Ch8. FRM Financial Risk Manager — Final Mock Exam (30 Questions) & Exam Strategy

FRM Master Formula Sheet — Final Review

Market Risk

Formula	Meaning
VaR_n = VaR_1 × √n	Scale daily VaR to n-day
GARCH(1,1): σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁	Conditional variance
Long-run variance = ω / (1−α−β)	Mean-reverting level
EWMA: λ ≈ 0.94	Daily volatility (RiskMetrics)

Credit Risk

Formula	Meaning
EL = PD × LGD × EAD	Expected Loss
LGD = 1 − Recovery	Loss in default
CDS spread ≈ PD × LGD	Simplified pricing

Liquidity & Regulatory

Metric	Formula	Threshold
LCR	HQLA / 30-day net outflows	≥ 100%
NSFR	ASF / RSF	≥ 100%
CET1 ratio	CET1 / RWA	≥ 4.5% (+2.5% buffer)
Leverage ratio	Tier 1 / Total exposure	≥ 3%

Investment Management

Metric	Formula
RAROC	(Revenue − Costs − EL) / Economic Capital
Duration Gap	D_A − (L/A) × D_L
Sharpe Ratio	(R_p − R_f) / σ_p
Information Ratio	α / Tracking Error

---

30-Question Final Mock Exam

Market Risk (Q1–8)

Q1. A portfolio has a 1-day 99% VaR of $500K. The 10-day VaR is:

A) $500K B)$1.58M C) $5.0M D)$10.0M

Q2. GARCH(1,1): α + β < 1 implies:

A) Volatility grows without bound
B) Volatility mean-reverts to a long-run level
C) Volatility follows a random walk
D) Volatility decays to zero

Q3. Under FRTB, the Expected Shortfall confidence level is:

A) 95% B) 97.5% C) 99% D) 99.9%

Q4. A VaR model shows 12 exceptions over 250 trading days. The Basel traffic-light zone is:

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

Q5. A bond has modified duration 8, convexity 100, rates rise 100bps. Approximate price change:

A) −7.5% B) −8.0% C) −8.5% D) +7.5%

Q6. Which VaR method requires NO distributional assumptions?

A) Variance-covariance B) GARCH C) Historical simulation D) EWMA

Q7. Decreasing λ in EWMA from 0.94 to 0.90 means:

A) Lower weight on recent observations
B) Higher weight on recent observations
C) Equal weight on all observations
D) Slower reaction to market shocks

Q8. In Extreme Value Theory (EVT), the Peaks-Over-Threshold method fits which distribution to exceedances?

A) Normal B) Student-t C) Generalized Pareto (GPD) D) Lognormal

---

Credit Risk (Q9–15)

Q9. PD = 3%, LGD = 40%, EAD = $50M. Expected Loss is:

A) $150K B)$600K C) $1.5M D)$6.0M

Q10. Under Basel III IRB, regulatory capital protects at what confidence level?

A) 95% B) 99% C) 99.9% D) 99.97%

Q11. In a CDS, the protection buyer:

A) Receives the spread and pays the notional on default
B) Pays the spread and receives the notional on default
C) Pays the notional and receives interest
D) Pays no premium

Q12. CVA is best defined as:

A) The FVA adjustment for funding costs
B) The fair value adjustment reflecting counterparty default risk
C) The DVA adjustment for own default risk
D) The MVA adjustment for initial margin costs

Q13. A zero-coupon bond matures in 1 year, face $100, risk-free rate 4%, CDS spread 200bps (continuous compounding, zero recovery). Its price is:

A) $94.18 B)$96.08 C) $92.31 D)$98.04

Q14. In a CDO, the senior tranche begins to absorb losses when:

A) Any single underlying defaults
B) Both equity and mezzanine tranches are exhausted
C) The loss rate exceeds the mezzanine attachment point
D) All underlying assets default

Q15. Under A-IRB, which parameter is NOT estimated by the bank internally?

A) PD B) LGD C) EAD D) Asset correlation (ρ)

---

Operational & Quantitative Risk (Q16–22)

Q16. Under Basel IV SMA, Internal Loss Multiplier (ILM) > 1 when:

A) Internal loss history is below the BIC reference level
B) Internal loss history exceeds the BIC reference level
C) It is always equal to 1
D) Total assets are below a threshold

Q17. The main weakness of the Gaussian copula for CDO modeling is:

A) It is computationally complex
B) It assumes zero tail dependence, underestimating co-movement in crises
C) It requires excessive data
D) It only applies to equities

Q18. GARCH(1,1): ω = 0.000002, α = 0.06, β = 0.92. Long-run variance is:

A) 0.0001 B) 0.00005 C) 0.00001 D) 0.000025

Q19. Negative excess kurtosis in a financial return distribution indicates:

A) Thicker tails than normal
B) Thinner tails than normal (platykurtic)
C) Same tails as normal
D) Negative skewness

Q20. An ARCH effect in equity returns indicates:

A) Serial correlation in returns
B) Volatility clustering
C) Returns are normally distributed
D) Constant volatility

Q21. Under Basel’s seven operational risk event types, an employee discrimination lawsuit falls under:

A) Internal Fraud B) External Fraud C) Employment Practices and Workplace Safety D) Execution, Delivery and Process Management

Q22. Under a normal distribution, Expected Shortfall (ES) at 95% versus VaR at 95%:

A) ES < VaR B) ES = VaR C) ES > VaR D) Always ES = 2 × VaR

---

Liquidity, Regulatory & Investment Management (Q23–30)

Q23. The LCR haircut for Level 2A HQLA is:

A) 0% B) 15% C) 25% D) 50%

Q24. Under NSFR, which item carries a 100% ASF factor?

