Use the rate$-$of$-$return data for the stock ad bond funds presented in spreadsheet $6\mathrm{.}1,$ but now assume that the probability of each scenario is as follows: severe recession: $0\mathrm{.}10$; mild recession: $0\mathrm{.}20$; normal growth: $0\mathrm{.}35$; boom: $0\mathrm{.}35$

$($a$)$ would you expect the variance of the stock fund to be more than, less than, or equal to the values computed in spreadsheet $6\mathrm{.}2?$ Why?

$($b$)$ calculate the new value of variance for the stock fund using a format similar to spreadsheet $6\mathrm{.}2.$ Confirm your intuition from part $($a$).$

$($c$)$ calculate the new value of the covariance between the stock and bond funds using a format similar to spreadsheet $6\mathrm{.}4.$ Explain intuitively why the absolute value of the covariance has changed.