Ch4. FRM Financial Risk Manager — Core Review & 20-Question Mock Exam

FRM Master Formula Sheet

Before the mock exam, review these core formulas. Bookmark this page for last-minute review.

Market Risk

Formula	Meaning
VaR = μ − z·σ	Parametric VaR (daily)
VaR_n = VaR_1 × √n	Scale to n-day horizon
ES = μ − σ·φ(z)/(1−c)	Expected Shortfall (normal)
GARCH: σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁	Conditional volatility
EWMA: σ²ₜ = (1−λ)·r²ₜ₋₁ + λ·σ²ₜ₋₁	λ ≈ 0.94 daily

Credit Risk

Formula	Meaning
EL = PD × LGD × EAD	Expected Loss
LGD = 1 − Recovery Rate	Loss in default
CDS spread ≈ PD × LGD	Simplified CDS pricing
CVA = (1−R) × ∑ PD(t) × DF(t) × EPE(t)	Counterparty risk adjustment

Fixed Income & Options

Formula	Meaning
Duration = −(dP/dr)/P	Price sensitivity to rates
Convexity = (d²P/dr²)/P	Curvature of price-yield
ΔP ≈ −D·Δr + ½·C·(Δr)²	Price change approximation
Delta = ∂V/∂S	Option price sensitivity to underlying
Gamma = ∂²V/∂S²	Rate of change of delta
Vega = ∂V/∂σ	Sensitivity to volatility

FRM Exam Strategy

Part I Tactics

Quantitative Analysis is where candidates struggle most — invest time here
For multiple choice: eliminate clearly wrong answers first, then calculate
Know the Basel Accord timeline: Basel I → II → 2.5 → III → IV (SMA)
GARCH, EWMA, VaR scaling appear in every sitting

Part II Tactics

Market Risk: Focus on FRTB and Expected Shortfall
Credit Risk: PD/LGD/EAD calculations appear in 3–5 questions
Operational Risk: SMA formula and the 7 event categories
Current Issues: Read the GARP-assigned readings; 10% of exam
Time management: 80 questions in 4 hours = 3 min per question

20-Question FRM Mock Exam

Market Risk (Q1–7)

Q1. A portfolio has daily mean return 0% and daily standard deviation 2%. What is the 10-day 99% VaR? (z₉₉ = 2.326)

A) $46,520 B)$ 73,678 C) $23,260 D)$ 14,697

Q2. Which VaR method makes no distributional assumptions and naturally captures fat tails?

A) Variance-covariance B) Monte Carlo C) Historical simulation D) EVT

Q3. GARCH(1,1) with ω = 0.00001, α = 0.08, β = 0.90. Yesterday’s variance was 0.0004 and yesterday’s return was −3%. What is today’s conditional variance?

A) 0.000442 B) 0.000378 C) 0.000436 D) 0.000421

Q4. Under FRTB, what replaces VaR as the primary market risk measure?

A) Stressed VaR B) Expected Shortfall C) Conditional VaR D) Scenario P&L

Q5. A 99% VaR model generates 12 exceptions over 250 trading days. According to Basel’s traffic-light framework, the model is in which zone?

A) Green B) Yellow C) Red D) Amber

Q6. Which statement about Expected Shortfall is CORRECT?

A) ES is always less than VaR at the same confidence level
B) ES satisfies the sub-additivity property; VaR may not
C) ES = VaR for normally distributed returns
D) ES ignores losses beyond the confidence threshold

Q7. A bond has duration 5 and convexity 30. If rates rise 100bps, the approximate price change per $1,000 face value is:

A) − $50.00 B) −$ 48.50 C) − $51.50 D) −$ 46.50

Credit Risk (Q8–13)

Q8. A corporate loan has PD = 2%, LGD = 45%, EAD = $10 million. What is the Expected Loss?

A) $90,000 B)$ 45,000 C) $900,000 D)$ 1,800,000

Q9. A CDS has a notional of $10 million and a spread of 150bps. Annual premium paid by the protection buyer is:

A) $1,500,000 B)$ 150,000 C) $15,000 D)$ 750,000

Q10. Under the Internal Ratings-Based (IRB) approach, regulatory capital is designed to cover:

A) Expected Loss only B) Unexpected Loss only C) Both EL and UL D) Neither EL nor UL

Q11. A CDO is tranched into equity (5%), mezzanine (15%), and senior (80%). If the underlying pool suffers 7% losses, which tranche(s) suffer impairment?

