which is the difference betwee a model like CAPM and a single index model?
Is the first a special case of the second?
Best
Answer
As you know the equation that describes them is the same.
The single index model is an empirical description of stock returns. You do some regressions using data and you come up with Alphas, Betas etc. That's all. It is useful for example in modeling risks of a bunch of stocks in a simple way.
The CAPM is an economic theory that says that Alpha in the long run has an expected value of zero, which means that the returns investors get are solely due to their exposure to the 'market factor'. This is justified by some reasoning like "other risks can be diversified away, so they will not be rewarded in equilibrium, only 'systematic risk' will be rewarded". However, as you know, this has not held up well and it seems that there are other factors that are 'rewarded' in practice. So the CAPM is seen by many as flawed in some ways.
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