- An investor buys a put option with a strike price of $180 for a premium of $5.50. The option expires when the underlying stock price is $182. What is the investor's net profit or loss per share?
Answer: A loss of $5.50
At expiration, the stock price ($182) is above the strike price ($180). This means the put option is out-of-the-money and expires worthless. The payoff is $0. The investor's net loss is the full premium paid for the option, which is $5.50 per share.
- An investor realizes a net loss of $150 on a single long put contract (100 shares). If the stock price at expiration was $32 and the strike price was $35, what was the premium paid per share for the option?
Answer: $4.50
First, find the per-share loss: $150/100 shares=$1.50 loss per share. Next, find the gross payoff per share at expiration: Payoff=K−ST=$35−$32=$3.00. The net profit formula is Profit=Payoff−Premium. We can rearrange this to solve for the premium: Premium=Payoff−Profit. Substituting the values: Premium=$3.00−(−$1.50)=$3.00+$1.50=$4.50. - An investor buys one put option contract on ABC Corp for $4.00 per share. The strike price is $95. Shortly before expiration, with the stock trading at $85, the investor closes the position. What is the approximate percentage return on this investment?
Answer: 150%
The initial investment is the total premium paid for one contract: $4.00/share×100 shares=$400. At expiration, the put is in-the-money. The payoff per share is K−ST=$95−$85=$10. The net profit per share is $10−$4=$6. The total net profit is $6×100=$600. The return on investment is (Net Profit / Initial Investment) = $600/$400=1.5, or 150%. - A trader writes one put option contract with a strike price of $120, receiving a premium of $6 per share. If the underlying stock price is $112 at expiration, what is the trader's total profit or loss on the position?
Answer: A loss of $200
As the writer of a put option, the trader is obligated to buy the stock at the strike price if the option is exercised. The payoff for a short put is −max(0,K−ST). Per share, this is −max(0,$120−$112)=−$8. The net profit per share is this payoff plus the premium received: −$8+$6=−$2. For one contract (100 shares), the total loss is −$2×100=−$200. - The profit/loss diagram represents a single option position at expiration. What is the maximum possible profit for the holder of this position? Based on the profit/loss diagram shown:
Answer: $5 per share
The diagram shows the profile of a short put. The profit is capped at the premium received, which occurs if the stock price at expiration is at or above the strike price. The y-intercept of the profit line, which represents the profit when the option expires worthless, is $5. Therefore, the maximum profit is $5 per share.
- An investor's option position has a payoff profile where the maximum possible loss is limited to the premium paid, and the potential profit is unlimited. The profit increases as the underlying stock price rises. Which of the following positions does this describe?
Answer: A long call
This describes the payoff profile of a long call option. The buyer's maximum loss is the premium paid if the option expires out-of-the-money. The profit potential is theoretically unlimited as the stock price can rise indefinitely, and the payoff (Stock Price - Strike Price) increases with it.
- A call option has a premium of $5. The strike price is $70, and the underlying stock is trading at $68. What are the intrinsic value and time value of this option, respectively?
Answer: $0 and $5
When analyzing option values, remember that an option's premium consists of two components: intrinsic value (immediate profit if exercised) and time value (additional premium for potential future profit).
For a call option, intrinsic value equals the greater of either (stock price - strike price) or zero. Since this stock trades at $68 and the strike price is $70, the intrinsic value is max(68−70,0)=max(−2,0)=0. The option is "out of the money" because the stock price is below the strike price, so there's no immediate profit from exercising.
Time value equals the total premium minus intrinsic value. With a $5 premium and $0 intrinsic value, the time value is 5−0=5. This represents the market's assessment of the option's potential to become profitable before expiration.
Answer A correctly identifies $0 intrinsic value and $5 time value. Answer B incorrectly assumes $2 intrinsic value, which would only occur if the stock were trading above the $70 strike price. Answer C reverses the components entirely, suggesting all value is intrinsic with no time premium—impossible for an out-of-the-money option. Answer D also incorrectly calculates $3 intrinsic value, again assuming the option is in-the-money.
Remember this key principle: for call options, intrinsic value only exists when the stock price exceeds the strike price. When options are out-of-the-money, their entire premium consists of time value, representing the possibility of future profitability. - An investor purchases one call option contract on XYZ stock with a strike price of $80 for a premium of $3.50 per share. At the expiration date, XYZ stock is trading at $88 per share. What is the investor's net profit from this position?
