Arithmetic average and geometric average are different in that latter accounts for losses more realistically than the former. Consider the following example to see the uniqueness of geometric average. You have the following rates of return for a risky portfolio for several recent years:

$2008$: $100\%$

$2009$: $100\%$

$2010$: $100\%$

$2011$: $-100\%$

If you invested $$100$ at the beginning of $2008,$ your investment at the end of $2011$ would be worth $\_\_\_\_\_\_\_\_\_\_\_.$

$$100$

$$300$

$$0$

$$800$