A client buys three put contracts on XYZ stock, each covering 100 shares, with a strike price of $60 and a premium of $5 per share. At expiration, XYZ trades at $48 per share.
What is the client's net profit on this options position? Answer: $2,100
Options payoff computation. Each put is in-the-money by $60 − $48 = $12 per share. Gross payoff = $12 × 300 shares = $3,600. The premium ($5 × 300 = $1,500) was paid at purchase and is NOT returned at exercise, so net profit = $3,600 − $1,500 = $2,100. $3,600 is the gross intrinsic value with the premium ignored. $5,100 ADDS the premium to the intrinsic value, as if the premium were refunded on exercise. $700 is the net profit on a SINGLE contract — ($12 − $5) × 100 — forgetting that three contracts were purchased.
- Which of the following statements regarding the maximum loss on an option position is true?
Answer: The maximum loss on a covered call writer is the cost of the underlying stock minus the call premium received, because the stock can fall to zero and the premium reduces the loss.
Option payoff conventions. A covered call writer owns the underlying stock, so the worst case is that the stock falls to zero; the net loss is the cost of the stock reduced by the call premium received. A naked put writer's maximum loss is the strike price minus the premium received, not merely the premium, because assignment can occur at the strike when the stock is worthless. A naked call writer's loss is potentially unlimited because the stock has no upper price limit. A long call's maximum loss is the premium paid; it is not the strike price minus the premium.
- Which of the following statements regarding the intrinsic value and time value of an equity option is true?
Answer: A call with a $50 strike and a $4 premium has $2 of time value while the stock is $52, and its time value is zero at expiration.
Option value convention: for a call, intrinsic value = max(S - X, 0); for a put, intrinsic value = max(X - S, 0); time value = premium - intrinsic value, and time value is zero at expiration. The call with a $50 strike, $4 premium, and $52 stock has $2 intrinsic value and $2 time value, and no time value at expiration. The put statement errs by calling the $5 in-the-money amount time value; the $6.50 premium would leave $1.50 of time value. The expiration call statement reports the $3 profit as the option's total value, but total value is $7. An out-of-the-money put at expiration has neither intrinsic nor time value; it expires worthless.
An airline will need 150,000 gallons of jet fuel in three months. Jet-fuel futures trade in contracts of 50,000 gallons each, and the three-month futures price is $3.00 per gallon. The airline enters the appropriate futures position to hedge its exposure. Three months later, at delivery, the spot price of jet fuel has risen to $3.40 per gallon.
What is the airline's net cost of the 150,000 gallons of jet fuel after accounting for its futures position? Answer: $450,000
Long futures hedge. The airline will buy fuel in the future, so it must BUY (go long) futures to lock in the price: 150,000 ÷ 50,000 = 3 contracts. At delivery the futures gain is ($3.40 − $3.00) × 150,000 = $60,000, offsetting the higher spot cost of $3.40 × 150,000 = $510,000, for a net cost of $450,000 — exactly the locked-in $3.00 per gallon. $510,000 ignores the hedge gain entirely, as if the airline were unhedged. $570,000 results from going SHORT (selling) futures when the airline should be long; the $60,000 futures loss ADDS to the spot cost. $430,000 results from over-hedging with 4 contracts (200,000 gallons), producing an $80,000 gain that overstates the offset.
- Assuming no withdrawals or additional deposits, which of the following statements regarding daily settlement of a futures margin account is true?
Answer: A long 5,000-bushel contract bought at $4.00 with $2,000 initial margin has $2,100 in the account after a $4.06 close followed by a $4.02 close.
Futures contracts are marked to market daily; the margin deposit is a performance bond, and account equity is adjusted for each day's gain or loss. From $4.00 to $4.06 is a $300 gain on a 5,000-bushel contract, moving $2,000 to $2,300; from $4.06 to $4.02 is a $200 loss, leaving $2,100. The $3.94/$3.98 long example would leave $1,900, not $1,800. The $3.96/$4.02 short example also leaves $1,900, not $2,200. Daily gains are credited every business day, not only when equity falls below maintenance.
