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Show that the beta of a portfolio is the weighted average of the beta's of the...

Show that the beta of a portfolio is the weighted average of the beta's of the portfolio's assets. Hint: Cov(aX+Y,Z)=aCox(X,Z)+Cov(Y,Z)

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Answer #1

Beta of a portfolio is the weighted average of the beta's of the portfolio's assets.

To determine the beta of the portfolio, you can follow these four steps:

  1. Add up the value (number of shares x share price) of each stock you own and your entire portfolio.
  2. Based on these values, determine how much you have of each stock as a percentage of the overall portfolio.
  3. Multiply those percentage figures by the appropriate beta for each stock. (Thus, if Amazon comprises 25% of your portfolio and has a beta of 1.43, it has a weighted beta of 0.3575.)
  4. Add up the weighted beta figures.
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