$($a$)$ The S&P$/$ASX $200$ Index $($ie the physical market$)$ is trading at $7315\mathrm{.}202.$ Price the

September SPI$200$ futures contract, which has $86$ days to expiry, when the continuously compounded risk free rate of return is $3\mathrm{.}5850\%,$ the dividend yield on the S&P$/$ASX $200$ Index is $4\mathrm{.}15\%$pa$,$ and custody costs $($ie the cost of holding

physical shares$)$ are $0\mathrm{.}22\%$pa $(1$ mark$)$

$($b$)$ How much profit or loss would you make if you went long $6090-$day bank bill futures contracts at $96\mathrm{.}35$ and closed them out $27$ days later at $96\mathrm{.}08$ when the continuously compounded risk free rate is $3\mathrm{.}5850\%?$

$(2$ marks$)$

$($c$)$ How much profit or loss would you make if you went short $1320-$year bond futures contracts at $94\mathrm{.}795$ and closed them out $45$ days later at $94\mathrm{.}745$ when the continuously compounded risk free rate is $3\mathrm{.}5850\%?$

$(2$ marks$)$

$($d$)$ A trader plans to make a profit from a yield spread flattening trade in bond futures, whereby the trader goes long $1293-$year bond futures contracts at $95\mathrm{.}025$ and correspondingly goes short $855-$year bond futures contracts at $95\mathrm{.}265.$ Seven days later, after the cash rate has been reduced to $3\mathrm{.}45\%$pa$,$ the trader unwinds the trades in the $3-$year bond futures contract at $94\mathrm{.}975$ and unwinds the trades in the $5-$year bond futures contracts at $95\mathrm{.}315.$ What was the trader$$s profit or loss on this trade? $(4$ marks$)$

$($e$)$ In question $1$d$)$ the spread trade involved $1293-$year bond futures contracts against $855-$year bond futures contracts, a ratio of $1\mathrm{.}52$:$1$ to be volatility hedged. What does it mean to volatility hedge? $(1$ mark$)$

$($f$)$ Explain, in detail, the process to properly determine the appropriate volatility hedge? $(1$ mark$)$