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Free CFA Derivatives and Risk Management Practice Questions & Answers
131 exam-style Derivatives and Risk Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 1
An investor buys an XYZ May 50 call for $6.26. At expiration the stock price is $58. What is the VALUE and PROFIT of the long call position?
Select an option first.
Correct answer: A — Value = $8; Profit = $1.74
Explanation: A is correct: Value at expiration = max(ST − X, 0) = max($58 − $50, 0) = $8. Profit = Value − Initial Premium = $8 − $6.26 = $1.74. The value at expiration equals only intrinsic value (no time value at expiration). B incorrectly ignores the premium paid. C is for OTM outcome. D confuses value with premium paid.
Question 2
A long May 50 call was purchased for $6.26. At what stock price at expiration does the long call break even?
Select an option first.
Correct answer: C — $56.26
Explanation: C is correct: Breakeven for a long call = Strike + Premium = $50 + $6.26 = $56.26. At this stock price, the value of the call = $56.26 − $50 = $6.26, which exactly covers the premium paid, giving zero profit. A reverses the calculation. B ignores the premium. D is just the premium.
Question 3
An investor buys a June 50 put for $4.88. At expiration the stock price is $44. What is the profit/loss?
Select an option first.
Correct answer: B — +$1.12 profit
Explanation: B is correct: Value at expiration = max(X − ST, 0) = max($50 − $44, 0) = $6.00. Profit = $6.00 − $4.88 (premium paid) = $1.12. A is the outcome when the put expires OTM. C ignores the premium. D is the intrinsic value with wrong formula.
Question 4
For a SHORT call position, which of the following best describes maximum profit and maximum loss?
Select an option first.
Correct answer: B — Maximum profit = premium received; Maximum loss = unlimited
Explanation: B is correct: The short call receives the premium upfront — this is its maximum profit (if the stock stays below the strike). However, if the stock rises without limit above the strike, the short call must deliver the stock at the strike, creating unlimited potential losses. This is the risk of a 'naked' (uncovered) short call. A reverses the profit/loss structure. C limits the loss incorrectly.
Question 5
A put option is said to be ITM (in the money) when:
Select an option first.
Correct answer: B — The underlying price is below the strike price
Explanation: B is correct: A put gives the right to sell at the strike. If the underlying is below the strike, the long put holder can buy the underlying cheaply in the market and sell at the higher strike — the intrinsic value is positive. A describes an ITM call. C describes ATM for both puts and calls. D is not a definition of ITM.
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Question 6
An option's total value equals intrinsic value plus time value. Which of the following is MOST accurate about time value?
Select an option first.
Correct answer: C — Time value is zero only at expiration
Explanation: C is correct: At expiration, the option has only intrinsic value — there is no remaining time for favorable moves, so time value is zero. A is correct that time value is positive before expiration but misses that it falls to zero at expiration. B is backwards — time value DECREASES as expiration approaches (theta effect). D describes intrinsic value.
Question 7
For a LONG PUT position, the profit graph at expiration shows:
Select an option first.
Correct answer: A — Unlimited upside as the stock price falls below the breakeven
Explanation: A is correct: A long put profits when the underlying falls below the breakeven (strike − premium). As the stock approaches zero, the put value approaches the strike price, giving maximum profit of (strike − premium). The lower the stock, the higher the profit — though bounded at zero stock price. B describes a long call. C describes a short put. D is incorrect — the long put does lose the full premium paid when the stock rises above the strike.
Question 8
Which combination of options creates a SYNTHETIC LONG FORWARD position on an underlying?
Select an option first.
Correct answer: B — Long call + short put (same strike, same expiry)
Explanation: B is correct: A long call + short put (same strike, same expiry) creates a position that has a payoff identical to a long forward: above the strike, the call is exercised (gain); below the strike, the short put is exercised by the counterparty (loss). The net payoff = ST − X, identical to a long forward. A is a long straddle. C is a short straddle. D is a synthetic short forward.
Question 9
Put-call parity states c₀ − p₀ = S₀ − PV(X). If S₀ = $52.14, X = $50, call premium = $6.26, put premium = $3.87, and PV($50) = $49.75, does put-call parity hold?
Select an option first.