A) Equity only B) Equity and mezzanine C) All tranches D) Mezzanine and senior

Q12. What does CVA measure?

A) The fair value of a derivative assuming no default risk
B) The expected loss due to the counterparty’s default
C) The probability that the counterparty defaults before maturity
D) The recovery rate on an OTC derivative

Q13. Under Basel III, which metric specifically measures short-term liquidity resilience over a 30-day stress period?

A) NSFR B) LCR C) LGD D) LVR

Operational & Quantitative Risk (Q14–20)

Q14. Under Basel IV’s Standardized Measurement Approach (SMA), operational risk capital is:

A) 15% of average gross income
B) Business Indicator Component × Internal Loss Multiplier
C) Fixed charge per transaction
D) VaR at 99.9% confidence

Q15. A time series of returns shows significant autocorrelation at lag 1. Which model is BEST suited to capture this pattern?

A) ARCH(1) B) GARCH(1,1) C) AR(1) D) EWMA

Q16. Financial return distributions typically exhibit:

A) Positive skew and negative excess kurtosis
B) Negative skew and positive excess kurtosis
C) Zero skew and zero excess kurtosis
D) Positive skew and zero excess kurtosis

Q17. In the Loss Distribution Approach for operational risk, which distribution is most commonly used for loss frequency?

A) Normal B) Poisson C) Exponential D) Lognormal

Q18. A Gaussian copula assumes what level of tail dependence?

A) Positive lower tail dependence
B) Positive upper and lower tail dependence
C) Zero tail dependence
D) Negative tail dependence

Q19. Which FRM exam category covers mis-selling and market manipulation?

A) External fraud B) Clients, products and business practices C) Execution errors D) Employment practices

Q20. EWMA assigns what kind of weights to past observations?

A) Equal weights B) Geometrically increasing weights (older = more weight)
C) Geometrically decreasing weights (recent = more weight) D) Weights determined by regression

Answer Key with Explanations

Q	Answer	Explanation
1	B	Daily VaR = 2.326 × 2% = 4.652%; 10-day = 4.652% × √10 = 14.71%; on $500K =$ 73,550 ≈ B
2	C	Historical simulation uses actual past returns — no distributional assumption
3	C	0.00001 + 0.08×(0.03²) + 0.90×0.0004 = 0.00001 + 0.000072 + 0.00036 = 0.000442 → D; recalc: 0.00001 + 0.08×0.0009 + 0.90×0.0004 = 0.00001 + 0.000072 + 0.00036 = 0.000442 → A
4	B	FRTB replaced 99% VaR with 97.5% Expected Shortfall
5	C	>10 exceptions in 250 days → Red zone; model must be replaced
6	B	ES is coherent (sub-additive); VaR violates sub-additivity for non-normal distributions
7	B	ΔP = −5×0.01 + ½×30×(0.01)² = −0.05 + 0.0015 = −0.0485; × $1,000 = −$ 48.50
8	A	EL = 0.02 × 0.45 × $10M = $ 90,000
9	B	$10M × 0.015 = $ 150,000 per year
10	B	Under IRB, capital covers UL; EL is priced into loan spreads/provisions
11	B	7% losses: absorbs equity (5%) fully and mezzanine partially (2% into 15% tranche)
12	B	CVA = market value of expected loss from counterparty default
13	B	LCR = Liquidity Coverage Ratio; 30-day stress horizon
14	B	Basel IV SMA: Capital = BIC × ILM
15	C	AR(1) captures first-order autocorrelation in levels/returns
16	B	Financial returns: negative skew (crash risk), positive excess kurtosis (fat tails)
17	B	Poisson is the standard for count/frequency data
18	C	Gaussian copula → zero tail dependence → underestimates co-movement in stress
19	B	Mis-selling and manipulation → “Clients, products and business practices” category
20	C	EWMA: recent observations get higher (geometrically decreasing as you look back)

Final Checklist Before Exam Day

VaR scaling (×√n) is second nature
PD × LGD × EAD for EL, not UL
FRTB → Expected Shortfall, not VaR
Basel capital covers UL at 99.9%
GARCH(1,1): α + β < 1 for mean reversion
CDS: protection buyer pays spread; seller pays notional on credit event
SMA = BIC × ILM under Basel IV operational risk
Copulas: Gaussian = zero tail dependence; t-copula = positive tail dependence

Good luck on your FRM exam!