Explain the relationship between the index model and the CAPM expected return beta

The Capital Asset pricing model and single index model will be having a higher degree of similarity because both the models will be reflecting the market movement of the stock and they both will be further focusing upon the balance relationship between the risk and the expected return on risky asset and even the functional form of expected return is similar for both the models.

The Alpha which is shown by the both the model will be highlighting a similarity between the two models and it will reflect the abnormal return of the stock of the portfolio and hence it will be similar for both the Capital Asset pricing model as well as the single index model.