Correct answer: B — Yes — both sides equal $2.39
Explanation: B is correct: Left side: c₀ − p₀ = $6.26 − $3.87 = $2.39. Right side: S₀ − PV(X) = $52.14 − $49.75 = $2.39. Both sides are equal, confirming put-call parity holds. This relationship must hold to prevent arbitrage. A and C show incorrect calculations. D confuses PV(X) with the parity result.
Question 10
In a long risk reversal strategy, an investor:
Select an option first.
Correct answer: B — Sells OTM puts and buys OTM calls on the same underlying (approximately delta-neutral)
Explanation: B is correct: A long risk reversal combines a long OTM call and a short OTM put. It is used when the trader believes the OTM put implied volatility is relatively high (overpriced) and OTM call implied volatility is low (underpriced). The position has net long exposure to the underlying. A is a short risk reversal. C is a straddle or strangle. D is a calendar spread.
Question 11
An investor buys stock at $43 and sells a call for $2.10 with a strike of $45. What are the maximum profit, maximum loss, and breakeven at expiration?
Select an option first.
Correct answer: A — Max profit = $4.10; Max loss = $40.90; Breakeven = $40.90
Explanation: A is correct: Covered call formulas: Max profit = (X − S₀) + c₀ = ($45 − $43) + $2.10 = $4.10 (achieved at stock price ≥ $45). Breakeven = S₀ − c₀ = $43 − $2.10 = $40.90. Max loss = breakeven = $40.90 (stock falls to zero, premium received partially offsets). B understates max profit. C has unlimited loss which is wrong for covered call (not naked call). D has incorrect max profit.
Question 12
When would an investor MOST LIKELY write a covered call with an in-the-money (ITM) call?
Select an option first.
Correct answer: C — When intending to reduce an existing long stock position at a favorable price
Explanation: C is correct: Writing ITM covered calls is best suited when the investor wants to reduce a position at a favorable price. The ITM call is likely to be exercised, meaning the shares will be sold at the strike. Adding the premium received to the strike gives a total effective proceeds exceeding the current market price. A describes yield enhancement using OTM calls. B describes target price realization using marginally OTM calls. D would suggest a different strategy entirely.
Question 13
A covered call profit/loss profile MOST RESEMBLES which other strategy at expiration?
Select an option first.
Correct answer: B — Short put
Explanation: B is correct: The reading explicitly notes that the covered call profit line has the same general shape as a short put. Both have limited profit (capped at premium received for the short put, or at strike − S₀ + premium for the covered call) and downside loss that increases as the stock falls. The maximum loss equals the breakeven price for both. A has the opposite shape (unlimited upside). C is a V-shaped volatility bet. D has unlimited upside and limited downside.
Question 14
For a covered call position, the written call strike determines the strategy's objective. Matching the correct strikes to objectives: (i) Yield enhancement; (ii) Target price realization; (iii) Reducing position at favorable price
Select an option first.
Correct answer: B — (i) OTM call; (ii) Marginally OTM; (iii) ITM
Explanation: B is correct: The reading distinguishes three covered call motivations by strike selection: (i) Yield enhancement uses OTM calls (possibly substantially so) — premium income without high probability of exercise; (ii) Target price realization uses marginally OTM calls just above the current price — investor would be happy to sell slightly above current price; (iii) Reducing position at favorable price uses ITM calls — high probability of exercise to exit at or near current price plus premium. A and C get the ITM/OTM assignments mixed up.
Question 15
An investor buys stock at $37.50 and buys a put for $1.40 with a strike of $35. At expiration, what are the maximum profit, maximum loss, and breakeven?
Select an option first.
Correct answer: A — Max profit = unlimited; Max loss = $3.90; Breakeven = $38.90
Explanation: A is correct: Protective put formulas: Max profit = unlimited (stock can rise without limit). Max loss = (S₀ − X) + p₀ = ($37.50 − $35.00) + $1.40 = $3.90 (this occurs at or below the put strike). Breakeven = S₀ + p₀ = $37.50 + $1.40 = $38.90 (premium cost raises the breakeven above initial stock price). B understates max loss and has incorrect breakeven. C has wrong max loss (ignores premium). D caps max profit incorrectly.
Question 16
At expiration, the payoff profile of a protective put MOST RESEMBLES:
Select an option first.