- An investor buys 5 put option contracts on a stock. Each contract covers 100 shares. The premium is $2.00 per share and the strike price is $20. If the stock becomes worthless at expiration, what is the investor's maximum net gain?
Answer: $9,000
A long put's maximum gain occurs if the stock falls to zero. The put payoff is the strike price × shares = $20 × 500 = $10,000. After subtracting the $1,000 premium paid ($2 × 500), the net gain is $9,000. The $10,000 figure ignores the premium; the $1,800 figure is the per-contract net gain without multiplying by 5 contracts; the $1,000 figure is the premium paid, which is the maximum loss, not the maximum gain.
- A speculator buys one crude oil futures contract at $70 per barrel. The contract unit is 1,000 barrels. The initial margin is $6,000 and the maintenance margin is $4,000. After the first day's close, the settlement price is $67.50 per barrel. How much must the speculator deposit into the futures account to meet the margin call?
Answer: $2,500
Futures positions are marked to market daily. The loss is (70 - 67.50) × 1,000 = $2,500, reducing the account equity from $6,000 to $3,500. Because that is below the $4,000 maintenance margin, the account must be restored to the $6,000 initial margin, so the required deposit is $6,000 - $3,500 = $2,500. The $500 figure would restore only the maintenance margin; the $4,000 figure is the maintenance margin itself; the $6,000 figure is the initial margin and ignores the $3,500 still in the account.
- Which of the following statements regarding cash settlement of a broad-based index option with a $100 multiplier is true?
Answer: If a call with a 2,000 strike expires when the index settles at 2,045, the writer pays the holder $4,500 in cash and delivers no stocks.
Index option settlement convention. Broad-based index options are cash-settled: the in-the-money amount times the $100 multiplier is paid from writer to holder, and no underlying securities are delivered. A 45-point in-the-money call at a 2,000 strike therefore settles for $4,500. The put example would also settle for $4,500, but the payment runs from writer to holder, not holder to writer. The portfolio-delivery statement and the $45 statement misstate both the form and the amount of settlement.
- An investor sells 3 call option contracts on a stock without owning the underlying stock. Each contract covers 100 shares. The premium received is $4.00 per share and the strike price is $50. At expiration, the stock is trading at $62. What is the investor's net loss on the position?
Answer: $2,400
Because the call is in the money at expiration, the seller must deliver the stock at $50 while it is worth $62, an exercise loss of (62 - 50) × 100 × 3 = $3,600. The $1,200 premium received offsets part of that loss, so the net loss is $3,600 - $1,200 = $2,400. The $3,600 figure ignores the premium received; the $1,200 figure treats the premium as the loss and ignores the exercise obligation; the $4,800 figure adds the premium to the exercise loss instead of subtracting it.
A client owns 500 shares of DEF stock, purchased at $75 per share. To hedge against a decline, she buys five put contracts with a strike price of $70, paying a premium of $2.00 per share. At expiration, DEF trades at $62 per share.
What is the client's net loss on the combined stock-and-put position relative to her original purchase cost? Answer: $3,500
Protective put. The stock lost ($75 − $62) × 500 = $6,500. The puts are in-the-money by $70 − $62 = $8 per share, paying $8 × 500 = $4,000, but the hedge cost the premium ($2 × 500 = $1,000). Net loss = $6,500 − $4,000 + $1,000 = $3,500. $6,500 is the stock loss alone, as if no put hedge existed. $7,500 adds the premium to the stock loss without counting the put payoff, treating the hedge as pure additional cost. $3,000 is the net GAIN on the puts alone ($4,000 − $1,000), treating the hedge as a separate winning trade rather than an offset to the stock loss.
- An investor buys 3 call option contracts on a stock. Each contract covers 100 shares. The premium is $2.10 per share and the strike price is $45. At expiration, the stock is trading at $49. What is the investor's net gain on the position?
