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Question 1Foundational Knowledge

In options trading, what does a call option give its holder the right to do?

  1. Lend the underlying asset to the issuer for a fixed fee
  2. Buy the underlying asset at the strike price before or at expiration Correct answer.
  3. Sell the underlying asset at the strike price before or at expiration
  4. Receive a guaranteed dividend from the underlying asset

Explanation

A call option is a contract granting the holder the right, but not the obligation, to purchase the underlying asset at a specified strike price on or before the expiration date. The seller of the call assumes the obligation to deliver the asset if the holder exercises. This asymmetry of rights and obligations is the defining feature of a call.

Question 2Foundational Knowledge

An investor buys one call with a strike of $50 and pays a premium of $3. At expiration the underlying trades at $58. What is the investor's profit?

  1. $3
  2. $5 Correct answer.
  3. $11
  4. $8

Explanation

At expiration the call is worth its intrinsic value, which is the underlying price minus the strike: $58 minus $50 equals $8. The investor paid $3 in premium, so net profit is $8 minus $3, or $5. Premium paid reduces any payoff and must be subtracted to find profit.

Question 3Foundational Knowledge

Which term describes the price at which the underlying asset can be bought or sold when an option is exercised?

  1. Time value
  2. Strike price Correct answer.
  3. Intrinsic value
  4. Premium

Explanation

The strike price, also called the exercise price, is the fixed price at which the option holder may buy or sell the underlying asset. It is set when the contract is created and does not change over the life of the option. The premium is the market price of the option itself, distinct from the strike.

Question 4Foundational Knowledge

An option is described as "out of the money" when which condition holds?

  1. The option has no remaining time until expiration
  2. Exercise would produce a negative cash flow for the holder Correct answer.
  3. Exercise would produce a positive cash flow for the holder
  4. The premium exceeds the strike price

Explanation

An option is out of the money when exercising it would result in a negative cash flow for the holder, meaning the strike is unfavorable relative to the current underlying price. For a call this means the underlying trades below the strike; for a put it means the underlying trades above the strike. Moneyness is judged against the current underlying price, not the premium.

Question 5Foundational Knowledge

Which party to an option contract holds a contingent obligation rather than a right?

  1. The writer of the option Correct answer.
  2. The clearing member of the exchange
  3. The buyer of a call
  4. The buyer of a put

Explanation

The writer, or seller, of an option receives the premium and in return is obligated to perform if the buyer exercises. Buyers hold rights without obligation, while writers hold obligations without rights. The clearing member facilitates settlement but is not a party to the contingent obligation in the same sense.

Question 6Foundational Knowledge

What does the term "premium" refer to in an options transaction?

  1. The price paid by the buyer to the seller for the option contract Correct answer.
  2. The commission charged by the broker
  3. The margin deposited with the clearinghouse
  4. The difference between the strike and the underlying price

Explanation

The premium is the market price of the option itself, paid by the buyer to the seller in exchange for the rights conveyed by the contract. It has two components, intrinsic value and time value. Commissions, margin, and intrinsic value are separate concepts that should not be confused with the premium.

Question 7Foundational Knowledge

A stock is trading at $42. A put with a strike of $45 is available. How is this put described?

  1. In the money Correct answer.
  2. Deep out of the money
  3. At the money
  4. Out of the money

Explanation

A put is in the money when the underlying price is below the strike, because the holder could sell at the higher strike. Here $42 is below $45, so the put has $3 of intrinsic value and is in the money. Moneyness for puts is the mirror image of moneyness for calls.

Question 8Foundational Knowledge

Which statement correctly describes the maximum loss for the buyer of a single option?

  1. Unlimited for both calls and puts
  2. Limited to the premium paid Correct answer.
  3. Equal to the intrinsic value at purchase
  4. Limited to the strike price

Explanation

An option buyer pays a premium and acquires a right without obligation, so the worst outcome is that the option expires worthless and the premium is lost. No further liability can attach to the buyer regardless of how far the underlying moves. This capped downside is a fundamental attraction of buying options.

Question 9Foundational Knowledge

An investor holds a call with a strike of $60 when the underlying trades at $72. What is the intrinsic value of the call?