Correct answer: C — Long call
Explanation: C is correct: The reading explicitly notes that 'stock plus the protective put has a net exposure equivalent to a long call.' Both have limited downside (premium paid for the call = net cost of protective put = premium + downside to put strike) and unlimited upside. The protective put acts like insurance — below the put strike, losses are capped, above it, the full stock upside is retained. A is incorrect — short put has limited upside and unlimited downside. B is incorrect — bull call spread has capped upside.
Question 17
The protective put is MOST useful for an investor who:
Select an option first.
Correct answer: B — Believes the stock may fall short-term but wants to retain long-term upside
Explanation: B is correct: The reading describes the protective put as 'ideal for an investor who thinks the stock may go down in the near future, yet who wants to preserve upside potential.' The put provides downside insurance while retaining unlimited upside exposure. A describes a long put (without owning the stock). C describes a covered call. D describes selling options, not buying them.
Question 18
The delta of a covered call position (long stock + short call) with call delta of 0.6 is:
Select an option first.
Correct answer: C — 0.4
Explanation: C is correct: Position delta = delta of long stock + delta of short call = (+1) + (−0.6) = +0.4. The long stock has delta +1. The short call has negative delta equal to −0.6 (short call takes the negative of the call's delta). The net position is long but with reduced delta compared to unhedged stock. A is just the short call delta. B ignores the stock delta. D incorrectly adds rather than subtracts.
Question 19
For a long call option, delta is closest to 1.0 when the option is:
Select an option first.
Correct answer: C — Deeply in the money
Explanation: C is correct: A deeply ITM call behaves like the underlying — a $1 rise in the stock produces nearly a $1 rise in the call value. The delta approaches 1.0 as the call moves deeply ITM. OTM options have deltas approaching 0 (little price change from stock movement). ATM options have deltas near 0.5. Near expiration ATM options have the highest gamma, not necessarily delta near 1.
Question 20
Gamma is HIGHEST for options that are:
Select an option first.
Correct answer: C — At the money with short time to expiration
Explanation: C is correct: The reading explains that gamma is highest for ATM options close to expiration. Near expiration, ATM options have very little time value; a small move in the underlying rapidly changes whether the option will expire ITM or OTM, causing large changes in delta. The option premium line is most curved around the ATM level near expiration. Deeply ITM or OTM options have lower gamma because their delta is already close to 1 or 0 respectively and changes slowly.
Question 21
Theta measures the effect of time passing on an option's value. Which statement about theta is MOST accurate?
Select an option first.
Correct answer: B — Theta is most negative for ATM options near expiration
Explanation: B is correct: Theta is always negative for long options (time passing reduces value). It is most negative (loses value fastest) for ATM options that are near expiration. The reading shows that ATM options lose time value at an accelerating rate as they mature. A has the sign wrong — theta is negative for long options. C has the direction wrong — theta becomes more negative (not positive) near expiration for ATM options. D is incorrect — puts also have negative theta.
Question 22
Vega measures the change in option value for a 1% change in volatility. Which statement about vega is MOST accurate?
Select an option first.
Correct answer: C — Vega is higher for options with more time to expiration
Explanation: C is correct: The reading states 'all other factors constant, vega is higher the more time there is to expiry.' With more time remaining, a change in volatility has a greater effect on the option's probability of expiring ITM, hence greater impact on value. A is wrong — vega is positive for long calls and puts (higher volatility benefits option holders). B is partially true for deep ITM options but not a general rule. D is wrong — vega diminishes for deep ITM or OTM options.
Question 23
A straddle is said to be 'long volatility.' Which combination of Greeks BEST describes the risk profile of a long straddle?
Select an option first.
Correct answer: B — Near-zero delta, positive gamma, positive vega, negative theta
Explanation: B is correct: A long straddle (long call + long put, same strike) when ATM has: (1) near-zero delta — the positive call delta and negative put delta approximately cancel; (2) positive gamma — both long options have positive gamma; (3) positive vega — both long options benefit from rising volatility; (4) negative theta — both long options lose time value as expiration approaches. The reading specifically notes the straddle can be 'delta-neutral but vega-positive.' B captures all four correctly.
Question 24
A collar consists of:
Select an option first.
