Questions: Options: Calls, Puts, and Basic Payoffs

Question 1

You buy a call option on a stock with a strike price of $50, paying a $3 premium. At expiration the stock is trading at $45. What is your outcome?

• A. You exercise the option and lose $5 — the difference between the strike price and the market price
• B. You lose $3 — the premium paid, which is the maximum possible loss on a long option position
• C. You profit $3 because the option still has value since you hold the right to buy
• D. You lose the full $50 strike price since you agreed to buy at that level

Answer: (B)

When the stock is below the strike at expiration, the call has zero intrinsic value — you would never pay $50 for a stock trading at $45. You simply let the option expire unexercised. Your loss is limited to the $3 premium you paid, nothing more. This is the defining asymmetry of a long option position: the maximum loss is always capped at the premium, regardless of how far the asset falls. Option A describes a common error — confusing the payoff of exercising (which you wouldn't do) with the actual outcome of letting it expire.

Question 2

A portfolio manager owns $500,000 of stock in a single company. She buys put options with a strike price near the current market price. What is her most likely purpose?

• A. To profit if the stock price rises sharply above the strike
• B. To generate premium income by selling her obligation to deliver shares
• C. To speculate on volatility without maintaining her stock position
• D. To create a price floor on her position, limiting losses if the stock falls

Answer: (D)

A long put gains value when the underlying asset falls — it pays max(K − S, 0) at expiration. Held alongside a stock position, it functions as insurance: if the stock drops below the strike, the put's gains offset the stock's losses, creating a floor on total portfolio losses. This is the protective put strategy. The premium paid is the cost of insurance. This illustrates that options are not purely speculative instruments — hedging existing positions is one of their primary legitimate uses.

Question 3

For a call option buyer, the maximum possible loss is the full value of the underlying asset, since the buyer agreed to a purchase price.

• T. True
• F. False

Answer: False

This is a key misconception. The buyer of a call has the right but not the obligation to purchase. If the option expires worthless (stock below strike), the buyer simply walks away — they never have to pay the strike price. The maximum loss is always limited to the premium paid, regardless of what the underlying asset does. This is what makes the option buyer's position fundamentally different from owning the stock outright.

Question 4

The seller (writer) of a call option faces potentially larger losses than the buyer, despite receiving the premium upfront.

• T. True
• F. False

Answer: True

The call writer's maximum gain is capped at the premium received — that's all they can ever make. But their potential losses grow dollar-for-dollar as the underlying price rises above the strike, and are theoretically unlimited (a stock can rise without bound). This is the asymmetry reversed: the seller has a capped upside and uncapped downside. This asymmetry is why options exchanges require sellers to post margin — the seller bears the obligation to deliver or buy shares at a disadvantageous price if the buyer exercises.

Question 5

Why is the payoff profile of an option called 'asymmetric,' and why does this asymmetry matter differently for buyers versus sellers?

Model answer: An option's payoff is asymmetric because gains and losses respond differently depending on which direction the underlying moves. For a call buyer: if the stock rises above the strike, gains increase dollar-for-dollar; if it falls, the loss is capped at the premium no matter how far it drops. The seller has the exact mirror: gains are capped at the premium regardless of outcome, while losses grow as the stock rises. This means buyers and sellers are not taking symmetric risks — the buyer pays a premium to participate only in favorable outcomes while offloading unfavorable ones; the seller accepts the unfavorable outcomes in exchange for the premium. The asymmetry is what makes options useful for hedging: you can cap your downside while retaining upside.

This asymmetry also explains why the same instrument can serve completely opposite purposes: a speculator buys a call hoping for large upside; a corporate treasurer sells a covered call on stock they own to generate income while willing to give up upside above a target price. The same asymmetric payoff structure serves both.