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Free Questions › FRM › Quantitative Analysis
Free FRM Quantitative Analysis Practice Questions & Answers
400 exam-style Quantitative Analysis questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 121
Regulatory capital arbitrage refers to:
Select an option first.
Correct answer: B — Structuring transactions to minimise regulatory capital requirements without a corresponding reduction in economic risk — exploiting gaps between regulatory capital charges and actual economic risk
Explanation: B
Question 122
Counterparty risk netting and collateral management under Basel III/IV:
Select an option first.
Correct answer: B — Reduce exposure in capital calculations through recognised netting sets and Initial Margin/Variation Margin — with SA-CCR computing EAD as alpha × (RC + PFE) where collateral reduces RC and margining reduces PFE multiplier
Explanation: B
Question 123
The Shapley value in risk allocation provides:
Select an option first.
Correct answer: B — A game-theoretic fair allocation of total portfolio risk to individual components, where each component receives its average marginal contribution to risk across all possible coalition orderings, satisfying efficiency, symmetry, and additivity axioms
Explanation: B
Question 124
The Solvency II framework for European insurers uses:
Select an option first.
Correct answer: B — Value-at-Risk at the 99.5% confidence level over a one-year horizon as the basis for the Solvency Capital Requirement (SCR), measuring the capital needed to survive a 1-in-200 year loss event
Explanation: B
Question 125
Concentration risk in credit portfolios is measured by the:
Select an option first.
Correct answer: A — Herfindahl-Hirschman Index (HHI) or Gini coefficient, which quantify the degree of concentration in a portfolio — a portfolio with equal-sized small exposures has lower concentration risk than one dominated by a few large exposures
Explanation: A
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Question 126
A forward contract is an agreement to:
Select an option first.
Correct answer: B — Buy or sell an asset at a specified future date at a price agreed upon today
Explanation: B
Question 127
The payoff of a long call option at expiration is:
Select an option first.
Correct answer: A — max(S_T - K, 0)
Explanation: A
Question 128
The payoff of a long put option at expiration is:
Select an option first.
Correct answer: B — max(K - S_T, 0)
Explanation: B
Question 129
Put-call parity states that:
Select an option first.
Correct answer: B — P + S = C + PV(K) for European options, linking put and call prices with the underlying and a risk-free bond
Explanation: B
Question 130
A futures contract differs from a forward contract primarily in that:
Select an option first.
Correct answer: B — Futures are exchange-traded with daily mark-to-market settlement; forwards are OTC with no daily settlement
Explanation: B
Question 131
A plain vanilla interest rate swap involves:
Select an option first.
Correct answer: B — One party paying a fixed interest rate and receiving a floating rate (or vice versa) on a notional principal
Explanation: B
Question 132
Delta of an option measures:
Select an option first.
Correct answer: B — The rate of change of option price with respect to changes in the underlying asset price
Explanation: B
Question 133
Vega of an option measures:
Select an option first.
Correct answer: B — The change in option value per unit change in implied volatility
Explanation: B
Question 134
A protective put strategy involves:
Select an option first.
Correct answer: B — Buying a put option on a stock already owned, providing downside protection
Explanation: B
Question 135
A straddle option strategy involves:
Select an option first.
Correct answer: B — Buying both a call and a put at the same strike and expiry
Explanation: B
Question 136
An interest rate cap provides:
Select an option first.
Correct answer: B — A series of call options (caplets) on interest rates, protecting a floating-rate borrower against rates rising above the cap strike
Explanation: B
Question 137
An interest rate floor provides:
Select an option first.
Correct answer: B — A series of put options (floorlets) on interest rates, protecting a floating-rate lender (investor) against rates falling below the floor strike
Explanation: B
Question 138
A European swaption is:
Select an option first.
Correct answer: B — An option that gives the holder the right to enter a specific interest rate swap on or before the expiry date
Explanation: B
Question 139
The futures price for a commodity with storage costs s (continuous) and convenience yield c is:
Select an option first.
Correct answer: B — F = S × e^{(r + s - c)T}
Explanation: B
Question 140
An Asian option differs from a standard European option because:
Select an option first.
Correct answer: B — The payoff depends on the average price of the underlying over a period, rather than the price at expiry only
Explanation: B
Question 141
An American option differs from a European option because:
Select an option first.
Correct answer: B — It can be exercised at any time before and including the expiration date, not just at expiration
Explanation: B
Question 142
The initial value of a newly entered forward contract is:
Select an option first.
Correct answer: B — Zero — the forward price is set so that no payment is required at initiation
Explanation: B
Question 143
A long strangle is similar to a long straddle but:
Select an option first.
Correct answer: B — Uses a put with a lower strike and a call with a higher strike (both OTM), reducing the premium paid but requiring a larger price move to profit
Explanation: B
Question 144
The intrinsic value of an out-of-the-money call option is:
Select an option first.
Correct answer: C — Zero — OTM options have zero intrinsic value
Explanation: C
Question 145
A covered call strategy involves:
Select an option first.
Correct answer: B — Holding a long position in the underlying and selling a call option against it, generating premium income but capping upside
Explanation: B
Question 146
The payer in an interest rate swap is the party that:
Select an option first.
Correct answer: B — Pays the fixed rate and receives the floating rate — benefiting if floating rates rise above the fixed rate
Explanation: B
Question 147
Gamma is highest for:
Select an option first.
Correct answer: C — At-the-money options with short time to expiry
Explanation: C
Question 148
Intrinsic value of an at-the-money call option is:
Select an option first.
Correct answer: B — Zero — ATM call has S = K, so max(S-K,0) = max(0,0) = 0
Explanation: B
Question 149
The payoff of a short put option at expiration is:
Select an option first.
Correct answer: C — -max(K - S_T, 0) = min(S_T - K, 0)
Explanation: C
Question 150
A long call option has limited downside and unlimited upside because:
Select an option first.
Correct answer: B — The maximum loss is the premium paid (the option expires worthless if OTM), while the profit is theoretically unlimited as the underlying price can rise without bound
Explanation: B
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