When we derive the CAPM (i.e. find equations for the capital market line and the security market line), we nowhere assume that the individual security return is linearly dependent on the marker return (i.e. the single index model) However, when we interpret the CAPM, we say that expected return on an individual security depends only on its non-diversifiable risk, which we denote by beta (β). But viewing β as the measure of non-diversifiable is only justified by the variance decomposition under the single index model. So the question is, does CAPM require assuming the single index model?

No, CAPM Does not Require Assuming Single Index Model CAPM Model Is Based On Economic Theory, whereas Single Index Model Is completely Emperical(based On Observations) CAPM Assumes That the Market Is perfect, which is not so the case of Single Index Model as it has Some randomness Associated With the Return On the Security. In Case you have a Supporting/Counter Answer For the same, Do reply Thanks.