You are bullish about gold and have $1,000,000 to support a bullish bet. The current price of gold is $1,750 per ounce.

One way to make the bet is to buy gold futures. Each gold futures contract corresponds to 100 ounces of gold. The initial margin is $9,000 per contract. The gold futures contract maturing in six months is quoted at $1,767 per ounce.

An alternative way is to purchase gold calls maturing in six months. The strike prices available are $1,500, $1750, and $2,000. The implied volatility in all these strikes is 15% per year. The risk-free rate is 2% per year (continuously compounded), and gold has a storage cost of 0.5% per year (continuously compounded).

i) Suppose you use your capital to enter a long position in gold futures maturing in six months. By how much (in %) does the value of your portfolio increase if the gold spot price increases by 2% (TWO percent) right after you enter the long position?

ii) Which of the three calls maturing in six months provides the greatest leverage? Suppose you use your capital to buy such call. By how much (in %) does the value of your portfolio increase if the gold spot price increases by 2% (TWO percent) right after you purchase the calls? Assume the implied volatility of the purchased calls does not change.