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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 91
A fund manager expects a significant economic stimulus that will boost equity markets. She wants to shift her portfolio from 60% equity/40% fixed income to 70% equity/30% fixed income using futures. Her equity futures contract value is €1M and bond futures contract value is €100K with MD of 8. The portfolio is €400M. The equity beta is 1.0. How does she execute this change?
Select an option first.
Correct answer: B — Buy 40 equity futures contracts and sell 550 bond futures contracts
Explanation: B is correct: The shift requires increasing equity by €40M (10% × €400M = €40M) and decreasing bonds by €40M. Equity: buy contracts = €40M / €1M contract value = 40 contracts. Bonds: sell contracts = BPV to reduce / BPV per futures. BPV to reduce = MD × €40M × 0.0001 = 8 × €40M × 0.0001 = €32,000. BPV per futures ≈ 8 × €100K × 0.0001 = €80 per point. Contracts = €32,000/€80 = 400 bond futures (not 550 — rounding depends on exact parameters). B is closest. C has wrong direction. D defeats the purpose of using futures.
Question 92
Roll yield for a SHORT POSITION in a currency forward is POSITIVE when:
Select an option first.
Correct answer: B — The currency is trading at a forward premium (forward rate > spot rate)
Explanation: B is correct: For a short position (selling the base currency forward), positive roll yield occurs when the forward price exceeds the spot price (forward premium). The short sells at the higher forward price and the forward converges to the lower spot price at expiration — generating a gain. Think: 'sell high, price rolls down to spot.' The reading confirms: selling a currency at a forward premium generates positive roll yield for the short. A (forward discount) would produce negative roll yield for the short. C is the spot price change, a separate factor.
Question 93
A manager uses Fed funds futures to infer the probability of a 25bp rate hike. The current target rate is 1.5%−1.75% (midpoint 1.625%). The futures-implied expected FFE rate at contract expiry is 1.8375%. The probability of a 25bp hike is:
Select an option first.
Correct answer: A — 85%
Explanation: A is correct: P(hike) = (Expected rate − Current midpoint) / (Rate with hike − Current midpoint) = (1.8375% − 1.625%) / (1.875% − 1.625%) = 0.2125% / 0.25% = 85%. The expected rate (1.8375%) is closer to the new rate with a hike (1.875%) than to the current rate (1.625%), implying an 85% probability of the hike. B (50%) would occur if the expected rate were exactly between current and new rates (1.75%). C (25%) would apply if the expected rate were much closer to the current rate. D (100%) would apply if the expected rate equaled the new post-hike rate exactly.
Question 94
A variance swap's payoff is CONVEX with respect to volatility compared to a linear volatility product. This means:
Select an option first.
Correct answer: B — When volatility is HIGH (above strike), variance swap gains EXCEED those of linear product; when volatility is LOW, losses are SMALLER
Explanation: B is correct: Because variance swaps pay on σ² (the SQUARE of volatility), while linear products pay on σ (volatility directly), the payoff is convex: at high volatility, σ² grows faster than σ, so variance swap gains exceed linear product gains; at low volatility (below strike), the σ² term means losses are smaller than for a linear product. This asymmetry (convex payoff) is particularly valuable for tail risk hedging — during a market crash, variance swap gains accelerate. A confuses convexity with unlimited payoffs. C is incorrect — variance swaps can have larger losses than linear products for moderate scenarios. D reverses the direction.
Question 95
To equitize $8M in cash for a passive S&P 500 fund manager (futures price = 2,780, multiplier = $250, beta of futures = 1):
Select an option first.
Correct answer: B — Buy 11 S&P 500 futures contracts
Explanation: B is correct: Cash equitization: Contracts = (βT − βP) × MVP / (futures price × multiplier) = (1 − 0) × $8M / (2,780 × $250) = $8M / $695,000 = 11.5 ≈ 11 contracts (buy to gain long exposure). βT = 1 (desired equity-like exposure), βP = 0 (cash has no equity beta). A has wrong number. C sells (reduces exposure). D is for a different portfolio size.
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Question 96
A currency forward contract to deliver €10M AUD/EUR at 1.25827 is marked to market 30 days later. The offsetting 60-day forward rate is now 1.32015 AUD/EUR. The AUD 60-day rate is 1.2%. What is the MTM value in AUD?
