A trader owns 40,000 units of widgets and decides to hedge these using futures contracts on grommets. Each futures contract is on 500 units (of grommets). The spot price of widgets is $20, and the standard deviation of the change in this price over the life of the hedge is estimated as $1.50. The grommet future price is $55, and the standard deviation of the grommet futures price is $1.10. The correlation between widget price changes and grommet futures price changes is -0.8.

(a) What is the minimum variance hedge ratio?

(b) Should the trader take a long or short position? (

c) What is the optimal number of contracts to take out? Hint: dont forget that this must be a whole number