  1. $72
  2. $60
  3. $0
  4. $12 Correct answer.

Explanation

Intrinsic value for a call equals the underlying price minus the strike, floored at zero. Subtracting $60 from $72 gives $12, which is the amount the holder would receive from exercising and immediately selling at market. Any premium above this amount reflects time value.

Question 10Foundational Knowledge

Which combination of positions is equivalent to a synthetic long stock position?

  1. Short call plus short put at the same strike and expiration
  2. Long call plus long put at the same strike and expiration
  3. Long call plus short put at the same strike and expiration Correct answer.
  4. Long put plus short call at different strikes

Explanation

A long call combined with a short put at the same strike and expiration produces a payoff that rises and falls with the underlying just like a stock position. The two options have offsetting obligations and rights that replicate linear exposure. This equivalence underlies put-call parity relationships.

Question 11Foundational Knowledge

According to put-call parity, which relationship holds for European options with the same strike and expiration?

  1. Call price minus put price equals underlying price minus the present value of the strike Correct answer.
  2. Call price plus strike equals put price plus underlying price
  3. Call price minus underlying price equals put price plus strike
  4. Call price plus put price equals the underlying price

Explanation

Put-call parity states that a call minus a put equals the underlying price minus the present value of the strike, discounted at the risk-free rate. Rearranged, a long call plus a discounted strike payment equals a long put plus the underlying. Violations of this relationship create arbitrage opportunities.

Question 12Foundational Knowledge

Which factor increases the value of a call option, all else equal?

  1. A decrease in the underlying price
  2. An increase in the risk-free interest rate Correct answer.
  3. A decrease in time to expiration
  4. A decrease in volatility

Explanation

Rising interest rates reduce the present value of the strike that must be paid at expiration, which raises the value of a call. Higher rates also raise the cost of carrying the underlying, reinforcing the effect. Volatility, time, and underlying price movements affect calls in the opposite direction described by the other options.

Question 13Foundational Knowledge

An investor writes a naked call option. What is the maximum potential loss?

  1. Unlimited Correct answer.
  2. The premium received
  3. The strike price
  4. The difference between strike and premium

Explanation

A naked call writer has no underlying position to deliver against and must buy the asset at market if assigned. Because the underlying price can rise without a theoretical ceiling, the loss is unbounded. The premium received is the maximum gain, not the maximum loss.

Question 14Foundational Knowledge

A trader buys a put with a strike of $80 for a premium of $4 while the underlying trades at $80. What is the break-even underlying price at expiration?

  1. $84
  2. $80
  3. $76 Correct answer.
  4. $72

Explanation

For a long put, break-even equals the strike minus the premium paid. Subtracting $4 from $80 gives $76, the underlying price at which the put's intrinsic value exactly offsets the premium. Below that level the position becomes profitable.

Question 15Foundational Knowledge

Which statement best captures the meaning of time value for an option?

  1. It is the strike price discounted to present value
  2. It is the amount by which the premium exceeds intrinsic value Correct answer.
  3. It is the premium minus the risk-free rate
  4. It is the intrinsic value divided by the days to expiration

Explanation

Time value is the portion of the option premium attributable to the possibility that the option will become more valuable before expiration. It equals the premium minus intrinsic value. Time value declines as expiration approaches, a phenomenon known as time decay.

Question 16Foundational Knowledge

An investor holds a long straddle consisting of a call and a put with the same strike of $100 and total premium of $9. What underlying price range produces a profit at expiration?

  1. Below $91 only
  2. Exactly at $100
  3. Between $91 and $109 Correct answer.
  4. Above $109 only

Explanation

A long straddle profits when the underlying moves far enough in either direction to overcome the combined premium. The break-even points are the strike plus and minus the total premium, giving $109 and $91. Any expiration price outside that band yields a profit.

Question 17Foundational Knowledge

Which position benefits most directly from a decline in implied volatility, assuming no change in the underlying price?

  1. Short straddle Correct answer.
  2. Long strangle
  3. Long put
  4. Long call

Explanation

A short straddle collects premium and is short vega, so falling implied volatility reduces the value of the options sold and benefits the position. Long option positions are generally long vega and lose value when implied volatility declines. The effect assumes the underlying price stays unchanged.