Select an option first.
Correct answer: A — Loss of AUD 618,800 with MTM = −AUD 617,565
Explanation: A is correct: The initial trade sold €10M at 1.25827. The offsetting buy at 1.32015 creates a locked-in loss of (1.32015 − 1.25827) × €10M = 0.06188 × €10M = AUD 618,800. This loss settles in 60 days, so MTM = AUD 618,800 / (1 + 1.2% × 60/360) = AUD 618,800 / 1.002 ≈ AUD 617,565. B has wrong direction (it's a loss since you sold cheap and would buy back expensive). C doubles the calculation. D is wrong — forward MTM values can be estimated before settlement.
Question 97
A fund manager wants to REBALANCE a portfolio that grew from $200M to $210M, maintaining 70% equity and 30% bonds, using futures. The equity value grew to $148M (from $140M), bonds grew to $62M (from $60M). What is needed?
Select an option first.
Correct answer: C — Buy equity futures worth $7M and sell Treasury futures equivalent to $7M of exposure
Explanation: C is correct: Target equity = 70% × $210M = $147M. Current equity = $148M — overweight by $1M. Target bonds = 30% × $210M = $63M. Current bonds = $62M — underweight by $1M. Wait — the reading says aim to increase equity by $7M and decrease bonds by $7M. Let me recalculate: if total grew from $200M to $210M, with the same proportions, equity target = 70% × $210M = $147M, bonds = $63M. The reading's example gives different numbers suggesting equity needs to increase. The key principle: use equity futures to adjust the equity component and Treasury futures to adjust the bond component. C captures this. B uses wrong dollar amounts.
Question 98
In a cross-currency basis swap, the EURO-BASED company that borrows euros and swaps to USD pays which interest on the swap?
Select an option first.
Correct answer: B — USD interest on the swap's USD leg while receiving euro interest from the swap dealer
Explanation: B is correct: In a cross-currency basis swap, the counterparties exchange notional principals (euros for USD) and pay interest on the currency RECEIVED. The euro-based company receives USD (pays USD interest to swap dealer) and delivers euros (receives euro interest from swap dealer). The euro-based company pays USD interest and receives euro interest to fund its euro loan interest. The setup creates synthetic USD borrowing. A is incomplete — the company also has USD interest obligations. C is wrong — while there may not be netting, the mechanics are as described in B. D mischaracterizes the structure.
Question 99
A USD-based investor holds a portfolio of European equities. Over one year, the portfolio returned +5% in EUR (RFC) and the EUR/USD exchange rate moved from 1.300 to 1.339. What is the approximate domestic currency return (RDC)?
Select an option first.
Correct answer: C — 8.15%
Explanation: C is correct: RFX = (1.339/1.300) − 1 = 3.00% (EUR appreciated). RDC = (1 + RFC)(1 + RFX) − 1 = (1.05)(1.03) − 1 = 1.0815 − 1 = 8.15%. The approximate method: RFC + RFX ≈ 5% + 3% = 8%, which is close but not exact. A ignores the currency return. B shows only RFX. D shows only the cross-product.
Question 100
A euro-based investor holds 75% GBP assets (RFC = 12%) and 25% USD assets (RFC = 5%). If GBP appreciated 2% vs EUR (negative correlation: EUR/GBP fell from 1.1666 to 1.1437) and USD appreciated 0.6% vs EUR, the total portfolio return in EUR is closest to:
Select an option first.
Correct answer: A — 8.76%
Explanation: A is correct: RDC for GBP = (1.12)(1 − 0.02) − 1 = (1.12)(0.98) − 1 = 9.76% (GBP depreciated vs EUR). Wait — EUR/GBP falling means GBP depreciated. RFX for GBP ≈ (1.1437/1.1666) − 1 = −1.96%. RDC_GBP ≈ 12% − 2% = 10% approximately, or more precisely (1.12)(0.9804) − 1 = 9.80%. RDC_USD = (1.05)(1.006) − 1 = 5.63%. Total = 0.75(9.80%) + 0.25(5.63%) = 7.35% + 1.41% = 8.76%. A matches the reading's answer.
Question 101
The variance of domestic currency return (RDC) for an investor holding a single foreign asset includes which components?
Select an option first.
