$(6$ Points$)$ The following table shows per$-$share price $(P_t)$ and dividend $(D_t)$ dynamics of

three stocks: A$,$ B$,$ and C$.$ The last row reports the number of outstanding shares of each

stock.

$($a$)$ Suppose that your investment strategy is to hold a value$-$weighted portfolio of A$,$

B$,$ and C at each point in time. For simplicity, we assume that shares are perfectly

divisible $($i$.$e$.,$ you can buy or sell a fraction of a share$).$ What is the net return on

your portfolio at time $t=1?$

$($b$)$ What is the net return on your portfolio at time $t=2($i$.$e$.,$ return from $t=1$ to

$t=2$

$($c$)$ Suppose that initially $($at time $t=0)$ you invested $$1,000.$ Suppose that your

dynamic strategy is to consume all dividends that you receive and to reinvest capital

gains $($in the value$-$weighted portfolio that you constructed earlier$).$ How much

money is in your investment account at the end of period $2($after you receive $t=2-$

dividends$)?$