For Question $29$ to Question $46,$ refer to the information below which was partially captured from FTNN at some point in time and partially hypothesized:

HSI index level today $($t$=0)$

$22688\mathrm{.}90$

Forward price $($T$=1$ month$)*$

$22759$

Forward Contract Size$**$

$1$

Spot annualized $1-$month interest rate

$2\mathrm{.}94\%$ p$.$a$.($continuously compounded$)$

Call option Premium $($Strike $=23000)$

$410$

Put option Premium $($Strike $=23000)$

$719$

Dividend yield

$0\%$

Expected HSI index level $1$ months later$***$

$22900$

$*$assume the forward price is the same as futures price quoted from the exchange

$**$assume that the forward has a contract size of $1,$ which is different from the futures' contract size

$***$ Expected HSI index level is just your expectation, the actual HSI index level could be higher or lower than this

A$.$ What is your expected profit $1$ month later if you have taken a long position on the stock at t$=0?$

B$.$ What is your expected profit $1$ month later if you have taken a short position on the stock at t$=0?$

$*$Please leave $2$ d$.$p$.$ for the answer.

C$.$ What is your expected payoff $1$ month later if you have taken a long position on the forward at t$=0?$

$*$Please leave $2$ d$.$p$.$ for the answer.

D$.$ What is your expected profit $1$ month later if you have taken a short position on the forward at t$=0?$

$*$Please leave $2$ d$.$p$.$ for the answer.