Suppose that the standard deviation of returns from a typical share is about $0\mathrm{.}47($or $47\%)$ a year. The correlation between the returns of each pair of shares is about $0\mathrm{.}4.$

a$.$ Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in $2$ shares, $3$ shares, and so on$,$ up to $10$ shares. $($Use decimal values, not percents, in your calculations. Do not round intermediate calculations. Round the "Variance" answers to $6$ decimal places. Round the "Standard Deviation" answers to $3$ decimal places.$)$

b$.$ How large is the underlying market variance that cannot be diversified away? $($Do not round intermediate calculations. Round your answer to $3$ decimal places.$)$

c$.$ Now assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in $2$ shares, $3$ shares, and so on$,$ up to $10$ shares. $($Use decimal values, not percents, in your calculations. Do not round intermediate calculations. Round the "Variance" answers to $6$ decimal places. Round the "Standard Deviation" answers to $3$ decimal places.$)$