Options on futures

[indra]

Question:
​

AJex Harrison expects that his company will need 50,000 pounds of copper in three
months and plans on using call options on copper futures to hedge the price risk
associated with this purchase. Assume the following copper prices:
Cash price: $3.25/pound
3-month futures price: $3.30/pound
Premium on call option with strike price of $3.30: $0.10
In th ree months (at expiration of the option), the cash price of copper has increased
to $3.50, the futures price has increased to $3.55, and the call option price is $0.25.
What is the profit/loss on a per pound

If no price risk is hedged:​

AH buys copper after 3 months at $3.50

Scenario 1:
AH profits ($3.55 - $3.30 i.e. strike price) = $0.25 per pound by selling those futures.
Net profit = $0.25 - $0.10 = $0.15/pound.
Buys the commodity at $3.50
Net CF = $3.50 - $0.15 = $3.35
Net P/L = $3.50 - $3.35 = $0.15

Scenario 2:
AH exercises the option and takes delivery of the commodity
So the futures let him buy copper for $3.30.
Net CF = $3.30 + $0.10 = $3.40
Net P/L = $3.50 - $3.40 = $0.10

Which of the above scenarios is correct?

 

[Dr. Jayanthi Sankaran]

Hi @indra,

I think Scenario 1 is correct:

Gain from call option exercise:

By exercising the call option now, AH gets to assume a long position in two underlying copper futures contract at strike price of $3.30/lb. This means that he gets to buy the underlying copper at only $3.30/lb on delivery day.

To take profit, AH enters into an offsetting short position in two contracts of the underlying copper futures at the market price of $3.55/lb, resulting in a gain of $0.25/lb. Since each NYMEX copper call option covers 25,000 lbs of copper, gain from the long call position is $12,500. Deducting the initial premium of $5,000 AH pays to buy the call option his net profit from the long call strategy is $7,500.

Long Copper Call Option Strategy

Gain from option exercise = (Market Price Of Underlying Futures - Option Strike Price) = ($3.55/lb - 3.30/lb)*50,000lbs

= $12,500
​

Initial premium paid = $5,000

Net Profit = $12,500 - $5,000 = $7,500
Net Profit/lb = $7,500/50,000 lbs = $0.15/lb
​

(Note: One NYMEX copper futures contract represents 25,000 lbs of copper)

​

Thanks!

​

 

[David Harper CFA FRM]

@indra do you mind if we ask the source of the question (due to its unusual format), it seems to resemble the scenario(s) illustrated in readings by Institute for Financial Markets, Futures and Options, but not exactly? Thanks,

 

[Dr. Jayanthi Sankaran]

Yes, I found it rather unusual too David

Jayanthi

 

[David Harper CFA FRM]

@Dr. Jayanthi Sankaran definitely unusual, although I agree with your $0.15.

By simply closing out the future contract, the per pound option payoff is (F-K) = 3.55 - 3.30 = $0.25 per pound.

Given an initial cost of $0.10 per pound (ie, option premium) this implies an option payoff = $0.25 - 0.10 = $0.15 per pound.

Although I am confused by the cash flow/P&L syntax employed, scenario #2 appears to make a mistake: rather than closing out the futures contract immediately, the option can be exercised would be exercised for a cash payoff of $0.25 plus the long position in the futures contract (K = $3.30), so I don't agree with the $0.10 in the second scenario. Thanks!

 

[Dr. Jayanthi Sankaran]

Hi David - totally agree with you - the CF and P/L syntax are confusing. Also, the second scenario does not make any sense!

Thanks for the clarification

 

[indra]

Hi..sorry I could not reply due to some technical issues on the portal, which now seems to have been resolved. The source of this particular question is Kaplan's Schweser notes 2015 for the FRM exam.

 

[indra]

Quote from Hull Chap 17 (8th edition) - "If a call futures option is exercised, the holder acquires a long position in the underlying futures contract plus a cash amount equal to the most recent settlement futures price minus the strike price"

In that case, for the above problem, in case the option is exercised,

1. Cash amount received = $3.55 - $3.30 = $0.25 (assuming last settlement price was $3.55)
Net gain = $0.25 - $0.10 = $0.15
2. The long position acquired as a result of exercising the option, allows AH to buy the commodity at $3.55.
Assuming that current futures price is same as last settlement price i.e $3.55, then net gain = 0
So total gain = $0.15 + $0 = $0.15

But since AH wants to take delivery of copper and the current cost of copper being $3.50,
So loss from using the futures contract to get the commodity = $3.50 - $3.55 = $-0.05

Hence net gain = $0.15 + $-0.05 = $0.10

Please comment.

 

[David Harper CFA FRM]

Hi @indra

The problem with that solution is that, if you only exercise the (futures) option, then you have a long position in a futures contract. This long position, as usual, can be either closed out (prior to maturity) or be held until the delivery period. Your solution posted implies the option is exercised simultaneous with the delivery period; but in that case, the question should have a futures price approximately the same as the spot price; i.e., $3.50. Otherwise an arbitrage is possible; in fact, your 0.05 discrepancy is only possible if there is an arbitrage. The original question appears to be written by somebody who does not quite understand the mechanics of the option on the futures contract; e.g., it is not the case that "AH exercises the option and takes delivery of the commodity."

Rather, the option is an option on a futures contract with a strike price. The long option holder pays the premium and, as usual, receives a right to exericise. To exercise, in this case, is to exercise into a futures contract at a pretermined strike price. If (as above) the call option holder exercises, then he/she

1. By exercising the option, he/she becomes the holder of a long position on the futures contract at the strike price (i.e., $3.30)
   
2. Assuming positive intrinsic value, receives a cash payment upon exercise due to the immediate market-to-market of the "in the money" futures contract (3.55 - 3.30); the source of this is the short option writer who becomes short the futures contract and is paying the mark-to-market.

Having exercised the option, the holder of the long position on the futures contract can (as usual) close it out, or wait until the delivery period. Differences in the "net P/L" between the two choices (i.e., exercise and hold versus close out immediately) would theoretically be driven by same time difference that allows for divergence between the spot and futures price. If there is a scenario where the option holder can exericse and immediately execute on the future's delivery, then the question creates confusion by allowing for a $0.05 difference between a converged futures and spot. I hope that helps!

 

[indra]

Thanks..your explanation helps.