Question $9$

Share $A$ is a platinum mining house share, relatively risky with a variance of $0\mathrm{.}38.$ It has a covariance of $0\mathrm{.}16$ with $B,$ a financial share, which has a variance of $0\mathrm{.}35.$ B has a covariance with $C$ of $0\mathrm{.}27,$ a commodities$-$based unit trust with a standard deviation of $0\mathrm{.}45.$ A and $C$ have a correlation coefficient of $0\mathrm{.}439.$

You propose the following portfolio: $\frac{1}{5}$ in $A,20\%$ in B$,$ and $4/10$ in C$,$ with the remainder being invested in government securities at the risk$-$free rate. Assume that the rate of return on the shares are as follows: $A=16\%,B=12\%,C=15\%,$ Risk Free $=5\%.$

The covariance between the above risky portfolio and a portfolio with the following proportions: $A=0\mathrm{.}35,B=0\mathrm{.}25,C=0\mathrm{.}45$ is closest to$?$

A$.0\mathrm{.}1791$

B$.0\mathrm{.}2660$

C$.0\mathrm{.}2132$

D$.0\mathrm{.}9944$

E$.$ None of the above