Answer: $450
A standard option contract represents 100 shares. First, calculate the per-share payoff at expiration: max(0,ST−K)=max(0,$88−$80)=$8. The net profit per share is the payoff minus the premium paid: $8.00−$3.50=$4.50. For one contract, the total net profit is $4.50×100=$450. - The profit/loss diagram shows a breakeven stock price of $96.50 and a strike price of $100. Based on this information, what was the premium associated with this option? Based on the profit/loss diagram shown:
Answer: $3.50
The diagram shows the profile of a long put option (profit increases as price falls, loss is limited). The breakeven formula for a long put is: Breakeven = Strike Price - Premium. We can rearrange to solve for the premium: Premium = Strike Price - Breakeven. Using the values from the diagram and stem: Premium = $100.00−$96.50=$3.50. - An options writer sells a call option with a strike price of $210 for a premium of $7.50. The position will become unprofitable for the writer if the stock price at expiration is above what level?
Answer: $217.50
The breakeven point for a short call writer is the strike price plus the premium received. Breakeven Price = Strike Price + Premium = $210.00+$7.50=$217.50. Above this price, the loss from the obligation to sell the stock will exceed the premium received, resulting in a net loss for the writer. - A put option on a stock has a strike price of $90 and expires with an intrinsic value of $8. The investor who purchased the option for a premium of $3 has a net profit per share of:
Answer: $5
An option's intrinsic value at expiration is its gross payoff. For a buyer, the net profit is the intrinsic value minus the premium paid. Therefore, the net profit per share is $8(intrinsic value)−$3(premium)=$5. - An investor buys a put option with a strike price of $45 for a premium of $2.75. At what stock price at expiration will the investor break even on the investment?
Answer: $42.25
The breakeven point for a long put is the price at which the profit from exercising the option exactly covers the premium paid. The formula is: Breakeven Price = Strike Price - Premium. In this case, $45.00−$2.75=$42.25. At this price, the payoff is $45.00−$42.25=$2.75, which equals the cost of the option. - A trader who believes that a stock's price will remain stable and trade within a narrow range would be most likely to profit from which of the following positions?
Answer: Writing a call option
Writing (selling) an option, either a call or a put, generates income from the premium. The writer's maximum profit is achieved if the option expires worthless. This occurs if the stock price does not move enough to make the option in-the-money. Therefore, a writer profits from low volatility or a stable stock price. Buying options or the stock itself is a directional or pro-volatility bet.
- Which of the following would cause the intrinsic value of a European put option to decrease, assuming all other factors remain constant?
Answer: An increase in the price of the underlying stock
When analyzing European put options, you need to understand how different variables affect the option's intrinsic value. A put option gives you the right to sell a stock at a specific strike price, so its value depends on how much the stock price is below that strike price.
The intrinsic value of a put option equals the maximum of zero or the strike price minus the current stock price: max(0,K−S). When the underlying stock price increases, this difference becomes smaller, reducing the put option's intrinsic value. If the stock price rises above the strike price, the put becomes worthless since you wouldn't want to sell a stock for less than its market value. This makes option A correct.
Option B is incorrect because decreasing the strike price would actually decrease the put's intrinsic value, not increase it. A lower strike price means you can sell the stock for less, making the option less valuable.
Option C represents a common misconception. While decreasing time to expiration reduces a put option's time value, it doesn't directly affect intrinsic value, which depends solely on the relationship between stock price and strike price.
Option D confuses intrinsic value with market price. The option premium is what you pay for the option, but intrinsic value is an internal calculation based on stock and strike prices. Premium changes don't alter intrinsic value.
Study tip: Remember that put options become more valuable as stock prices fall below the strike price. Always think about whether you'd actually want to exercise the option at current market conditions. - A call option with a strike price of $60 is purchased for a premium of $4. The underlying stock is currently trading at $63. Which statement accurately describes the position?
Answer: The option is in-the-money, but the position is not yet profitable.
When analyzing call options, you need to distinguish between two separate concepts: whether the option is "in-the-money" versus whether your position is profitable.
A call option is in-the-money when the stock price exceeds the strike price. Here, the stock trades at $63 while the strike is $60, so the option has $3 of intrinsic value ($63 - $60). This confirms the option is in-the-money.
However, profitability depends on whether the intrinsic value exceeds what you paid. You purchased this call for a $4 premium but can only capture $3 of intrinsic value if exercised today. Your net position is therefore -$1 ($3 intrinsic value - $4 premium paid), making the position unprofitable despite being in-the-money.
Answer A incorrectly assumes that in-the-money automatically means profitable, ignoring the premium cost. Answer B makes two errors: calling an option out-of-the-money when the stock price clearly exceeds the strike, and coincidentally getting the profitability assessment right for the wrong reasons. Answer C incorrectly states the option is at-the-money, which would only be true if the stock traded exactly at the $60 strike price.
