Question
You know that as the number of stocks (i.e., the number of different companies) in an equally weighted portfolio is increased, with each additional stock
You know that as the number of stocks (i.e., the number of different companies) in an equally weighted portfolio is increased, with each additional stock (i.e., company) chosen at random, the unique risk of the portfolio decreases. You also know that a typical stock has a beta of 1. Assume that the market's returns have a standard deviation of 20% and that a typical stock's returns have a standard deviation of 40% and a correlation coefficient with market returns of +0.5. All else being the same, what must be true for the returns of such a portfolio as the number of stocks in it increases? (a) Its standard deviation increases, and its correlation with the market decreases (b) Its standard deviation decreases, and its correlation with the market decreases (c) Its standard deviation stays the same, and its correlation with the market increases (d) Its standard deviation decreases, and its correlation with the market increases
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