Answer: $570
A long call's gain at expiration is (market price - strike price - premium) × 100 × number of contracts. Here (49 - 45 - 2.10) × 100 × 3 = 1.90 × 300 = $570. The $190 figure is the per-contract gain before multiplying by the 3 contracts. The $1,200 figure is the option's intrinsic value at expiration but omits the $630 premium paid. The $1,830 figure adds the premium paid to the intrinsic value instead of subtracting it.
A stock is trading at $48 per share. Several options on this stock are quoted as follows: a $50-strike call at $3.50, a $50-strike put at $4.00, a $45-strike call at $6.00, and a $45-strike put at $1.00.
Which option has the greatest time value? Answer: The $50-strike call
Option time value = premium − intrinsic value. For the $50 call: intrinsic = max(0, $48 − $50) = $0, so time value = $3.50. For the $50 put: intrinsic = max(0, $50 − $48) = $2.00, so time value = $4.00 − $2.00 = $2.00. For the $45 call: intrinsic = max(0, $48 − $45) = $3.00, so time value = $6.00 − $3.00 = $3.00. For the $45 put: intrinsic = max(0, $45 − $48) = $0, so time value = $1.00. The $50-strike call's $3.50 exceeds all the others. The $50 put is a distractor if its $2.00 intrinsic value is not subtracted from its $4.00 premium. The $45 call is the deepest in-the-money and highest-premium option, but $3.00 of its $6.00 premium is intrinsic. The $45 put is an out-of-the-money option whose entire $1.00 premium is time value — the lowest of the four.
- An investor buys one put option contract, which covers 100 shares, with a strike price of $60 for a premium of $4.00 when the stock is trading at $57. At expiration, the stock is trading at $55. What are the option's time value at purchase and the investor's net gain or loss at expiration, respectively?
Answer: $1 time value; $100 gain
At purchase, the put is $3 in the money ($60 - $57), so its intrinsic value is $3 and its time value is $4 - $3 = $1. At expiration, time value is zero; with the stock at $55, the put's intrinsic value is $5. Net gain is ($5 - $4) × 100 = $100. The $3 time value choices confuse intrinsic value with time value. The $500 gain choices use the $5 intrinsic value at expiration but omit the $4 premium paid.
- A wheat farmer sells one wheat futures contract at $5.60 per bushel to hedge an anticipated harvest sale. The contract covers 5,000 bushels. At harvest, the cash market price is $5.30 per bushel and the farmer closes the futures position by buying the contract back at $5.25 per bushel. What effective price per bushel does the farmer receive for the wheat?
Answer: $5.65
The short futures hedge gains $5.60 - $5.25 = $0.35 per bushel. The farmer sells the crop in the cash market at $5.30 and adds the futures gain: $5.30 + $0.35 = $5.65. The $5.30 figure ignores the futures gain. The $5.60 figure would be the result only if the futures position were closed at the cash price of $5.30. The $5.95 figure incorrectly adds the futures gain to the original futures price rather than to the cash market price.
A client owns 200 shares of ABC stock, purchased at $52 per share. She writes two call contracts with a strike price of $58, receiving a premium of $3.50 per share. At expiration, ABC is trading at $60 per share and the calls are exercised.
What is the total value of the client's position at expiration (proceeds from the stock plus the option premium)? Answer: $12,300
Covered call at expiration. With ABC at $60, the $58-strike calls are $2 in-the-money and will be exercised, so the client must deliver her shares at the strike. Sale proceeds = $58 × 200 = $11,600, plus the premium $3.50 × 200 = $700, for a total of $12,300. $12,700 values the stock at the market price ($60 × 200) and adds the premium, ignoring that the shares must be delivered at $58. $12,000 is the market value of the shares alone, ignoring both the exercise obligation and the premium. $11,600 reflects the forced sale at the strike price but omits the premium she collected.
