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I am new to quantitative finance so, please excuse me if the terms are not correct.

I am trying to apply CAPM on a portfolio which has multiple indices (S&P 500, Russel 1000 and S&P Financials).

The portfolio looks something like this : Stated market exposure ---> large cap, small cap, financials.

How do I go ahead with this? Do I :

  1. Average the indices and then work with it's $\beta$ and $\alpha$ ?
  2. Run a simple Multiple Regession and report it's $\beta$ and corresponding t stats ?

Help will be very much appreciated.

Thank you in advance.

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It's not clear what you're trying to accomplish by applying CAPM, or it that a goal in itself?

For example, you could, for each stock in your universe, calculate the historical $\rho$ to each of the indices. Then use the index with the highest $\rho$ for this stock. (If you see negative $\rho$'s, then you may need more rules.) You can then use the following dynamics for a Monte Carlo:

The changes in the indices are driven by the historical volatilities and correlations of the indices.

The changes in each individual stock are driven by two components:

the change in this stock's index $\times$ the $\beta$ of this stock to its index

the idiosyncratic movements of the stock explained by the stock's historical volatility, and not correlated to anything.

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