# Part.1 Book 3 questions regarding Options on Futures

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

6-month futures price: \$1,300

6-month 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:

1. Does not hedge its cash position.

2. Use futures to hedge its cash position.

3. Use long put on futures to hedge its cash position.

From my knowledge,

1. 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

1. 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.

1. Unhedged profit/loss = -\$100

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

3. Long put profit/loss = \$100 - \$60 = \$40. Thus, net profit/loss = -\$100 + \$40 = -\$60

Where are the misunderstandings?

Thank you very much

Brian

For part 3:

If you liquidate all positions after 6 months then you have a \$100 loss on gold and a \$40 gain on the put.

For Part 2:

Assume you take an offsetting (long) position on a futures contact at the end of 6 months. You will have a gain of \$100. You will also have a \$100 loss on gold in you inventory.

Thanks Dwheats, but could you explain more?

I still could’t get it…

Thanks again

Is this a put option on a futures contract, or a put option on one ounce of gold? It sounds like the latter, but you describe it as the former. If it’s really an option on a futures contract, I’d assume that the futures contract starts 6 months from today, and expires 6 months thereafter, but that’s not explicit here.

(I’m basing the answer to #3 on the idea that it’s an option on gold, not an option on a futures contract.)

After one month the price of gold has dropped from \$1,200/oz. to \$1,100/oz. They’ve lost \$100/oz.

Because they give you the new 6-month futures price, it appears that they expect you to roll over your futures position for another 6 months. So in 6 months you sell your gold for \$1,300/oz. for a profit of \$100/oz. and buy it in the spot market at \$1,100/oz. In another 6 months you sell it for \$1,200/oz., for another profit of \$100/oz. In total, you have a gain of \$200/oz. I have no idea what their calculation means.

Again, because they give you the new 6-month put option strike and price, it appears that they expect you to continue the hedge for another 6 months. So in 6 months you sell your gold for \$1,300/oz. for a profit of \$100/oz., less the \$60/oz. option premium, for a net of \$40/oz. You’ll buy it back at \$1,100/oz. In another 6 months you sell it for \$1,200/oz. (I assume that that’s the strike price; you weren’t clear on that one) for a profit of \$100/oz., less the \$100/oz. option premium, for a net of zero. In total, you have a gain of \$40/oz. Again, I have no idea what their calculation means.

(Note: if the put option is really on a 6-month futures contract starting 6 months from today, the profit ends up being \$40/oz. as well: \$1,300/oz. (futures price) – \$1,200/oz. (spot price) – \$60/oz. (option premium).)

After going through the book, I think the answers are correct. It asks you to hedge the “cash position” which actually means that they are not using the gold from inventory. (Using ETFs or other like products).

The only inconsistency I am seeing (and cannot wrap my head around) is that the futures price should converge to the spot price at expiration, or there is a clear arbitrage opportunity.

The way the previous examples illustrate is to sum the components of your cash position and your futures position.

That is exactly what I have done in my above post.

Exactly what do you see that’s inconsistent? (I don’t see an inconsistency.)

The spot price of the underlying and the futures price will need to converge at expiration or there is an arbitrage opportunity.

It is hard to tell from this example, but the wording of the previous examples (I am using Schweser as well) make it sound like it is not the futures price on a new contract that is \$1200, but on the current contract.

Sorry for the confusion.

Got it.

Yes, the futures price for an expiring contract must be the same as the spot price.