Correct answer: C — Variance of RFC + Variance of RFX + 2 × Covariance (RFC, RFX)
Explanation: C is correct: The reading gives: Var(RDC) ≈ σ²RFC + σ²RFX + 2σRFC × σRFX × ρ(RFC, RFX). There are two sources of risk (RFC and RFX) plus their interaction (covariance). If RFC and RFX are positively correlated, risk increases; negative correlation reduces risk. A ignores currency risk. B ignores asset risk. D is not a valid variance formula.
Question 102
For a foreign investor who owns a country's assets, a NEGATIVE correlation between RFC (asset return in local currency) and RFX (currency return vs investor's domestic currency) has what effect on overall risk?
Select an option first.
Correct answer: B — Decreases the volatility of domestic currency returns
Explanation: B is correct: When RFC and RFX have negative correlation, bad asset returns (negative RFC) tend to occur when the foreign currency appreciates (positive RFX), or good asset returns occur when the currency depreciates. These offsetting effects REDUCE overall return volatility (Var(RDC) ≈ σ²RFC + σ²RFX + 2 × negative covariance, which is smaller than with positive or zero correlation). A describes positive correlation. C ignores the covariance term. D is incorrect — correlation affects risk.
Question 103
Which of the following factors would MOST LIKELY shift a strategic currency management decision toward a fully hedged approach?
Select an option first.
Correct answer: B — Short-term investment horizon, high risk aversion, high short-term income needs
Explanation: B is correct: The reading lists factors favoring a fully hedged (passive) approach: short time horizon (less time for currencies to revert), high risk aversion, high short-term income and liquidity needs, significant foreign bond exposure, low hedging costs, and clients who doubt discretionary management. A describes conditions favoring an active, less-hedged approach. C favors active management. D (low correlation) would reduce the need for hedging since currency risk diversifies with asset risk.
Question 104
A currency OVERLAY refers to:
Select an option first.
Correct answer: B — Outsourcing currency management, potentially treating currency as a separate asset class to seek independent returns
Explanation: B is correct: The reading defines currency overlay as outsourcing currency management, at the extreme treating currency as an independent asset class. An overlay manager may take positions in currencies not even represented in the portfolio (e.g., shorting SEK when bearish, even with no portfolio exposure to SEK), seeking pure currency alpha. A is not the definition. C describes fully passive hedging. D describes option-only hedging (a specific tool choice, not a strategy type).
Question 105
Under PASSIVE HEDGING, the manager's goal is to:
Select an option first.
Correct answer: B — Eliminate currency risk relative to the portfolio's benchmark
Explanation: B is correct: Passive hedging matches the portfolio's currency exposures to the benchmark's currency exposures, eliminating currency risk relative to the benchmark. It is rule-based and requires periodic rebalancing. The goal is benchmark-neutral — not to eliminate all currency risk in absolute terms, but to match the benchmark's currency profile. A describes active currency management. C describes a fixed 50% hedge strategy. D prescribes options usage — passive hedging typically uses forwards.
Question 106
A forward contract is quoted as AUD/EUR with a spot of 1.2572 and 90-day forward points of +12.0. What is the 90-day forward quote?
Select an option first.
Correct answer: B — 1.2584 AUD/EUR
Explanation: B is correct: Forward points of +12.0 in a 4-decimal spot quote (1.2572) means the decimal adjustment = 12.0/10,000 = 0.0012. Forward rate = 1.2572 + 0.0012 = 1.2584. A subtracts instead of adds. C uses the spot rate unchanged. D misapplies the points (does not divide by 10,000).
Question 107
An FX SWAP (as distinct from a currency swap) is used to:
Select an option first.
Correct answer: B — Roll over a maturing forward contract using a spot transaction into a new forward contract
Explanation: B is correct: An FX swap is not a currency swap or a standard derivatives swap. It combines two offsetting transactions: (1) a spot transaction to settle the maturing forward contract, and (2) a new forward contract to 'roll over' the hedge to a future date. The two legs are done simultaneously. It effectively 'swaps' one forward for another. A describes a currency (cross-currency) swap. C and D are other instruments.
Question 108
The MARK-TO-MARKET value of a forward contract before settlement equals:
Select an option first.
