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Unformatted text preview: the same size, and you are adding up more (N) of them, but each one is divided by N-squared. So as N approaches infinity, the second term gets small--eventually small enough to ignore. .. An even funnier thing happens if we consider the variance of a portfolio made up of a large number of stocks (N large), for which the average beta happens to be one. • Then the first term is simply sigma-squared-m, and the second term is negligible: the variance of the portfolio is the variance of the "market" Conclusion: If an investor is doing his or her job--trying to get to a portfolio that has the minimum risk for a given expected return--then "idiosyncratic" risk can be diversified away: by putting all your eggs into many baskets, you essentially eliminate any idiosyncratic risk factors from your portfolio. Hence a security's "riskiness"--from the point of view of its impact on the overall riskiness of your portfolio as a whole--is summarized by its beta. .....
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- Fall '10