In terms of securities (stock) - how to

(1) Calculate the mean, variance, and the standard deviation of a securitys annual rate of return.

(2) Calculate the correlation coefficient between every possible pair of securities annual rates of return.

(3) Choose percentages of the initial investment that one may want to allocate amongst the five securities (weights in the portfolio).

(a) Create embedded formulae which generate statistical properties of the portfolio upon insertion of the weights.

(b) Observe the mean, the standard deviation, and the CV of the annual rate of return of the portfolio.

(4) Find the combination of the weights that minimizes CV of the portfolio.

(a) How does the CV of the optimal portfolio compare with the CVs of its constituents?

(b) What is the expected rate of return and standard deviation of the rate of return of the portfolio?

(5) Choose different values within the range of the standard deviation of the portfolio, and for each chosen value, locate the corresponding point on the efficient frontier by finding the weights that maximize the expected rate of return of the portfolio.

(a) Subsequently, construct the efficient frontier of your portfolio.

(6) Assume that one initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal.

(a) What is the distribution of the return of the portfolio 20 years after its formation?

(b) how to create the graph of the distribution of the return of the portfolio