An investor funds $$5$ million initially for a $4-$year program. The holding period return for each year is $-4\%,5\%,6\%$ and $9\%,$ respectively. At the end of the second year, they add an addtional $0\mathrm{.}5$ million.

Time $01234$

Fund to nvestment $($$ millions$)500\mathrm{.}50$

HPR $(\%)0\%-4\%5\%6\%9\%$

a$.$Compute the arithmetic return $($simple average$)$

b$.$Compute the geometrics return $($time weighted average$)$

c$.$Compute the internal rate of return $($dollar weighted average$)$

d$.$Compute the standard deviation for this $4-$year investment

e$.$Assume the risk free rate is constant of $0\mathrm{.}5\%$ in those $4$ years, what's the sharpe ratio of this investment using simple average return?