Question 18Foundational Knowledge

An investor buys a call with a strike of $40 and simultaneously writes a call with a strike of $55, both with the same expiration. Which strategy is this?

  1. Bull call spread Correct answer.
  2. Covered call
  3. Bear put spread
  4. Long straddle

Explanation

Buying a lower-strike call and selling a higher-strike call is a bull call spread, a debit strategy that profits from moderate upside. The long call provides upside participation while the short call caps gains in exchange for reducing cost. Both legs share the same expiration, which defines the spread.

Question 19Foundational Knowledge

What does the delta of a call option approximate?

  1. The change in option price for a one-unit change in the underlying price Correct answer.
  2. The sensitivity of option price to implied volatility
  3. The change in option price for a one-day passage of time
  4. The sensitivity of option price to interest rates

Explanation

Delta measures the rate of change of the option price with respect to the underlying price. For calls, delta ranges between zero and one, and it can be interpreted roughly as a hedge ratio. The other Greek measures capture different risk dimensions.

Question 20Foundational Knowledge

A trader holds a long call with a delta of 0.60 and wants to be delta neutral. Which action achieves neutrality, ignoring other Greeks?

  1. Buy 0.60 shares of the underlying per option
  2. Sell 60 shares of the underlying per 100 options held Correct answer.
  3. Sell 0.60 options per share held
  4. Buy 60 shares of the underlying per 100 options held

Explanation

A long call with delta 0.60 behaves like ownership of 60 shares per contract of 100. To offset that positive delta, the trader sells 60 shares for every 100 options held, producing a net delta near zero. Delta hedging requires trading the underlying in proportion to the option's delta.

Question 21Foundational Knowledge

Two European options have the same strike and expiration. The call trades at $6 and the put at $2, while the underlying is $104 and the present value of the strike is $100. Which arbitrage is indicated?

  1. No arbitrage exists because parity is satisfied
  2. Both options are overpriced and should be sold
  3. The call is underpriced relative to parity and should be bought while selling the put and underlying
  4. The put is underpriced relative to parity and should be bought while selling the call and buying the underlying Correct answer.

Explanation

Parity implies the call minus put should equal the underlying minus the present value of the strike, or $4 here. The observed difference is $6 minus $2, also $4, so parity appears satisfied at first glance; however, checking the put side shows the put is cheap relative to the synthetic put implied by the call, underlying, and strike. The correct arbitrage buys the relatively cheap put and sells the synthetic equivalent.

Question 22Foundational Knowledge

An investor is short a put with a strike of $50 and receives a premium of $3. At expiration the underlying settles at $44. What is the investor's net result?

  1. A loss of $6
  2. A gain of $3
  3. A gain of $6
  4. A loss of $3 Correct answer.

Explanation

The short put is assigned because the underlying finished below the strike. The investor buys at $50 an asset worth $44, a $6 loss on the underlying, offset by the $3 premium received, for a net loss of $3. Premium partially offsets but does not eliminate the exercise loss.

Question 23Foundational Knowledge

A stock trades at $100. A one-year European call with a strike of $100 is priced at $8 and the risk-free rate is 5 percent. Using put-call parity, what is the approximate price of the matching put?

  1. $8.00
  2. $3.24 Correct answer.
  3. $4.76
  4. $12.76

Explanation

Parity gives put equals call minus underlying plus the present value of the strike. The present value of $100 discounted one year at 5 percent is about $95.24. So the put equals $8 minus $100 plus $95.24, which is approximately $3.24.

Question 24Foundational Knowledge

A trader is long a call with a delta of 0.50 and gamma of 0.05. If the underlying rises by $2, what is the approximate new delta, ignoring higher-order effects?

  1. 0.50
  2. 0.60 Correct answer.
  3. 0.45
  4. 0.55

Explanation

Gamma measures the change in delta per one-unit change in the underlying price. A $2 rise times a gamma of 0.05 increases delta by 0.10, moving it from 0.50 to approximately 0.60. This convexity means delta hedging must be rebalanced as the underlying moves.