A) Short-term wholesale funding (<3 months)
B) Long-term debt with maturity ≥ 1 year
C) Illiquid assets
D) Commercial paper

Q25. Duration Gap = +3 years, Total Assets = $2B. Interest rates rise 50bps. Change in economic equity:

A) −$10M B) −$30M C) +$30M D) +$10M

Q26. A bank business unit has RAROC of 14% and cost of equity of 12%. This means:

A) The unit carries excessive risk
B) The unit creates shareholder value
C) Regulatory capital is insufficient
D) Economic capital should be reduced

Q27. Portfolio annual return 12%, risk-free rate 4%, tracking error 8%, alpha 2%. Information Ratio is:

A) 0.25 B) 0.40 C) 0.53 D) 1.00

Q28. Correcting for survivorship bias in hedge fund databases will:

A) Increase average reported returns
B) Decrease average reported returns
C) Have no effect on returns
D) Increase return volatility

Q29. The convexity condition (C_A > C_L) in full immunization ensures:

A) Higher asset yields
B) Asset value exceeds liability value after large rate moves
C) Reduced leverage
D) Duration is set to zero

Q30. G-SIBs face a leverage ratio requirement that is:

A) Lower than the 3% standard B) Equal to 3%
C) Higher than 3% D) Not applicable

---

Answer Key

Q	Answer	Explanation
1	B	$500K × √10 =$500K × 3.162 = $1.58M
2	B	α + β < 1 → variance mean-reverts to ω/(1−α−β)
3	B	FRTB ES at 97.5% (not 99% VaR)
4	C	12 exceptions in 250 days → Red zone (>10)
5	A	−8×0.01 + ½×100×(0.01)² = −0.08 + 0.005 = −7.5%
6	C	Historical simulation uses actual past returns; no distribution assumed
7	B	Lower λ → higher (1−λ) → more weight on recent returns
8	C	POT method → Generalized Pareto Distribution
9	B	EL = 0.03 × 0.40 × $50M = **$600K**
10	C	Basel IRB: 99.9% confidence, 1-year horizon
11	B	Protection buyer: pays spread → receives notional on credit event
12	B	CVA = fair value reduction for counterparty default risk
13	A	P = 100 × e^(−0.06) = $94.18
14	B	Waterfall: equity absorbs first, mezzanine second → senior only after both exhausted
15	D	Asset correlation (ρ) is set by Basel regulations, not bank-estimated
16	B	ILM > 1 when actual internal losses exceed the BIC benchmark
17	B	Gaussian copula: zero tail dependence → underestimates crisis co-movement
18	A	LR variance = 0.000002/(1−0.06−0.92) = 0.000002/0.02 = 0.0001
19	B	Negative excess kurtosis = platykurtic (thinner tails)
20	B	ARCH effect = volatility clustering (calm/turbulent periods)
21	C	Discrimination = Employment Practices and Workplace Safety
22	C	ES = average loss beyond VaR threshold → always ES > VaR
23	B	Level 2A HQLA: 15% haircut
24	B	Long-term debt ≥1 year: ASF 100%
25	B	ΔE = −3 × $2B × 0.005 = **−$30M**
26	B	RAROC (14%) > CoE (12%) → shareholder value created
27	A	IR = 2%/8% = 0.25
28	B	Removing survivorship bias includes failed funds → average returns decrease
29	B	Convexity cushion ensures assets > liabilities for large parallel rate shifts
30	C	G-SIBs: 3% + G-SIB surcharge → higher than 3%

---

FRM Exam Day Strategy

The Night Before

• Review the formula sheet only — no new material
• Replace HP 12C / BAII Plus calculator batteries
• Confirm venue, bring valid ID and printed admission ticket

Exam Day (4 hours per part, 80 questions each)

• Pace: ~3 minutes per question; flag and return on tough ones
• Calculation questions: write the formula first, then substitute
• Regulatory questions: focus on the number (4.5%, 6%, 8%, 3%, 72.5%)

Obtaining the FRM Certification

1. Pass Part I (quantitative foundations)
2. Pass Part II (applied risk management)
3. Maintain GARP membership
4. Demonstrate 2 years of relevant professional risk management experience
5. Submit to GARP → FRM Certification awarded

FRM Financial Risk Manager series complete! Best of luck on your exam!