Neha Singh, a BBA graduate of UTSC now working at Alberta Investment Management

Corporation $($AIMCo$),$ manages a $$200$ million Canadian equity fund that tracks the

performance of the S&P$/$TSX $60$ index. Neha wants to ensure that the value of the

portfolio doesn't drop by more than $5\%$ within the next six months. The portfolio has a

volatility of $32\%$ and dividend yield of $1\mathrm{.}8\%$ p$.$a$.,$ mirroring the S&P$/$TSX $60$ index. The

risk$-$free rate is currently at $4\mathrm{.}25\%$ p$.$a$..$

a$.$ Please help Neha figure out how much she should sell her holdings in order to

execute a synthetic$-$put$-$option insurance. Suppose the market drops by $2\mathrm{.}2\%$

immediately afterwards. How should Neha adjust her portfolio?

b$.$ Suppose instead Neha wants to use $9-$month S&P$/$TSX $60$ futures to execute the

synthetic hedge. How many contracts does she need to short? How should she

adjust the futures position after the $2\mathrm{.}2\%$ decrease? $($The current level of

$S$&$\frac{P}{T}Sx60$ is $1,400,$ and the index futures contract is $250$ times the index level.$)$