# How to apply the CAPM to 6 stocks from different markets?

I would like to apply the capital asset pricing model (CAPM) for selecting proportions of 6 different stocks. In introductory books, the CAPM model assumes that there is one market index (e.g. the S&P 500) the individual stocks are regressed against.

However, suppose the 6 stocks are from different markets (NASDAQ, NYSE, AMEX) but the same market sector (information technology). How do I determine the efficient frontier and tangency portfolio?

• From the title I assumed you were talking about 6 different countries! The distinction between Nyse, Nasdaq, Amex is not very significant. These are all US stocks and can be modeled with a single US Equity Model (CAPM or multifactor model). Jun 21, 2016 at 15:02
• The closed form expression for portfolio variance on any portfolio with more than 3 assets is overly complicated. You need to compute the covariance matrix, which can be simplified to the variance of the sum of securities' weights multiplied by logarithmic returns: $\sigma(r_p)^2 = \sigma (\Sigma_i^j w_i r_i)^2$. Select securities weightings which optimizes the efficient frontier (usually the Sharpe ratio). Mar 22, 2017 at 0:04

## 3 Answers

As the six different stocks belongs to different indices, first you need to calculate separate betas for each of them. Now considering that the the six different stocks belong to same portfolio, you need to calculate portfolio beta, standard deviation and expected return at portfolio level by assigning weights to each of the stock.

In this way you can have different portfolio by assigning different weights to each of them and then you can have the efficient frontier graph in order to have the optimum portfolio. You can also find out the optimum portfolio through finding of the sharpe ratio for each of the portfolio.

• I think that this is incorrect. Betas from different indices are not comparable and the aggregate beta on the portfolio level as described above is therefore meaningless. Sep 20, 2016 at 7:28

Depends on what you want to measure. Personally, as these are all tech stocks, I would go with the NASDAQ. So then you have the betas relative to other tech stocks. However, if you are a truly global investor then you could best proxy the market by MSCI world.

The market index in the definition of CAPM should be viewed in slightly broader terms, in that, the right choice of the market instrument may not be a physical market/exchange in itself. CAPM basically allows you to differentiate between the systematic risk and the idiosyncratic risk in your portfolio. Hence the systematic risk is best reflected in that index which has the maximum intersection with all of the constituent stocks

In your case, since all of them are US IT stocks, the right choice of a market index would be an index that specifically tracks that sector - something like the MSCI US Information Technology Index (MXUS0IT Index on Bloomberg), which would reflect the systematic risk, and then, you can have a more accurate measure of the alpha, and hence the portfolio weights by drawing from CAPM.