A trader owns $55,000$ units of a particular asset and decides to hedge the value of her

position with futures contracts on another related asset. Each futures contract is on $5,000$

units. The spot price of the asset that is owned is $$28$ and the standard deviation of the

change in this price over the life of the hedge is estimated to be $$0\mathrm{.}43.$ The futures price of

the related asset is $$27$ and the standard deviation of the change in this over the life of the

hedge is $$0\mathrm{.}40.$ The coefficient of correlation between the spot price change and futures

price change is $0\mathrm{.}95.$

$($a$)$ What is the minimum variance hedge ratio?

$($b$)$ Should the hedger take a long or short futures position?

$($c$)$ What is the optimal number of futures contracts when issues associated with daily

settlement are not considered?

$($d$)$ How can the daily settlement of futures contracts be taken into account?