linear function of many factors. In this approach, each factor is a source of systematic risk. Since investors cannot diversify systematic risk, they are assumed to be compensated for bearing this risk. A security's sensitivity to each factor affects the assumed return-generating process for the security. This sensitivity is captured by a 'factor beta'. Except for the fact that multiple factors make this a richer model than the single index model, the use of a multi-factor model is similar to the single-index model. A broad generalization of these models is the Arbitrage Pricing Theory.