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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 181
In a cross-currency swap, counterparties exchange:
Select an option first.
Correct answer: B — Principal and interest payments in different currencies — typically at inception the principals are exchanged at the current spot rate, then periodic interest payments in different currencies, and principals are re-exchanged at maturity at the original spot rate
Explanation: B
Question 182
The P&L from delta hedging a short option position is approximately:
Select an option first.
Correct answer: B — Negative (loss) when the underlying makes large moves, as the delta-neutral hedge must buy at high prices and sell at low prices — this is the gamma-theta trade-off
Explanation: B
Question 183
The relationship between the price of a variance swap and options prices is that:
Select an option first.
Correct answer: B — The fair variance swap strike equals the risk-neutral expectation of realised variance, which can be approximated by a portfolio of European options: specifically a log-contract replication using a continuum of options across all strikes
Explanation: B
Question 184
The Vanna-Volga method for FX options pricing:
Select an option first.
Correct answer: B — Adjusts the Black-Scholes price by adding a weighted combination of vega, vanna, and volga (second derivative of price with respect to vol) to account for the volatility smile without a full stochastic volatility model
Explanation: B
Question 185
The Garman-Kohlhagen model extends Black-Scholes for:
Select an option first.
Correct answer: B — European currency (FX) options, treating the foreign interest rate as a continuous dividend yield on the foreign currency — the foreign currency holder earns the foreign risk-free rate analogously to a dividend yield
Explanation: B
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Question 186
In the context of CDS index tranches, the equity tranche spread is most sensitive to:
Select an option first.
Correct answer: B — Default correlation — higher correlation increases the equity tranche spread (more concentrated risk of first losses) while reducing mezzanine/senior spreads. At zero correlation, equity tranche absorbs diversified small losses; at perfect correlation, all or nothing — equity tranche behaves like a scaled version of a single CDS
Explanation: B
Question 187
The risk reversal in FX options markets is defined as:
Select an option first.
Correct answer: B — The difference in implied volatility between OTM calls and OTM puts (same delta, opposite sign) — typically quoted as 25-delta risk reversal = σ_call_25Δ - σ_put_25Δ, reflecting the skewness of the FX implied vol distribution
Explanation: B
Question 188
A constant maturity swap (CMS) spread trade involves:
Select an option first.
Correct answer: B — Paying one CMS rate (e.g., 10-year swap rate reset quarterly) and receiving another CMS rate (e.g., 2-year swap rate reset quarterly) — profiting from changes in the yield curve shape (steepening/flattening), with convexity adjustments required because CMS rates are not martingales under the standard swap measure
Explanation: B
Question 189
The price of a share according to the Gordon Growth Model is:
Select an option first.
Correct answer: B — Dividends next period divided by (required return minus dividend growth rate)
Explanation: B
Question 190
Short selling a stock involves:
Select an option first.
Correct answer: B — Borrowing and selling a stock expecting it to fall, then buying it back at a lower price
Explanation: B
Question 191
The price-to-earnings (P/E) ratio is:
Select an option first.
Correct answer: B — Share price divided by earnings per share (EPS) — a measure of how much investors pay per dollar of earnings
Explanation: B
Question 192
The dividend discount model (DDM) values a stock as:
Select an option first.
Correct answer: B — The present value of all expected future dividends discounted at the required rate of return
Explanation: B
Question 193
Beta in the CAPM framework measures:
Select an option first.
Correct answer: B — The stock's sensitivity to market movements — its systematic (non-diversifiable) risk relative to the market portfolio
Explanation: B
Question 194
The Capital Asset Pricing Model (CAPM) states that the expected return of an asset is:
Select an option first.
Correct answer: B — Risk-free rate plus beta times the equity risk premium
Explanation: B
Question 195
The beta of a portfolio relative to the market index is:
Select an option first.
Correct answer: B — The ratio of the portfolio's covariance with the market to the market's variance: β = Cov(R_p, R_m) / Var(R_m)
Explanation: B
Question 196
The Fama-French three-factor model extends CAPM by adding:
Select an option first.
Correct answer: B — Size (SMB — small minus big) and value (HML — high minus low book-to-market) factors to the market factor
Explanation: B
Question 197
The Modigliani-Miller theorem (in its basic form) states that:
Select an option first.
Correct answer: B — In a perfect capital market (no taxes, bankruptcy costs, information asymmetries), the firm's value is independent of its capital structure — the mix of debt and equity financing is irrelevant
Explanation: B
Question 198
A hedge fund employing a long/short equity strategy:
Select an option first.
Correct answer: B — Buys stocks expected to outperform (long) and short sells stocks expected to underperform (short), with the goal of generating returns from relative performance rather than market direction
Explanation: B
Question 199
Short selling restrictions affect market efficiency by:
Select an option first.
Correct answer: B — Preventing arbitrageurs from correcting overvalued securities — when short selling is impossible, overvaluation can persist longer, creating asset price bubbles and reducing price discovery efficiency
Explanation: B
Question 200
The volatility surface in equity markets typically exhibits:
Select an option first.
Correct answer: B — A volatility skew (higher vol for lower strikes) combined with a term structure of volatility that is often inverted in near-term stress periods
Explanation: B
Question 201
The efficient market hypothesis (EMH) in its semi-strong form asserts:
Select an option first.
Correct answer: B — All publicly available information is immediately and fully reflected in security prices, so fundamental analysis cannot generate consistent excess returns
Explanation: B
Question 202
The yield to maturity (YTM) of a bond is:
Select an option first.
Correct answer: B — The discount rate that equates the present value of all cash flows to the bond's current market price
Explanation: B
Question 203
Duration of a bond measures:
Select an option first.
Correct answer: B — The sensitivity of the bond's price to changes in yield (interest rate risk), expressed in years for Macaulay duration
Explanation: B
Question 204
A bond trading at a price above its face value is said to be trading:
Select an option first.
Correct answer: C — At a premium
Explanation: C
Question 205
The relationship between bond price and yield is:
Select an option first.
Correct answer: B — Inverse and convex
Explanation: B
Question 206
Convexity in bond pricing represents:
Select an option first.
Correct answer: A — The second derivative of price with respect to yield, capturing the curvature of the price-yield relationship
Explanation: A
Question 207
The spot rate for maturity T is:
Select an option first.
Correct answer: B — The yield on a zero-coupon bond (strip) for that maturity
Explanation: B
Question 208
The forward rate f(T1, T2) represents:
Select an option first.
Correct answer: B — The interest rate agreed upon today for borrowing or lending between future dates T1 and T2
Explanation: B
Question 209
Duration of a zero-coupon bond equals:
Select an option first.
Correct answer: B — Its maturity
Explanation: B
Question 210
The duration of a floating-rate bond resets to approximately zero at each coupon payment date because:
Select an option first.
Correct answer: B — The coupon resets to the current market rate, so the bond always prices near par, giving duration approximately equal to the time to the next reset date
Explanation: B
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