Answer D correctly identifies both components: the option is in-the-money (stock price > strike price) but not yet profitable (intrinsic value < premium paid).
Study tip: Always separate these two evaluations when analyzing options. First determine moneyness by comparing stock price to strike, then assess profitability by comparing total value to premium paid. Many exam questions exploit confusion between these concepts.
- An investor writes a covered call by selling one call contract (strike $40, premium $2) against 100 shares of stock purchased at $38. At expiration, the stock price is $45. What is the net profit on the entire position?
Answer: $400
The position has two parts. First, the stock profit: the stock was bought at $38 and is called away at the strike price of $40, so the stock profit is ($40−$38)×100=$200. Second, the option profit: the investor received a $2 premium per share, and since the option was exercised, this is the entire profit from the option itself, totaling $2×100=$200. The total net profit is the sum of the stock profit and the option profit: $200+$200=$400. - An investor purchases a call option with a strike price of $150 for a premium of $6. At expiration, the underlying stock is trading at $154. What is the financial result for the investor on a per-share basis?
Answer: A net loss of $2
At expiration, the stock price ($154) is above the strike price ($150), so the option is in-the-money. The gross payoff (intrinsic value) is $154−$150=$4. However, the investor paid a $6 premium. The net result is the payoff minus the premium: $4−$6=−$2. The investor has a net loss of $2 per share, even though the option finished in-the-money. - An options trader's position on a single contract resulted in a net profit of $150. This profit was realized when the underlying stock finished at $48 per share at expiration, which was below the option's strike price of $53. The premium for the option was $3.50 per share. Which position did the trader hold?
Answer: Long one put contract
When analyzing options profits at expiration, you need to determine which position would generate the stated profit given the stock price relative to the strike price. Since the stock finished at $48, below the $53 strike price, any call options are worthless while put options have intrinsic value.
For a long put position (A), you have the right to sell at $53 when the stock is worth $48, giving you an intrinsic value of $5 per share. Since you paid a $3.50 premium, your net profit is $5.00 - $3.50 = $1.50 per share, or $150 per contract (100 shares). This matches the stated profit exactly.
Looking at the wrong answers: (B) Short one call contract would generate a profit of only $350 (the premium collected) since the call expires worthless, which is too high. (C) Short one put contract would result in a loss of $150 because you'd collect $350 in premium but be assigned to buy stock worth $48 for $53, losing $500 in intrinsic value ($350 - $500 = -$150). (D) Long one call contract would result in a total loss of $350 since the call expires worthless when the stock is below the strike price.
Study tip: When working through options problems, always calculate the intrinsic value first (the difference between stock price and strike for in-the-money options), then subtract premiums paid or add premiums received. Remember that puts gain value when stock prices fall below the strike, while calls gain value when stock prices rise above the strike.
- Examine the profit/loss diagram. Based on this diagram, what is the strike price of the option? Based on the profit/loss diagram shown:
Answer: $110
For any single call or put option, the 'kink' in the profit/loss diagram occurs at the strike price. This is the point where the option's payoff transitions from being zero to having a positive value. In the given diagram, this kink is located at a stock price of $110.
- An investor writes a put option with a strike of $50 for a premium of $3. The investor's maximum possible loss on this position is:
Answer: $4,700
When analyzing options positions, you need to understand the maximum risk exposure for each strategy. For a written (sold) put option, the writer has collected a premium upfront but faces potential losses if the stock price falls below the strike price.
As the put writer, you're obligated to buy the stock at the $50 strike price if the option is exercised. The worst-case scenario occurs when the stock becomes worthless (falls to $0). In this situation, you must still buy the stock for $50, giving you a loss of $50 per share. However, since you collected a $3 premium when writing the put, your net loss is $50 - $3 = $47 per share. Since options contracts represent 100 shares, your maximum possible loss is $47 × 100 = $4,700.
Looking at the incorrect answers: Answer B ($5,000) represents the strike price multiplied by 100 shares, but this ignores the premium you collected, which reduces your loss. Answer C ($300) is simply the premium collected—this would be your maximum gain, not your maximum loss. Answer D (unlimited) applies to certain strategies like writing naked calls, but put writers have limited downside since stocks cannot fall below zero.
Remember this key pattern: for written puts, maximum loss equals (strike price minus premium received) times 100. The premium you collect always reduces your maximum loss, and puts have limited downside because stock prices are bounded at zero.
