a$)$ The current price of gold is $$300$ per ounce. Carrying costs in total are $0\mathrm{.}5\%($not including interest$)$ of the gold value payable in $6$ months time. If the interest rate is $8\%,$ is there an arbitrage opportunity if the gold futures price for delivery in six months is $$310$ per ounce?

b$)$ If an arbitrage opportunity exists, explain how you would conduct it and calculate the arbitrage profit.

c$)$ Why is it not possible in reality to perfectly hedge a portfolio using options and$/$or futures Instruments?