Richards & Co. Analysts has recently published a study claiming that the benefits to diversification are constant. In other words, adding one more stock to a three-stock portfolio will have the same impact as adding one more stock to a 500-stock portfolio. You are not convinced and you decide to evaluate the claim.
a. Assume that all the stocks have the same standard deviation, 10 percent, and all are independent (correlation equals 0.0). Create equally weighted portfolios of 1 to 10 stocks and calculate the standard deviation for each portfolio. Graph the portfolio standard deviation as a function of the number of stocks. Based on the results of your analysis, evaluate the Richard & Co. Analysts’ claim.
b. As the number of firms increases, what do you expect will happen to the risk of the portfolio? Can the risk of the portfolio come close to zero?