Question

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?

Answer 1

Solution :

Profit = 2S(t) – 2,017

Question 1 .  company decides NOT to hedge, Let price be X that will lead to $140 profit

So, 140 = 2 * X -2017

2X = 2017+140 = 2147

X = 2147/2 = 1073.5

Question 2 . Hedging strategy 1 is used means they are selling at 1070 by forward contracts

Profit = 2 * 1070 -2017 = 2140-2017 = 123

Question 3 .

Buying a put option at 1070, the company is paying 45.611

and taking int the consideration of interest rate this value should be worth = 45.611 *Exp (0.06*0.5) = 47

So effective selling price = X-47

Now using profit equation

140 = 2 * (X -47) - 2017

140 = 2x - 94 - 2017

2X= 2251

X = 1125.5

Another possible answer

Let's say the price goes below 1070 and company gains due to put option is exercised

cost of option = 47 , effective selling price = 1070 - 47 = 1023

Now, let say price goes below 1023 and company gains profit

Profit = (1023 ) * 2 - 2017 = 29

NOw profit = 140 , 29 profit will come when price is 1023

Now 140 -29 = 111, will come from share price reduction

(1023 - X ) * 2 = 111

1023 - x = 55.5

X = 1023-55.5 = 967.5

Question 4. Minimum profit will happen if share price remains at 1070 because the company will be losing full premium of 47. Price above this point will be good and price below this will make put option exercisable

So

Minimum profit

= (1070 - 47 )* 2 - 2017 = 1023*2 - 2017 = 2046 - 2017 = 29