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Free CFA Derivatives and Risk Management Practice Questions & Answers
150 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 31
A bear put spread involves:
Select an option first.
Correct answer: B — Long higher-strike put + short lower-strike put; net premium outflow
Explanation: B is correct: A bear put spread: long the higher-strike put (more valuable, since puts gain value as strike rises) and short the lower-strike put (less valuable). Since the long option is more valuable, there is a net premium outflow — it is a debit spread. This creates a bearish, but capped, exposure. Max loss = net premium paid. Max profit = difference between strikes minus net premium. Breakeven = higher strike − net premium. A has the strikes reversed. C is a bear call spread (credit spread). D is a bull put spread.
Question 32
Which of the following statements about CREDIT SPREADS (bear call spread, bull put spread) is MOST accurate?
Select an option first.
Correct answer: B — The maximum profit for a credit spread equals the net premium received
Explanation: B is correct: Credit spreads (bear call spread and bull put spread) receive a net premium at initiation — this is the maximum profit. Maximum loss = difference between strikes − net premium received. For a bear call spread: max profit at or below lower strike; for a bull put spread: max profit at or above higher strike. A has it backwards — credit spreads receive premium (inflow). C is wrong — neither type is always preferable; selection depends on market view. D is wrong — max loss is capped at strike difference minus premium.
Question 33
For both call and put spreads, the breakeven price is found using which formula?
Select an option first.
Correct answer: B — For call spreads: lower strike + net premium; For put spreads: higher strike − net premium
Explanation: B is correct: The breakeven rules for spreads: Bull call spread (debit): breakeven = lower strike + net premium paid. Bear put spread (debit): breakeven = higher strike − net premium paid. For credit spreads: Bear call spread: breakeven = lower strike + net premium received. Bull put spread: breakeven = higher strike − net premium received. In both cases, call spreads use lower strike + net premium, and put spreads use higher strike − net premium. A has the formulas reversed. C and D apply only one formula to all spreads.
Question 34
A stock trades at $51. A bear spread using calls has a short $47 call priced at $5.25 and a long $53 call priced at $0.75. What is the initial investment (cash flow) and the breakeven price?
Select an option first.
Correct answer: A — Initial inflow of $4.50; Breakeven = $51.50
Explanation: A is correct: Bear call spread: sell lower strike ($47 call at $5.25) and buy higher strike ($53 call at $0.75). Net initial inflow = $5.25 − $0.75 = $4.50 (credit spread). Breakeven = lower strike + net premium received = $47 + $4.50 = $51.50. Maximum profit = $4.50 (achieved at $47 and below). Maximum loss = ($53 − $47) − $4.50 = $1.50 (at $53 and above). B incorrectly identifies as outflow. C has wrong breakeven. D has wrong calculations.
Question 35
A LONG calendar spread involves:
Select an option first.
Correct answer: B — Buying a longer-dated option and selling a shorter-dated option with the same strike
Explanation: B is correct: A long calendar spread buys the longer-dated option and sells the shorter-dated option with the same strike and underlying. The rationale is that the shorter-dated ATM option has a higher (more negative) theta — it loses value more rapidly as expiration approaches. Thus, the short position gains more than the long position loses, creating a net profit when the underlying remains near the strike. A is a short calendar spread. C describes a strangle. D describes a spread between strikes (bull or bear spread).
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Question 36
A long calendar spread is MOST profitable when:
Select an option first.
Correct answer: B — The underlying remains near the strike at expiration of the short-dated option
Explanation: B is correct: A long calendar spread profits when: (1) the underlying stays near the strike — ATM options have the highest (most negative) theta, so the shorter-dated short option loses value faster than the longer-dated long option; and (2) implied volatility increases — which boosts the remaining long option's value. Large moves hurt the strategy (the long option's time value falls if it moves far OTM or far ITM). C is incorrect — falling implied volatility hurts the long (longer-dated) option. D is also incorrect — deeply ITM options have high intrinsic value but low theta advantage.
Question 37
Why would a bearish investor use PUTS rather than calls to construct a calendar spread?
Select an option first.
Correct answer: C — After the short-dated option expires, the investor is left with a long put, consistent with their bearish view
Explanation: C is correct: The reading explains that an investor who has a long-term bearish view would use puts in the calendar spread so that, when the near-dated short put expires, they retain a long put position that benefits from a subsequent fall in the underlying. Using calls would leave the investor long a call, which is inconsistent with a long-term bearish outlook. A is incorrect — the choice between calls and puts in calendar spreads is driven by directional view, not cost. B is incorrect — theta depends on moneyness and time, not call vs. put.
Question 38
A 'volatility skew' in equity options MOST commonly describes which pattern of implied volatility?
Select an option first.