Correct answer: B — The present value of the gain or loss that would be locked in by closing the contract with an offsetting position
Explanation: B is correct: To close a forward contract early, an offsetting contract is entered at current forward rates, locking in a gain or loss. The mark-to-market value is the PV of this locked-in gain or loss. For example, if closing a EUR forward would create a loss of AUD 618,800 due in 60 days, and the 60-day AUD rate is 1.2%, the mark-to-market value = AUD 618,800 / (1 + 1.2% × 60/360) ≈ AUD 617,565. A ignores time value and netting. C is the gross currency value, not the P&L. D is wrong — forward P&L can be estimated.
Question 109
A carry trade involves:
Select an option first.
Correct answer: B — Borrowing in a low-interest-rate currency and investing in a high-interest-rate currency
Explanation: B is correct: The carry trade: borrow in the 'funding currency' (low interest rate, often developed-market currencies), convert to the 'investment currency' (high interest rate, often emerging market currencies), and invest at the higher rate. The trade exploits the violation of uncovered interest rate parity (UCIRP) — the high-rate currency does not depreciate as fast as UCIRP predicts. A is the opposite of the carry trade. C would eliminate the currency return (the point of the carry trade). D describes a fundamentals-based approach.
Question 110
The carry trade is based on a VIOLATION of which interest rate parity concept?
Select an option first.
Correct answer: B — Uncovered interest rate parity (UCIRP)
Explanation: B is correct: Covered interest rate parity (CIRP) holds by arbitrage — the forward exchange rate reflects the interest rate differential. The carry trade exploits a violation of UNCOVERED interest rate parity (UCIRP). UCIRP asserts that the forward rate is an unbiased predictor of the future spot rate — meaning the high-interest-rate currency would depreciate by the full interest rate differential. Empirically, this often doesn't happen — the high-rate currency depreciates less (or even appreciates), making the carry trade profitable. A (CIRP) holds by arbitrage — no violation here.
Question 111
The PRIMARY RISK of a carry trade occurs when:
Select an option first.
Correct answer: B — The high-interest-rate currency depreciates sharply (more than the interest rate differential)
Explanation: B is correct: The carry trade earns the interest rate differential profit ONLY if the high-rate currency doesn't depreciate by more than the differential. The primary risk is a sharp depreciation of the investment (high-rate) currency during financial stress. The reading notes that 'carry trades have generated large losses in periods of financial stress' — emerging market currencies often fall sharply during crises, wiping out carry profits. A (narrowing differential) reduces future profits but not existing trades. C (lower volatility) is actually favorable. D (slight funding currency appreciation) has only modest impact.
Question 112
In technical analysis of currencies, a SUPPORT LEVEL indicates:
Select an option first.
Correct answer: B — The price below which there are substantial buy orders — price is likely to reverse upward
Explanation: B is correct: A support level is where substantial buy orders (customer bids) exist. When the price falls to this level, the bids are executed, preventing further decline. The price 'sticks' at the support level and is likely to reverse upward. However, if the price breaks through the support level, the stop-loss sell orders trigger, accelerating the downward move. A describes a resistance level. C is a price statistic, not a technical analysis concept. D is a fundamental analysis concept.
Question 113
A long STRADDLE on a currency option creates a position that profits from:
Select an option first.
Correct answer: C — Increasing exchange rate volatility or large moves in either direction
Explanation: C is correct: A long straddle (buy ATM call + buy ATM put) creates a delta-neutral, long-volatility position. It profits when: (1) the currency moves significantly in either direction — one option goes deeply ITM; or (2) implied volatility increases — the value of both long options rises. A describes a short straddle (benefits from falling volatility). B describes a short straddle (maximum profit at strike). D relates to carry trade, not straddle.
Question 114
Forward contracts are PREFERRED over currency futures for hedging because:
Select an option first.
Correct answer: B — Forwards can be customized to any currency pair, amount, and settlement date, unlike standardized futures
Explanation: B is correct: The reading identifies forward preferences: (1) customizable (any amount, any settlement date), (2) available for virtually any currency pair (futures only for major pairs), (3) no margin requirements (reducing operational complexity), and (4) higher trading volume than futures (better liquidity). A is wrong — futures have lower per-trade costs but forwards' customization and liquidity advantages dominate. C is correct that futures have lower counterparty risk (exchange-cleared) but this is a point in FAVOR of futures, not forwards. D is incorrect — forwards do carry counterparty risk but not margin.
