The Z-Tech Corporation (probably owned by Elon Musk) has found a way to turn lead into gold. The company’s pre-hedge profit can be approximated by: 2S(t) – 2,017, where S(t) is the price of gold at time t. The current spot price of gold is 1,045 per oz. The continuously compounded risk-free rate is 6%. Two possible hedging strategies are available to the company to reduce their risk to the price of gold six months from today.
Strategy 1 – Take the short side of two six-month forward contracts, with a forward price of 1,070 per oz.
Strategy 2 – Buy two six-month put options on gold, with a strike price of 1,070 per oz. The price of each put option is 45.611.
1. If the company decides NOT to hedge, what price of gold, per oz., six months from today would result in a profit of 140?
2. If hedging Strategy 1 is used, the company’s after-hedge profit would be:
3. If hedging Strategy 2 is used and the company’s after-hedge profit is 140, what must the price of gold per oz. be after six months?
4. If hedging Strategy 2 is used, what is the company’s minimum after-hedge profit?