Question 25Foundational Knowledge

An investor holds a covered call: long 100 shares at $48 and short one call with a strike of $55 for a premium of $2. At expiration the stock is $62. What is the total profit?

  1. $14 per share
  2. $9 per share Correct answer.
  3. $2 per share
  4. $7 per share

Explanation

The shares are called away at $55, producing a $7 gain from $48 to $55, plus the $2 premium, for $9 per share. Upside beyond $55 is forgone because of the short call. The premium partially compensates for that capped upside.

Question 26Foundational Knowledge

Which term describes the price a buyer pays to acquire an option contract?

  1. Margin requirement
  2. Premium Correct answer.
  3. Intrinsic value
  4. Strike price

Explanation

The premium is the market price of the option itself, paid by the buyer to the seller at the outset. It compensates the writer for accepting the obligation the contract creates. The strike price is the fixed exercise level, not a payment, and intrinsic value is only one component of the premium.

Question 27Foundational Knowledge

An investor buys a call with a strike of $50 and pays a premium of $3. The underlying is trading at $54 at expiration. What is the investor's profit or loss per share?

  1. A loss of $3
  2. A gain of $4
  3. A gain of $7
  4. A gain of $1 Correct answer.

Explanation

At expiration the call is worth its intrinsic value of $54 minus $50, which is $4. The investor paid $3 for that payoff, so the net gain is $4 minus $3, or $1 per share. Break-even for this position is the strike plus the premium, $53.

Question 28Foundational Knowledge

Which measure of an option's sensitivity estimates the change in the option's price for a one-unit change in the price of the underlying?

  1. Rho
  2. Delta Correct answer.
  3. Theta
  4. Vega

Explanation

Delta expresses how much an option's price is expected to move for a one-point move in the underlying. Call deltas are positive and put deltas are negative, ranging from zero to one in magnitude. The other Greeks capture different risk dimensions entirely.

Question 29Foundational Knowledge

A trader is short one call option and holds no underlying shares. Which risk exposure does this position carry?

  1. Limited loss and limited gain
  2. Unlimited loss potential as the underlying rises Correct answer.
  3. Loss limited to the premium received
  4. Profit that increases as the underlying falls

Explanation

A short call obligates the writer to sell the underlying at the strike if assigned, and the underlying price can rise without a ceiling. The writer's loss therefore grows as the underlying appreciates, offset only by the premium collected. The maximum gain is the premium, but the loss side is unbounded.

Question 30Foundational Knowledge

A put option has a strike of $70 and the underlying trades at $62. What is the intrinsic value of the put?

  1. $8 Correct answer.
  2. $62
  3. $0
  4. $70

Explanation

A put is in the money when the underlying trades below the strike. Intrinsic value equals the strike minus the underlying price, so $70 minus $62 gives $8. Any premium beyond $8 would represent time value.

Question 31Foundational Knowledge

An investor buys a put with a strike of $90 for a premium of $5. What is the break-even price of the underlying at expiration?

  1. $90
  2. $95
  3. $80
  4. $85 Correct answer.

Explanation

A long put profits when the underlying falls far enough below the strike to cover the premium paid. Break-even equals the strike minus the premium, so $90 minus $5 gives $85. Below $85 the position is profitable, and above it the position loses.

Question 32Foundational Knowledge

An investor holds a long call and a long put on the same underlying with the same strike and expiration. Which position does this describe?

  1. A long strangle
  2. A bull call spread
  3. A long straddle Correct answer.
  4. A covered call

Explanation

Combining a call and a put with identical strikes and expirations produces a straddle, which profits from a large move in either direction. A strangle uses different strikes, typically both out of the money. Spreads and covered positions involve offsetting legs that cap risk or return.

Question 33Foundational Knowledge

A trader is long a straddle with a strike of $100 and pays total premium of $10. The underlying settles at $118 at expiration. What is the profit or loss per share?

  1. A gain of $10
  2. A gain of $18
  3. A gain of $8 Correct answer.
  4. A loss of $10

Explanation

At expiration only the call has value, equal to $118 minus $100, which is $18. Subtracting the combined premium of $10 leaves a net gain of $8. The upper break-even for the straddle is the strike plus total premium.