Correct answer: B — Higher implied volatility for OTM puts and lower for OTM calls
Explanation: B is correct: Volatility skew describes the empirically common pattern where OTM puts have higher implied volatility than OTM calls. This is explained by high demand for OTM puts as insurance against market declines, bidding up their prices (and implied volatility). OTM calls have lower demand (and lower implied volatility). The reading notes this is more common than the volatility smile. C is the less common situation indicating bullish sentiment. A and D do not describe typical patterns.
Question 39
A sharp increase in the volatility skew, combined with a surge in absolute implied volatility levels, MOST likely indicates:
Select an option first.
Correct answer: B — Bearish market sentiment turning, with increasing demand for OTM puts
Explanation: B is correct: The reading states that 'a sharp increase in the level of the skew, plus a surge in the absolute level of implied volatility, is an indicator that market sentiment is turning bearish.' Higher skew means put implied volatility is rising faster than call implied volatility — investors are paying more for downside insurance. The surge in overall volatility reflects increased uncertainty and fear. A is opposite — bearish sentiment, not bullish. C is wrong — high demand drives up prices and implied volatility. D is not supported by the text.
Question 40
The term structure of volatility describes:
Select an option first.
Correct answer: B — The variation of implied volatility across different option maturities
Explanation: B is correct: The term structure of volatility shows how implied volatility varies across different option maturities for a fixed underlying — it is the 'maturity dimension' of implied volatility. Contango in volatility term structure (longer-dated options having higher implied volatility) is common when current volatility is low. A describes the volatility smile/skew (cross-sectional by strike). C describes the volatility risk premium. D describes historical/realized volatility.
Question 41
An investor believes a stock will fall by up to 10% in one week and wants downside protection at minimum cost. Among several put options, the BEST selection maximizes the ratio of:
Select an option first.
Correct answer: B — Expected profit to cost (assuming the anticipated price move occurs)
Explanation: B is correct: The reading's application example explains that when selecting a protective put for a short holding period (not held to expiration), the relevant metric is how the put value changes if the anticipated price decline occurs. The best put maximizes the ratio of expected profit to cost — this selects the put that delivers the most gain per dollar of premium paid. Delta and gamma are also relevant because the put will be closed (not held to expiration). A is not the right metric. C and D are not meaningful selection criteria for this purpose.
Question 42
A client holds a stock with a very low cost basis, making outright sale impractical due to tax consequences. The client needs downside protection. Which strategy is MOST appropriate?
Select an option first.
Correct answer: B — Implement a zero-cost collar: buy OTM puts and sell OTM calls
Explanation: B is correct: The reading's collar application scenario describes this exact situation: 'A client has a long position in a low cost basis stock, which means that selling is ruled out. Need to protect against a decline in price.' The solution is a zero-cost collar — buying puts eliminates the left tail (large losses) while selling calls finances the put purchase. A generates income but doesn't prevent large losses. C requires selling the stock (tax-inefficient). D adds upside exposure when the goal is protection.
Question 43
A fund manager expects little price movement in the Euro Stoxx 50 over the next month but has a long-term bearish view. Which strategy is MOST appropriate?
Select an option first.
Correct answer: B — Long calendar spread using puts — sell three-month put, buy six-month put
Explanation: B is correct: This matches the reading's calendar spread application scenario. The investor has: (1) short-term neutral view → sell the near-dated put to benefit from the higher theta; (2) long-term bearish view → stay long the longer-dated put so after the near-dated expires, a long put remains. A (long straddle) requires a large price move. C (short straddle) profits from no movement but has unlimited risk and doesn't provide bearish long-term position. D doesn't exploit the short-term stability.
Question 44
A short position in NAKED CALLS can be hedged by:
Select an option first.
Correct answer: B — Buying the underlying asset
Explanation: B is correct: A naked (uncovered) call creates unlimited upside risk — if the stock rises, the short call must be covered at increasingly high prices. Buying the underlying stock converts the naked call into a covered call, eliminating this unlimited risk. If the stock rises, the gain on the long stock offsets the loss on the short call. A (long put) adds downside protection but doesn't hedge the call's upside risk directly. C adds more short call exposure. D (long forward) would add positive exposure that offsets the short call's negative exposure — this could work but buying the underlying is simpler.
Question 45
An investor wants exposure to an expected stock price rise from £60 to £70 without owning the stock. Among several three-month call options, the BEST choice MAXIMIZES which ratio?
Select an option first.
Correct answer: B — Expected profit to initial investment cost
Explanation: B is correct: The reading's 'long calls as a proxy' application scenario evaluates calls based on maximizing 'the ratio of expected profit to cost (assuming the stock rises to £70).' This selects the call with the best return on capital invested. Any call where breakeven (strike + premium) exceeds £70 is automatically ruled out. The reading also notes delta and gamma matter if the position may be closed before expiration rather than held to expiry. A, C, and D are not the primary selection criteria in the reading.
