$1$c$)$ Suppose that you have identified two quoted shares $($Apple and Orange$)$ which you believe will exhibit negative correlation in their possible returns over the next year as follows:

Scenario Probability Apple $\%$ Orange $\%$

Contraction $30\%-8\%5\%$

No growth $40\%5\%7\%$

Expansion $30\%17\%-7\%$

Apple $\%$ Orange $\%$

Expected Return $4\mathrm{.}7\%2\mathrm{.}2\%$

Standard Deviation $9\mathrm{.}7\%6\mathrm{.}1\%$

Calculate the covariance and correlation between Apple and Orange shares.

$(7$ marks$)$