Question 34Foundational Knowledge

An investor buys a call with a strike of $30 and writes a call with a strike of $45, both with the same expiration. Which description fits this position?

  1. A bull call spread Correct answer.
  2. A bear call spread
  3. A covered call
  4. A long straddle

Explanation

Buying the lower-strike call and selling the higher-strike call is a bull call spread, which profits from a moderate rise in the underlying. The short leg caps the maximum gain at the difference in strikes minus the net premium. Maximum loss is limited to the net premium paid.

Question 35Foundational Knowledge

A trader holds a long call with a delta of 0.60 and wants to be delta neutral. Ignoring other Greeks, which action achieves neutrality?

  1. Buy 60 shares of the underlying
  2. Buy 40 shares of the underlying
  3. Sell short 60 shares of the underlying Correct answer.
  4. Sell short 40 shares of the underlying

Explanation

A long call with delta 0.60 behaves like ownership of 60 shares for small price moves. To offset that positive exposure, the trader shorts 60 shares, whose delta of negative 60 cancels the call's positive 60. The resulting net delta is zero.

Question 36Foundational Knowledge

Which statement correctly describes the effect of an increase in implied volatility on the price of a fairly priced option?

  1. It raises both call and put prices, all else equal Correct answer.
  2. It affects only options that are in the money
  3. It lowers both call and put prices
  4. It raises call prices and lowers put prices

Explanation

Higher implied volatility widens the distribution of possible future underlying prices. Because option payoffs are asymmetric, a wider distribution increases the expected payoff of both calls and puts. Both types therefore gain value when volatility rises, regardless of moneyness.

Question 37Foundational Knowledge

A trader holds a long call with a delta of 0.50 and gamma of 0.05. If the underlying rises by $2, what is the approximate new delta, using a gamma-adjusted estimate?

  1. 0.60 Correct answer.
  2. 0.55
  3. 0.50
  4. 0.45

Explanation

Gamma measures how much delta changes per one-point move in the underlying. A $2 rise times a gamma of 0.05 adds 0.10 to the original delta of 0.50, giving approximately 0.60. Delta therefore rises as a call moves further into the money.

Question 38Foundational Knowledge

A European call and a European put share the same strike and expiration. The call trades at $6, the put at $2, and the underlying at $100 with a risk-free rate of zero. Which relationship should hold under put-call parity?

  1. The strike must equal $100
  2. The strike must equal $108
  3. The strike must equal $104
  4. The strike must equal $96 Correct answer.

Explanation

With a zero interest rate, put-call parity reduces to call minus put equals underlying minus strike. Substituting gives $6 minus $2 equals $4, so the underlying minus strike equals $4. With the underlying at $100, the strike must therefore be $96.

Question 39Foundational Knowledge

An investor buys 100 shares at $48 and writes one call with a strike of $55 for a premium of $2. If the underlying settles at $58 at expiration, what is the total profit on the position?

  1. $700 Correct answer.
  2. $500
  3. $1,000
  4. $900

Explanation

The shares gain $10 each, or $1,000 on 100 shares, but the short call is assigned and loses $3 per share, or $300. Adding the $200 premium received gives a net profit of $1,000 minus $300 plus $200, which equals $900. The short call caps the stock gain at the strike.

Question 40Foundational Knowledge

Which factor causes the time value of an option to decline as expiration approaches, all else equal?

  1. The passage of time, known as theta decay Correct answer.
  2. A rise in the risk-free interest rate
  3. An increase in the underlying's dividend yield
  4. An increase in implied volatility

Explanation

Time value reflects the chance that the option finishes further in the money, and that chance shrinks as expiration nears. This erosion is captured by theta, which is negative for long option positions. Volatility, interest rates, and dividends change option value through other channels.

Question 41Application and Analysis

A company's income statement shows revenue of $500,000, cost of goods sold of $300,000, and operating expenses of $120,000. What is the operating profit margin?

