Using Multiple Market Indices in CAPM and Monte Carlo Models

Summary

The discussion considers how to model a portfolio exposed to several equity indices, including broad-market, small-cap, and financial-sector benchmarks. One reply suggests estimating each stock’s historical correlations to the indices, assigning it to the index with the strongest relationship, and using that index’s return and the stock’s beta to model systematic movement. The remaining stock movement is treated as idiosyncratic, with volatility estimated from its own history.

For a portfolio-level simulation, the indices’ returns can be generated jointly using their historical volatilities and correlations. The exchange does not establish whether averaging indices or running a multiple regression is the right approach for every purpose; it first advises clarifying what the CAPM analysis is meant to accomplish. The proposed highest-correlation assignment is a simple modeling suggestion, and negative correlations may require additional rules. No empirical validation or comparative results are provided.

Key ideas

• Clarify the purpose of applying CAPM before choosing a model specification.
• Estimate each stock’s historical relationship to candidate indices to identify a potential benchmark.
• Model index movements jointly using their historical volatilities and correlations.
• Decompose stock returns into benchmark-driven movement and uncorrelated idiosyncratic movement.
• Negative index correlations can make a simple highest-correlation assignment inadequate.

Tags

# Multiple Indices for CAPM model


# Multiple Indices for CAPM model












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 :

- Average the indices and then work with it's $\beta$ and $\alpha$ ?

- Run a simple Multiple Regession and report it's $\beta$ and corresponding t stats ?

Help will be very much appreciated.

Thank you in advance.

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/63074

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.