A Mutual Fund $($AMF$)$ has $$100m$ in assets and $100$ million shares outstanding. AMF paid out dividend of $$4m$ and had a price depreciation of $5\%$ during the year. Assume no capital gain distribubion. The $12b-1$ fee is $0\mathrm{.}5\%$ and is deducted from the portfolio assets at year$-$end.

Calculate AMF's NAV at the end of the year and the rate of return.

NAV$\_1$ is $1\mathrm{.}0305$ ; and Return is $+1\mathrm{.}475\%$

NAV$\_1$ is $0\mathrm{.}94525$ ; and Return is $+1\mathrm{.}475\%$

NAV$\_1$ is $1\mathrm{.}0305$ ; and Return is $-1\mathrm{.}475\%$

NAV$\_1$ is $0\mathrm{.}94525$ ; and Return is $-1\mathrm{.}475\%$

Question $4$

Calculate the correlation coefficient between $x$ and $Y.$

$\backslash$table$[[$State$,$Probability,Return X$,$Return Y$],[$Crisis$,0\mathrm{.}1,10\%,-10\%$