A manager buys three shares of stock today, and then sells one of those shares each year for the next three years. His actions and the price history of the stock are summarized below. The stock pays no dividends.

$\backslash$table$[[$Time$,$Price,Action$],[0,$$$90,$Buy $3$ shares,$],[1,100,$Sell $1$ share,$],[2,100,$Sell $1$ share,$],[3,100,$Sell $1$ share,$]]$

Required:

a$.$ Calculate the time$-$weighted geometric average return on this portfolio. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Geometric average return

b$.$ Calculate the time$-$weighted arithmetic average return on this portfolio. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Arithmetic average return