Choosing a CAPM Benchmark for a Cross-Listed Sector Portfolio
Summary
The discussion explains how to apply CAPM when a portfolio contains technology stocks traded on different US exchanges. Exchange membership alone does not determine the appropriate market benchmark: the index should reflect the systematic risk relevant to the investor and the stocks being studied. Suggested choices include a technology-sector index for US technology stocks, a broad global index for a global investor, or NASDAQ when the intended comparison is with other technology stocks.
After selecting a benchmark, estimate each stock’s beta against it, then evaluate portfolio expected return, risk, and beta under candidate weights. The efficient frontier can be constructed from those portfolio outcomes, and a tangency portfolio can be selected using the Sharpe ratio. The answers offer conceptual guidance rather than data, calculations, or a worked example. The choice of index depends on the investment universe and the meaning of systematic risk; the discussion does not establish one universally correct benchmark or detail how to estimate expected returns and covariances.
Key ideas
- Choose a CAPM benchmark that represents the systematic risk relevant to the portfolio and investor.
- A sector index can be more suitable than an exchange index for stocks concentrated in one sector.
- Estimate each stock’s beta relative to the selected benchmark.
- Compare candidate portfolio weights using expected return and risk to form an efficient frontier.
- The Sharpe ratio can help identify a tangency portfolio.
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Full text
# How to apply the CAPM to 6 stocks from different markets? # 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? ## Answer by user18663 (score 1) https://quant.stackexchange.com/a/27731 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. ## Answer by Tim (score 1) https://quant.stackexchange.com/a/27740 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. ## Answer by Rehan (score 1) https://quant.stackexchange.com/a/31972 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.
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