  1. 16% Correct answer.
  2. 40%
  3. 60%
  4. 24%

Explanation

Operating profit equals revenue minus cost of goods sold minus operating expenses, which is $500,000 - $300,000 - $120,000 = $80,000. Dividing operating profit by revenue gives $80,000 / $500,000 = 16%.

Question 42Application and Analysis

Which financial statement reports a firm's assets, liabilities, and equity at a single point in time?

  1. Statement of retained earnings
  2. Statement of cash flows
  3. Balance sheet Correct answer.
  4. Income statement

Explanation

The balance sheet presents a snapshot of what a firm owns and owes as of a specific date. The other statements report activity over a period rather than a position at a moment.

Question 43Application and Analysis

A firm has current assets of $240,000 and current liabilities of $160,000. What is its current ratio?

  1. 1.50 Correct answer.
  2. 1.33
  3. 2.40
  4. 0.67

Explanation

The current ratio divides current assets by current liabilities: $240,000 / $160,000 = 1.50. A ratio above 1.0 indicates the firm holds more short-term assets than short-term obligations.

Question 44Application and Analysis

In capital budgeting, which method discounts all expected cash flows to their present value and compares the total to the initial investment?

  1. Internal rate of return
  2. Net present value Correct answer.
  3. Payback period
  4. Accounting rate of return

Explanation

Net present value discounts every projected cash flow at the required rate and subtracts the initial outlay. A positive result signals that the project adds value at that discount rate.

Question 45Application and Analysis

Which of the following best describes diversifiable risk in a portfolio context?

  1. Risk that affects all securities and cannot be reduced
  2. Risk measured by the portfolio's beta coefficient
  3. Risk arising from changes in the general level of interest rates
  4. Risk tied to a single firm that can be reduced through diversification Correct answer.

Explanation

Diversifiable, or unsystematic, risk stems from firm-specific factors and can be largely eliminated by holding many securities. Market-wide risk remains regardless of diversification.

Question 46Application and Analysis

A bond with a face value of $1,000 pays an annual coupon of $60. If the bond currently trades at $1,200, what is its current yield?

  1. 5.0% Correct answer.
  2. 6.0%
  3. 4.0%
  4. 3.3%

Explanation

Current yield equals the annual coupon divided by the market price: $60 / $1,200 = 5.0%. The yield falls below the coupon rate because the bond trades at a premium.

Question 47Application and Analysis

Which ratio measures how efficiently a firm uses its assets to generate sales?

  1. Return on equity
  2. Dividend payout
  3. Asset turnover Correct answer.
  4. Debt-to-equity

Explanation

Asset turnover divides sales by average total assets and indicates how many dollars of revenue each dollar of assets produces. Higher values suggest more efficient asset utilization.

Question 48Application and Analysis

A company expects to receive $10,000 one year from now. If the discount rate is 10%, what is the present value of that cash flow?

  1. $11,000.00
  2. $9,000.00
  3. $10,000.00
  4. $9,090.91 Correct answer.

Explanation

Present value equals the future amount divided by one plus the discount rate: $10,000 / 1.10 = $9,090.91. Discounting reduces the value because money received later is worth less today.

Question 49Application and Analysis

A firm reports net income of $90,000, total assets of $600,000, and total equity of $300,000. Using the DuPont framework, what is its return on equity?

  1. 60%
  2. 45%
  3. 15%
  4. 30% Correct answer.

Explanation

Under DuPont analysis, ROE equals net profit margin times asset turnover times equity multiplier. Margin is 15%, turnover is 1.0, and the multiplier is 2.0, giving 15% x 1.0 x 2.0 = 30%.

Question 50Application and Analysis

A project requires an initial outlay of $50,000 and generates $20,000 per year for four years. At a discount rate of 8%, which conclusion is correct?

  1. The project should be rejected because payback exceeds three years
  2. The project should be rejected because the IRR is below 8%
  3. The project should be accepted because its NPV is positive Correct answer.
  4. The project is indifferent because NPV equals zero

Explanation

The present value of four annual $20,000 payments at 8% is roughly $66,240, which exceeds the $50,000 outlay, so NPV is positive and the project adds value. A positive NPV at the required rate is the accept criterion.