Correct answer: C — A long stock position plus a long put plus a short call
Explanation: C is correct: A collar combines a protective put (long put to hedge downside) and a covered call (short call to sell off upside and partially finance the put). The result is a bounded range for gains and losses — the collar 'collars' the return distribution between the put and call strikes. A is a long straddle. B has the call/put directions wrong. D involves a short stock position.
Question 25
A zero-cost collar is created when:
Select an option first.
Correct answer: B — The put premium equals the call premium, creating no net initial outflow
Explanation: B is correct: A zero-cost collar occurs when the call strike is selected such that its premium matches the put premium. For example, buying a $50 put for $4.88 and selling a $55.87 call for $4.88 creates zero net cost. In practice, for OTC options this is achieved by adjusting the call strike until premiums balance. The collar limits the range of outcomes with no initial cash outflow. A confuses low premium with zero cost. C relates to stock cost basis, not option premiums. D would be a short straddle.
Question 26
For a zero-cost collar on stock initially at $52.14, with a long $50 put and short $55.87 call, what is the maximum profit and maximum loss at expiration?
Select an option first.
Correct answer: B — Max profit = $3.73; Max loss = $2.14
Explanation: B is correct: Max profit = call strike − initial stock price = $55.87 − $52.14 = $3.73 (the stock gain is capped at the call strike). Max loss = initial stock price − put strike = $52.14 − $50 = $2.14 (the downside is floored at the put strike). With a zero-cost collar, no net premium changes the breakeven — it remains the initial stock price of $52.14. C has unlimited upside which is wrong (upside is capped). D has unlimited downside which is wrong (put limits downside).
Question 27
An investor buys a straddle: a call with exercise price $45 and premium $3, plus a put with the same exercise price $45 and premium $2. What is the MAXIMUM LOSS and the BREAKEVEN price(s)?
Select an option first.
Correct answer: A — Max loss = $5; Breakevens = $40 and $50
Explanation: A is correct: Long straddle: Max loss = total premium paid = $3 + $2 = $5 (occurs if stock expires exactly at strike). Breakeven prices = strike ± total premium = $45 ± $5 = $40 and $50. Below $40, the put value exceeds total premium. Above $50, the call value exceeds total premium. C uses wrong breakeven values. B understates max loss. D is incorrect on both.
Question 28
A SHORT straddle has which profit profile at expiration?
Select an option first.
Correct answer: B — Maximum profit equals the total premium received, achieved when the stock expires at the strike
Explanation: B is correct: The short straddle (sell call + sell put, same strike) collects premium upfront. It makes the most profit when the stock expires exactly at the strike (both options worthless) — profit equals total premium received. As the stock moves away from the strike in either direction, the short call or short put goes ITM, reducing profit or creating loss. A describes the long straddle. C is incorrect — as stock falls, the short put creates increasingly large losses. D is incorrect — the strategy is symmetric.
Question 29
A long straddle is described as a 'bet on volatility.' What is the PRIMARY condition needed for a long straddle to profit if held to expiration?
Select an option first.
Correct answer: B — The underlying must end up far enough from the strike to cover both premiums paid
Explanation: B is correct: At expiration, the long straddle profits when one option (either the call or put) has intrinsic value exceeding the total premiums paid for both. The stock must move more than the total premium above the call breakeven or below the put breakeven. A describes the condition for a short straddle to profit. C is relevant pre-expiration (vega effect) but not the condition at expiration. D is impossible — at expiration only one option can be ITM (not both, unless stock is exactly at strike).
Question 30
An investor buys a bull call spread: long $45 call for $2.10, short $50 call for $0.50. What is the maximum profit, maximum loss, and breakeven?
Select an option first.
Correct answer: A — Max profit = $3.40; Max loss = $1.60; Breakeven = $46.60
Explanation: A is correct: Bull call spread (debit spread): Net premium paid = $2.10 − $0.50 = $1.60 = Maximum loss. Difference between strikes = $50 − $45 = $5. Maximum profit = $5 − $1.60 = $3.40. Breakeven = lower strike + net premium = $45 + $1.60 = $46.60. B and D overstate the max loss using only the long call premium. C has the wrong max profit ($2.80 would need different strike spread or premiums).
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