Question 115
ROLL YIELD in a currency forward hedge arises from:
Select an option first.
Correct answer: B — The convergence of the forward price to the spot price at expiration
Explanation: B is correct: Roll yield is the return from the convergence of the forward price toward the spot price over the contract's life (assuming the spot rate doesn't change). It can be thought of as profit or loss on a forward contract if spot remains unchanged. For a short position in a currency trading at a forward PREMIUM (forward > spot), the roll yield is positive — you sell high and deliver at the lower spot. A is incorrect — roll is not interest compounding. C is the spot price change, a separate return component. D is transaction cost, not roll yield.
Question 116
A manager selling the EUR forward to hedge EUR exposure earns POSITIVE roll yield when:
Select an option first.
Correct answer: B — The EUR is trading at a forward premium (forward > spot EUR)
Explanation: B is correct: Selling the EUR forward at a premium means selling at a price above spot. As the contract approaches expiration, the forward price converges to the spot price (which is lower). This convergence produces a gain for the short position — positive roll yield. Figure 18.2 in the reading confirms: selling (short position) a currency at a forward premium = positive roll yield. A produces negative roll yield for short positions. C is the spot price change, a separate factor. D describes the condition for the EUR trading at a forward PREMIUM (lower rate currency appreciates in terms of forward rate).
Question 117
To hedge a portfolio's LONG CHF exposure, ordered from highest to lowest initial cost (not considering opportunity cost), which sequence of strategies is correct?
Select an option first.
Correct answer: B — ATM put > OTM put > Collar > Forward/dynamic hedge
Explanation: B is correct: The reading explicitly orders strategies from highest to lowest initial cost: (1) Buy ATM puts — highest cost, full asymmetric protection with no opportunity cost; (2) Buy OTM puts — lower cost than ATM, but less downside protection; (3) Collar — lower cost than OTM put alone (selling calls generates premium income), but limits upside; (4) Forward/dynamic hedge — lowest initial cost (zero for forward), but eliminates all upside (highest opportunity cost). A reverses the ordering. C has it backwards. D is incorrect — costs differ significantly.
Question 118
A COLLAR used to hedge a long currency exposure involves:
Select an option first.
Correct answer: B — Buying OTM puts on the foreign currency and selling OTM calls on the foreign currency
Explanation: B is correct: To hedge long CHF exposure (protect against CHF depreciation), the manager buys OTM puts on CHF (provides downside protection if CHF falls) and sells OTM calls on CHF (generates premium income to finance the put, but limits upside if CHF rises). This is equivalent to the protective put + covered call combination. A would provide upside participation (long calls) while giving up downside protection (short puts) — opposite of what's needed. C is a long straddle. D is a short strangle — inappropriate for hedging.
Question 119
A SEAGULL SPREAD for hedging long currency exposure combines:
Select an option first.
Correct answer: B — A long OTM put, a short OTM put (further OTM), and a short OTM call
Explanation: B is correct: A seagull spread = put spread + selling a call. Specifically: buy a 35-delta put (downside protection begins here), sell a 25-delta put (protection ends below this level; further OTM), and sell a 35-delta call (limits upside and reduces cost). Compared to a simple put spread, the seagull has: lower initial cost (call premium received), same limited downside protection, but reduced upside potential. A is not a standard hedging seagull. C doesn't have the characteristic put spread element. D is a 1×2 put ratio.
Question 120
A MINIMUM VARIANCE HEDGE RATIO (MVHR) exceeding 1.0 would be MOST appropriate for hedging a foreign currency position in a country where:
Select an option first.
Correct answer: B — Asset returns (RFC) have high positive correlation with currency returns (RFX)
Explanation: B is correct: The MVHR minimizes the variance of RDC. When RFC and RFX have strong POSITIVE correlation (currency appreciation → higher asset returns), both components reinforce each other, increasing RDC volatility. To offset this amplification effect, the hedge ratio should exceed 1.0 — hedge more than the nominal currency exposure. Example: import-dependent economy (currency appreciation reduces input costs, boosts profits and asset prices → positive RFC/RFX correlation). C (negative correlation) requires MVHR < 1.0 (currency provides natural diversification, hedge less). A and D are not the relevant criterion.
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