Question 46
Before expiration, both a covered call and a protective put have positive deltas. This is MOST consistent with which statement?
Select an option first.
Correct answer: B — Both strategies reduce but do not eliminate the delta of the long underlying position
Explanation: B is correct: The reading (LOS 16.d) explicitly states that 'the effect of the covered call and protective put, during the option's life, is to reduce the asset's delta, but not eliminate it.' Both written calls (negative delta) and purchased puts (negative delta) reduce the overall portfolio delta from +1 toward lower values, but since option deltas are between 0 and 1, they cannot fully offset the stock's +1 delta. A is wrong — short forward would be needed to reduce delta to zero. C and D are not supported — the specific deltas depend on option moneyness.
Question 47
A short call position has delta of −0.55. What is the POSITION delta for 10 option contracts (each on 100 shares)?
Select an option first.
Correct answer: B — −550
Explanation: B is correct: Position delta = number of contracts × shares per contract × option delta = 10 × 100 × (−0.55) = −550. A incorrectly multiplies by 100 again. C ignores the 100 multiplier. D reverses the sign (would be long position).
Question 48
The options market exhibits a volatility SMILE when:
Select an option first.
Correct answer: C — Options further from ATM (both OTM puts and OTM calls) have higher implied volatility than ATM options
Explanation: C is correct: A volatility smile produces a U-shaped (smiling) curve when implied volatility is plotted against strike price — both OTM puts and OTM calls have higher implied volatility than ATM options. This is less common than volatility skew. A describes volatility skew. B is the opposite of a smile (ATM lower, not higher). D describes the term structure of volatility.
Question 49
A delta hedge is needed because a long risk reversal (long OTM call, short OTM put) has net long exposure to the underlying. If the risk reversal has a delta of 0.3 and involves 1,000 shares worth of options, how many shares must be sold to create a delta-neutral position?
Select an option first.
Correct answer: B — 300 shares
Explanation: B is correct: Delta-neutral hedge: shares to sell = portfolio delta × shares per option = 0.3 × 1,000 = 300 shares. The short stock position (delta = −300) offsets the risk reversal's long delta (+300). A uses 10% of the exposure. D would fully short the stock position. C = 1,000 − 300 = 700, which is wrong.
Question 50
An implied volatility surface uses which axes to display implied volatility information?
Select an option first.
Correct answer: B — X-axis: maturity; Y-axis: strike price; Z-axis: implied volatility
Explanation: B is correct: An implied volatility surface is a three-dimensional graph showing: X-axis = maturity (term structure dimension), Y-axis = strike price (skew/smile dimension), Z-axis = implied volatility. It captures both the term structure of volatility and the volatility skew/smile simultaneously for a given underlying.
Question 51
A parity diagram for a long straddle at expiration shows a V-shape centered on the strike. Which statement about the VALUE LINE (before considering premium) is MOST accurate?
Select an option first.
Correct answer: B — The value line shows positive value for all stock prices except exactly at the strike
Explanation: B is correct: At expiration, one of the two options — either the call or the put — will always be ITM for any stock price except exactly at the strike. Above the strike, the call has positive value. Below the strike, the put has positive value. Only when the stock expires exactly at the strike do both options expire worthless, giving zero total value. This creates the characteristic V-shape with the trough (zero value) at the strike.
Question 52
Which of the following is a key RISK of writing a bear call spread using American-style options?
Select an option first.
Correct answer: B — The short call could go ITM while the long call is still OTM, with early exercise by the counterparty
Explanation: B is correct: The reading warns that with American-style options in credit spreads, there is a risk that the short call (lower strike) goes ITM early while the long call (higher strike) is still OTM. If the counterparty exercises the short call early, the spread writer must deliver the stock at the lower strike but cannot yet exercise their own call. This disrupts the strategy. A has it wrong — only the short call can be exercised against you (the long call is exercised by you, at your discretion). C is the risk for the long call buyer, not the spread.
Question 53
A collar established on a stock position with a LONG time to expiration differs from one near expiration. Pre-expiry, the collar MOST LIKELY:
Select an option first.
Correct answer: B — Considerably dampens the variability (delta) of the position compared to unhedged stock
Explanation: B is correct: The reading shows that pre-expiry, the collar 'considerably dampens down the variability of the position (to about 15-20% of its unhedged level).' This is because the short call (negative delta) and long put (negative delta) work together to significantly reduce the net position delta. It doesn't go to zero unless the hedge is a short forward (delta = +1 − 1 = 0). A is incorrect — options give curved, not linear, pre-expiry profiles. C (delta = 0) requires a forward, not a collar. D is wrong — the collar caps upside.
Question 54
A long call position is valued at $6 with the stock at $52. Delta = 0.6, Gamma = 0.05. If the stock rises by $2, the BEST ESTIMATE of the new call value is:
Select an option first.
