An investor buys three shares of XYZ at the beginning of $2021,$ buys another two shares at the beginning of $2022,$ sells one share at the beginning of $2023,$ and sells all four remaining shares at the beginning of $2024.$ Required: a$.$ What are the arithmetic and geometric average time$-$weighted rates of return for the investor? Suppose the portfolio can be purchased for the amount you found in $($a$).$ What will the expected rate of return on the portfolio be$?$