Valuation & Risk Models

FRM® Part I, published weight 30%. VaR and ES, option valuation, bond risk, stress testing, credit and op risk.

What the outline covers

Value-at-Risk and Expected Shortfall; coherent risk measures
Volatility and correlation estimation
Economic and regulatory capital
Stress testing and scenario analysis
Option valuation; the binomial model and Black–Scholes–Merton
Fixed-income valuation, duration, convexity and hedging
Country and sovereign risk; external ratings and rating transition matrices
Credit risk: expected loss, unexpected loss, credit VaR
Operational risk: loss distributions, capital approaches, Monte Carlo estimation

Sample questions

These 5 questions are free in the app too. Try each one before opening the answer.

Question 1

A portfolio worth $200m has a daily volatility of 1.2% and a mean daily return of zero. The 1-day 99% VaR is closest to:

V $200m · σ 1.2% · z₉₉ = 2.326

A. $2.4m
B. $3.9m
C. $5.6m
D. $8.5m

Show the answer

C. VaR = 2.326 × 0.012 × 200m = $5.58m. Using the 95% z-score of 1.645 gives $3.9m, the planted distractor.

Reading: Valuation and Risk Models — Value-at-Risk

Question 2

A loan has a probability of default of 3%, loss given default of 45% and exposure at default of $10m. Expected loss is:

PD 3% · LGD 45% · EAD $10m

A. $135,000
B. $300,000
C. $450,000
D. $1,350,000

Show the answer

A. EL = PD × LGD × EAD = 0.03 × 0.45 × 10,000,000 = $135,000. Provisions cover this; capital covers the unexpected loss around it.

Reading: Valuation and Risk Models — Credit Risk

Question 3

Which statement about expected shortfall is correct?

A. ES is never greater than VaR at the same confidence level
B. ES is sub-additive; VaR need not be
C. ES ignores the shape of the tail
D. ES requires an assumption of normality

Show the answer

B. ES is a coherent risk measure and therefore sub-additive, while VaR can violate sub-additivity. ES also always equals or exceeds VaR at the same confidence.

Reading: Valuation and Risk Models — Coherent Risk Measures

Question 4

Historical simulation VaR differs from delta-normal VaR chiefly because it:

A. Assumes returns are normally distributed
B. Requires no distributional assumption
C. Cannot handle option positions
D. Always produces a lower VaR estimate

Show the answer

B. Historical simulation reorders actual past returns, so no distribution is assumed — at the cost of needing a long, representative sample.

Reading: Valuation and Risk Models — Non-parametric Approaches

Question 5

A delta-neutral options book is long gamma. A large move in the underlying in either direction will produce:

A. A loss
B. A gain
C. No profit or loss, since the book is delta neutral
D. A gain only if the move is upward

Show the answer

B. Long gamma means the position’s delta moves favourably as the underlying moves, producing gains on large moves in either direction.

Reading: Valuation and Risk Models — Option Sensitivities

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