Dear all,
I hope that you all are well preparing for FRM exam now.
I have a couple of questions regarding options on futures.
On pg.44, Schweser Book3 2014, there is sample quesiton as below.
The AUG specialty Fund(AUG) currently holds gold in its inventory. However, AUG would like to minimize proce risk over the next six months. Assume the following gold price:
Cash price: $1,200
6month futures price: $1,300
6month put on futures with strike price of $1,300: $60
Now assume that in six months, the cash price of gold has fallen to $1,100, the futures price has fallen to $1,200, and the put option price is $100. Calculate the profit/loss on a per ounce basis if AUG:

Does not hedge its cash position.

Use futures to hedge its cash position.

Use long put on futures to hedge its cash position.
From my knowledge,
 Unhedged Cash Position is $100
2.The short futures contract indicates that underlying asset is a gold and they have an obligation to deliver the gold at $1,300 in 6 months. The fallen futures price of $1,200 is not relevant here and the spot price of gold in 6 month is $1,100. Thus, payoff from the short futures is ($1,300  $1,100)= $200
 Long puts on futures means that underlying asset is a futures contract, not a gold itself and the put option pice of $100 in 6 month is not relevant here. From the graph, BEP is $1,240 and the fallen futures price is $1,200. Thus, the profit would be $40.
but from the answers, they are calculated just the difference between current price and the price in 6 months.

Unhedged profit/loss = $100

Short futures prfit/loss = $100. Thus, net profit/loss= $100 + $100 =$0

Long put profit/loss = $100  $60 = $40. Thus, net profit/loss = $100 + $40 = $60
Where are the misunderstandings?
Please correct me !!!
Thank you very much
Brian