Correct answer: B — $7.30
Explanation: B is correct: Using delta and gamma adjustment: Change in call value ≈ Delta × ΔS + 0.5 × Gamma × ΔS² = 0.6 × 2 + 0.5 × 0.05 × 4 = 1.20 + 0.10 = $1.30. New value = $6 + $1.30 = $7.30. A uses only delta (0.6 × 2 = 1.20; $6 + $1.20 = $7.20, ignoring gamma). C is incorrect. D uses wrong delta.
Question 55
A European-style option can only be exercised at expiration, while an American-style option can be exercised anytime up to expiration. In practice, how does this distinction typically affect DEEP ITM American call options on non-dividend-paying stocks?
Select an option first.
Correct answer: B — American calls are rarely exercised early because retaining the option retains time value
Explanation: B is correct: For non-dividend-paying stocks, it is generally optimal to NOT exercise an American call early because the option retains time value. Early exercise forfeits that remaining time value. The holder would do better to sell the call in the market (receiving intrinsic + time value) rather than exercise (receiving only intrinsic value). The right to exercise early adds no value for non-dividend-paying stocks. C is wrong — there is no requirement. D is wrong — American ≥ European in value because early exercise is always optional.
Question 56
An investor correctly notes that implied volatility for XYZ options is much higher than historical (realized) volatility. What does this suggest about option pricing?
Select an option first.
Correct answer: B — Options are priced as if the future will be more volatile than it has historically been
Explanation: B is correct: Implied volatility reflects market consensus about future volatility embedded in current option prices. If implied volatility exceeds historical volatility, options are priced for a more volatile future than the historical record suggests. This doesn't mean options are 'wrong' — it means market participants currently expect more future movement. A incorrectly frames 'underpriced' — higher implied vol means higher-priced options. C is not implied — BSM can be used with implied volatility. D is not implied — implied and realized volatility often diverge.
Question 57
A company has issued a floating-rate note (FRN) and is concerned about rising interest rates. Which swap position converts its floating-rate liability to a fixed-rate liability?
Select an option first.
Correct answer: B — Enter a payer swap (pay fixed, receive floating)
Explanation: B is correct: A payer swap (pay fixed, receive floating) offsets the company's floating payments on the FRN. The floating received on the swap cancels the floating paid on the FRN, leaving only the fixed-rate payment on the swap. The company has effectively converted to fixed-rate borrowing. A (receiver swap) does the opposite — it would increase floating exposure. C is an equity swap, not an interest rate swap. D is a different instrument (futures hedge discussed separately).
Question 58
A fund manager wants to INCREASE a portfolio's modified duration. Which swap should be added?
Select an option first.
Correct answer: B — Receiver swap (receive fixed, pay floating)
Explanation: B is correct: A receiver swap (receive fixed, pay floating) replicates holding a fixed-rate bond (receive fixed) while having issued a floating-rate bond (pay floating). Fixed-rate bonds have longer duration than FRNs, so a receiver swap has POSITIVE duration. Adding it increases portfolio duration. A (payer swap) has NEGATIVE duration — it reduces duration because it replicates issuing a fixed-rate bond and buying an FRN. C is wrong — they have opposite effects on duration.
Question 59
The notional principal (NP) of an interest rate swap to achieve a target portfolio duration is calculated as: NP = (MDT − MDP) × VP / MDswap. A portfolio with value £120M, current MD = 4.5, target MD = 6, and a receiver swap with MD = +2. What is the required notional principal?
Select an option first.
Correct answer: B — £90 million
Explanation: B is correct: NP = (MDT − MDP) × VP / MDswap = (6 − 4.5) × £120M / 2 = 1.5 × £120M / 2 = £90M. Receiving fixed (receiver swap) adds positive duration. The NP of £90M at MD of +2 adds 90 × 2 = 180 MD-units to the portfolio's 120 × 4.5 = 540 MD-units, giving (540 + 180)/120 = 6.0 target MD. A = £45M (divides incorrectly). C = £270M (uses wrong formula direction). D = £180M (doesn't divide by MDswap).
Question 60
In an interest rate swap with quarterly settlement dates, what determines the FLOATING PAYMENT at each settlement date?
Select an option first.
Correct answer: A — The floating rate set at the beginning of each settlement period (beginning of the quarter)
Explanation: A is correct: In a standard interest rate swap, the floating payment for each settlement period is determined by the floating rate (MRR) at the BEGINNING of that settlement period. The first floating payment is known at swap initiation. Subsequent payments are determined at the start of each successive settlement period. This 'set in advance, paid in arrears' convention means the rate is set at the beginning of the quarter but paid at the end. B is wrong — the rate is set at the beginning, not end. C is wrong — it resets each period.
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