Question $1(10$ Marks$)$

The West Texas Intermediate $($WTI$)$ Light Sweet Crude Oil futures contract, as one of the world's most liquid energy futures contract, provides market participants with direct exposure to the crude oil market.

On $15$ February $2006$ a speculator who expects the crude oil price to fall over the short term sells ten June $2006$ WTI futures contracts at a price of USD $$62\mathrm{.}17$ per barrel. The speculator closes out the futures position on $1$ March $2006$ at a price of USD $$66\mathrm{.}36$ per barrel. Each contract is written on $1,000$ barrels of crude oil $("$contract size"$).$ The initial and maintenance margins are USD $$5\mathrm{.}00$ and USD $$3\mathrm{.}00$ per barrel, respectively.

The daily settlement prices for the June $2006$ WTI futures contract during the holding period are shown in the table below. Note futures contracts are traded only on business days.

Required:

$($a$)$ At the time the futures position is established on $15$ February $2006,$ what is the minimum price movement on a per barrel basis that would generate a margin call? Report your answer in $2$ decimal places $(dps).$

$(2$ marks$)$

$($b$)$ Construct a table as below to illustrate the daily marking$-$to$-$market $($and final settlement$)$ of the speculator's overall futures position for the ten contracts. Assume no withdrawals of any money deposited to the "Initial and Margin account balance". If there is a shortfall in the "Initial and Margin account balance" at the end of any trading day, the speculator will receive the margin call soon afterwards $($i$.$e$.,$ within the same day$),$ and is able to top up the margin account balance back to initial margin level by the start of the next trading day as instructed.

$(6$ marks$)$

$\backslash$table$[[$Date$,\backslash$table$[[$Trade$],[$Price$]],\backslash$table$[[$Settlement$],[$or Futures$],[$Price$]],\backslash$table$[[$Daily$],[$gain$/$loss$]],\backslash$table$[[$Cumulative$],[$gain$/$loss$]],\backslash$table$[[$Margin$],[$account$],[$balance$]],\backslash$table$[[$Margin$],[$call$]]],[,($$$/$barrel$),($$$/$barrel$),($$$),($$$),($$$),($$$)],[2006-02-15,62\mathrm{.}17,62\mathrm{.}17,0,0,?,?],[2006-02-16,,663\mathrm{.}04\_,?,?,?,$:$\text{'}],[2006-02-17,,63\mathrm{.}92,?,?,?,?],[2006-02-21,,64\mathrm{.}99,?,?,?,?],[2006-02-22,,\backslash$bar $(64\mathrm{.}60),?,?,?,?],[2006-02-23,,65\mathrm{.}13,?,?,?,?],[2006-02-24,,66\mathrm{.}30\_,?,?,?,?],[2006-02-27,,65\mathrm{.}28,?,?,?,?],[2006-02-28,,65\mathrm{.}91,?,?,?,?],[2006-03-01,666\mathrm{.}36\_,66\mathrm{.}36,?,?,?,?],[,,$Profit$/$loss$,,?,\backslash$bar $(?),?]]$

Note: the format of the table is identical to Table $2\mathrm{.}1$ on page $46$ of the prescribed textbook.

$($c$)$ What is the overall profit$/$loss of the speculator? Decompose the overall profit$/$loss into two components: $($i$)$ total margin calls, and $($ii$)$ the change in the margin account balance.

$(2$ marks$)$