To capitalize on your expectation of a 10% gold price appreciation, you consider buying futures or option contracts to speculate. The spot price of gold is $400. Near-delivery futures contracts are quoted at $410 per ounce with a margin of $1,000 per contract of 100 ounces. Call options on gold are quoted with the same delivery date. A call with an exercise price of $400 costs $20 per ounce. The rate of return on your speculation will be the return on your invested capital, which is the initial margin for futures and the option premium for options.

a. Based on your expectation of a 10% rise in gold price, what is your expected return at maturity on futures contracts?

b. Based on your expectation of a 10% rise in gold price, what is your expected return at maturity on option contracts? 

c. Simulate the return of the two investments for various movements in the price of gold.