Consider the following fund $($answer all questions$)$:

A investor funds $5$ millions initially for a $4-$year program. The Holding period return for each year is $-4\%,5\%,6\%$ and $9\%,$ correspondingly. At the end of second year, he$/$she add addtional $0\mathrm{.}5$ millions.

Time

$0$

$1$

$2$

$3$

$4$

Fund to nvestment $($$ millions$)$

$5$

$0$

$0\mathrm{.}5$

$0$

HPR $(\%)$

$-4\%$

$5\%$

$6\%$

$9\%$

Compute the Arithmetic return $($simple average$)$:

a$.3\mathrm{.}88\%$

b$.4\mathrm{.}00\%$

c$.4\mathrm{.}05\%$

d$.4\mathrm{.}12\%$

QUESTION $2$

Compute the Geometrics return $($time weighted average$)$:

a$.3\mathrm{.}88\%$

b$.4\mathrm{.}00\%$

c$.4\mathrm{.}05\%$

d$.4\mathrm{.}12\%$

QUESTION $3$

Compute the Internal rate of return $($dollar weighted average$)$:

a$.3\mathrm{.}88\%$

b$.4\mathrm{.}00\%$

c$.4\mathrm{.}05\%$

d$.4\mathrm{.}12\%$

QUESTION $4$

Compute the standard deviation for this $4-$year investment:

$($hint: this is time$-$series analysis $--$ evenly distributed probability for each period$)$

a$.0\mathrm{.}31\%$

b$.4\mathrm{.}00\%$

c$.4\mathrm{.}85\%$

d$.2\mathrm{.}16\%$

QUESTION $5$

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?

a$.11\mathrm{.}17$

b$.1\mathrm{.}67$

c$.0\mathrm{.}88$

d$.0\mathrm{.}72$