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7. (30 points) Suppose there are 500 stocks, all of which have a standard deviation of 0.30, and a correlation with each other of 0.4. mold (a) Calculate the variance of an equally-weighted portfolio of n such stocks, for n = 2,4, 10, 20, 50, 100, 500 may on Graph your results. (b) Does the variance of this portfolio tend to zero as n (that is, if there were many more than 500 stocks)? If so, explain why. If not, what does it converge to then? (c) Repeat the above calculations for the case in which the stocks have a correlation of 0.1. Compare the results from sections (a) and (b). 8. (40 points) Using the internet to find return data for the Energy, Financial, Health Care, Industrial, Materials, Utilities, Consumer Staples, and Consumer Discretionary sectors of the S&P index (use annual data starting 1945 to end of 2018). (a) Estimate the expected return for each of these indexes. (b) Since this is an estimate, you know there is some error in your estimation. What is the standard error of your estimate for the expected return of each stock? Estimate the standard deviation of each of these indexes, and the correlations for each of these indexes. 7. (30 points) Suppose there are 500 stocks, all of which have a standard deviation of 0.30, and a correlation with each other of 0.4. mold (a) Calculate the variance of an equally-weighted portfolio of n such stocks, for n = 2,4, 10, 20, 50, 100, 500 may on Graph your results. (b) Does the variance of this portfolio tend to zero as n (that is, if there were many more than 500 stocks)? If so, explain why. If not, what does it converge to then? (c) Repeat the above calculations for the case in which the stocks have a correlation of 0.1. Compare the results from sections (a) and (b). 8. (40 points) Using the internet to find return data for the Energy, Financial, Health Care, Industrial, Materials, Utilities, Consumer Staples, and Consumer Discretionary sectors of the S&P index (use annual data starting 1945 to end of 2018). (a) Estimate the expected return for each of these indexes. (b) Since this is an estimate, you know there is some error in your estimation. What is the standard error of your estimate for the expected return of each stock? Estimate the standard deviation of each of these indexes, and the correlations for each of these indexes