Question

LUVE produces bracelets. Each band generates $460 in revenue and requires one
ounce of gold as an input. LUVE plans to produce and sell one widget in exactly
one year. The c.c. risk-free rate is zero percent.

1. LUVE is considering hedging their gold exposure with a long forward contract.
   The one-year forward price of gold is $420 per ounce. If the spot price of gold is $450
   per ounce in one year, what is LUVE's hedged profit?

The answer I got was 30

2. LUVE is considering hedging their gold exposure with a call option. The premium on a one-year call option on gold with a strike of $420 per ounce is $8.77. If the
price of gold is $450 per ounce in one year, what is LUVE’s hedged profit?

I got 21.23

3. The call option hedge outperforms the long forward hedge (in terms of profits) whenever the gold price is below S*. What value of S* makes this statement true?

I got -38.77

Answer 1

1. LUVE will be able to buy gold at $420 per ounce using long forward contract. and sell at $460

So, the hedged profit = profit from forward contract + profit from Selling

= ($450-$420) + ($460-$450) =$30+ $10 = $40

2. If gold exposure is hedged with a call option, and the price of gold after one year is $450 per ounce, the gold can be bought at $420 by exercising the call option

Hedged profit = profit from options contract + profit from Selling

= ($450-$420 -$8.77) + ($460-$450) =$21.33+ $10 = $31.33

3. Call option gives the benefit as compared to futures when the price of gold decreases below ($420-$8.77) = $411.23

Let Spot price after one year be $411.23

From forward contract , hedged profit = profit from forward contract + profit from Selling

= ($411.23-$420) + ($460-$411.23) = - $8.77+ $48.77 = $40

From Call options contract , hedged profit = profit from options contract which will not be exercised + profit from Selling

= -$8.77 + ($460-$411.23) = - $8.77+ $48.77 = $40

If price is below $411.23 say $410

From forward contract , hedged profit = profit from forward contract + profit from Selling

= ($410-$420) + ($460-$410) = - $10+ $50 = $40

From Call options contract , hedged profit = profit from options contract which will not be exercised + profit from Selling

= -$8.77 + ($460-$410) = - $8.77+ $50 = $41.23

So, call options hedge outperform long forward hedge whenever gold price is below $411.23