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 start
Question 301
The price of a bond paying annual coupons C, face value F, maturity n, yield y is:
Select an option first.
Correct answer: D — P = C/y × (1 - 1/(1+y)^n) + F/(1+y)^n
Explanation: D
Question 302
The reinvestment risk of a coupon bond refers to:
Select an option first.
Correct answer: B — The uncertainty about the rate at which future coupons can be reinvested when received, which affects total realised return
Explanation: B
Question 303
A bond with positive convexity will:
Select an option first.
Correct answer: B — Gain more in price when yields fall than it loses when yields rise by the same amount — this asymmetric benefit is the value of convexity
Explanation: B
Question 304
A bond portfolio manager with a view that the yield curve will steepen (short rates fall, long rates rise) would:
Select an option first.
Correct answer: B — Sell long-duration bonds and buy short-duration bonds (or buy short-dated and sell long-dated bonds)
Explanation: B
Question 305
Dollar duration (DV01) of a fixed-rate bond paying 6% annual coupon, face value $1,000, modified duration 5, current price $1,050 is:
Select an option first.
Correct answer: B — $5.25
Explanation: B
Get the full FRM question bank — free
Drop your email and we'll send you fresh FRM practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Correct answer: B — The value-weighted average of the durations of the individual bonds in the portfolio
Explanation: B
Question 307
A duration-neutral trade that benefits from a flattening yield curve (long rates fall more than short rates) is:
Select an option first.
Correct answer: B — Short long-duration bonds and long short-duration bonds — both weighted to be duration-neutral
Explanation: B
Question 308
The effective convexity of a mortgage-backed security is typically:
Select an option first.
Correct answer: B — Negative when rates fall, because prepayments accelerate and shorten the duration unexpectedly, causing less price appreciation than expected from duration alone
Explanation: B
Question 309
A bond with negative convexity:
Select an option first.
Correct answer: B — Has a price-yield relationship where price appreciation is less than duration predicts when yields fall (and price decline is greater than duration predicts when yields rise), due to embedded options or prepayment features
Explanation: B
Question 310
To hedge a $100M bond portfolio with duration 6 against parallel yield shifts using Treasury futures (DV01 per contract = $85):
Select an option first.
Correct answer: B — Sell 7,059 futures contracts (short futures to offset long bond duration)
Explanation: B
Question 311
Duration of an interest rate swap (pay fixed, receive floating) is approximately:
Select an option first.
Correct answer: B — The duration of the fixed leg minus the (near-zero) duration of the floating leg — giving the receiver of the floating rate approximately negative duration equal to the fixed bond duration
Explanation: B
Question 312
Key rate duration analysis is preferred over effective duration for:
Select an option first.
Correct answer: B — Analysing exposure to non-parallel yield curve shifts — it measures the price sensitivity at each specific maturity point on the curve, allowing precise identification and hedging of curve risk from twists, steepeners, flatteners, and butterfly movements
Explanation: B
Question 313
The net present value (NPV) of a swap at inception should be:
Select an option first.
Correct answer: B — Zero, since the fixed rate is set so that the present value of fixed payments equals the present value of floating payments
Explanation: B
Question 314
In a swap rate curve, the spread between the swap rate and the corresponding government bond yield (the swap spread) reflects:
Select an option first.
Correct answer: B — Bank credit risk (inter-bank lending premium), liquidity differences, supply/demand for fixed income, and regulatory effects, making it a barometer of financial system stress
Explanation: B
Question 315
The Fisher equation relates nominal interest rates to real rates and inflation as:
Select an option first.
Correct answer: B — Nominal rate ≈ Real rate + Expected inflation (Fisher approximation) or exactly: (1 + nominal) = (1 + real) × (1 + inflation)
Explanation: B
Question 316
The Nelson-Siegel model parametrises the yield curve as:
Select an option first.
Correct answer: B — y(τ) = β₀ + β₁×(1-e^{-λτ})/(λτ) + β₂×[(1-e^{-λτ})/(λτ) - e^{-λτ}], where β₀ is the long-term level, β₁ determines the slope, and β₂ determines the curvature
Explanation: B
Question 317
The ISDA Standard Initial Margin Model (SIMM) calculates initial margin for non-cleared OTC derivatives by:
Select an option first.
Correct answer: B — Computing a risk-sensitive margin that accounts for delta, vega, and curvature sensitivities across six risk classes (interest rate, credit, equity, FX, commodity, non-linear), aggregating with correlations to reflect diversification
Explanation: B
Question 318
The relationship between the real yield curve and nominal yield curve is captured by the:
Select an option first.
Correct answer: B — Break-even inflation rate: nominal yield - TIPS (real) yield ≈ Expected inflation + Inflation risk premium, allowing market-based inflation expectations to be extracted from bond prices
Explanation: B
Question 319
Parametric VaR assumes:
Select an option first.
Correct answer: B — Asset returns follow a normal (or parametric) distribution, allowing VaR to be expressed analytically as a function of mean and standard deviation
Explanation: B
Question 320
Rho of an option measures:
Select an option first.
Correct answer: B — Sensitivity of option value to changes in the risk-free interest rate
Explanation: B
Question 321
A stop-loss order is:
Select an option first.
Correct answer: B — An order to sell a security if its price falls to a specified level, limiting potential losses
Explanation: B
Question 322
The Sharpe ratio measures:
Select an option first.
Correct answer: B — Excess return per unit of total risk (standard deviation)
Explanation: B
Question 323
The Sharpe ratio of a portfolio measures:
Select an option first.
Correct answer: B — Excess return per unit of total risk (standard deviation): (R_p - R_f) / σ_p
Explanation: B
Question 324
The loss distribution approach (LDA) to operational risk VaR:
Select an option first.
Correct answer: B — Separately models loss frequency (Poisson/negative binomial) and loss severity (log-normal/lognormal variants), then convolves them to derive an aggregate loss distribution
Explanation: B
Question 325
Scenario analysis in risk management involves:
Select an option first.
Correct answer: B — Assessing the impact of specific hypothetical or historical stress scenarios on a portfolio, complementing statistical risk measures
Explanation: B
Question 326
The risk of a portfolio decreasing when two uncorrelated assets are combined demonstrates:
Select an option first.
Correct answer: B — Diversification — the portfolio's variance is less than the weighted average of individual variances when correlation < 1
Explanation: B
Question 327
The maximum loss a portfolio can sustain regardless of market movements is theoretically:
Select an option first.
Correct answer: A — The initial portfolio value only
Explanation: A
Question 328
Delta of a long position in the underlying asset is:
Select an option first.
Correct answer: C — 1
Explanation: C
Question 329
Beta (systematic risk) is calculated as:
Select an option first.
Correct answer: B — Cov(R_stock, R_market) / Var(R_market), estimated by regressing stock returns on market returns — the slope coefficient of the regression
Explanation: B
Question 330
A long position in a stock has positive delta because:
Select an option first.
Correct answer: B — The value of the position increases when the stock price increases — delta = 1 for a direct stock holding
Every question on this page stays free and open either way.
Add Your Testimonial
Privacy Preference
We use cookies to enhance your browsing experience, serve personalized content, and analyze our traffic. By clicking "Accept All", you consent to our use of cookies on this platform.
Before you go, can we ask you one thing?
We are just getting started, and knowing what is holding you back would help us a lot. It takes about 20 seconds.
Overall rating
★★★★★
How likely are you to recommend us to a friend? (0 to 10)What is stopping you from creating a free account?
🎉
Thank you
We read every response. This is exactly how we make PCC better for you.
CCarr
Free assistant · no signup
Carr only reads what is public on PCC, plus your own practice progress.