FRM Part I 2025 Quantitative Analysis: Extreme Value Theory—How to Answer in 90 Seconds

Kateryna Myrko
Jul 25
3 min read

1. Why EVT matters in Quantitative Analysis

Extreme Value Theory (EVT) sits inside the Quantitative Analysis (QA) topic, which accounts for 20 percent of the FRM Part I curriculum. GARP’s 2025 Learning Objectives list EVT under Reading 10, “Parametric and Non-parametric Risk Models.” One to three multiple-choice questions on tail modelling appear in every exam window. Because QA questions are evenly weighted, treating EVT as “optional” is risky. Candidates who master it gain two concrete advantages:

High-confidence points. EVT questions are highly formulaic; once you know the two models and one VaR equation, you can score quickly.
Time savings. A disciplined 90-second routine frees minutes for time-consuming items elsewhere (e.g., valuation or market risk).

2. EVT in two minutes—core concepts you must know

Approach	Model	When to apply	Core idea
Block Maxima	Generalised Extreme Value (GEV)	You keep the single highest (or lowest) observation per block (annual, quarterly, monthly).	The distribution of those maxima converges to GEV, parameterised by location, scale, and shape.
Peak-over-Threshold (POT)	Generalised Pareto (GPD)	You retain all observations that exceed a high cutoff uuu.	Exceedances beyond uuu follow GPD, sharing the same tail index ξ\xiξ as the corresponding GEV.

3. Mapping EVT to the 2025 Learning Objectives

GARP AIM code	Action verb	What you must do	Critical formula/concept
QA-10.a	Explain	Differentiate block-maxima vs POT modelling.	GEV vs GPD mapping.
QA-10.b	Calculate	Derive VaR or Expected Shortfall with GPD parameters.	VaRp_pp equation above.
QA-10.c	Estimate	Compute the Hill tail index.	Hill estimator formula.
QA-10.d	Identify	Spot data issues (threshold bias, non-IID).	Hill-plot stability cues.

These verbs—explain, calculate, estimate, identify—signal exactly how questions are framed. Tailor your flashcards and drills to those commands.

4. The 90-second solution framework

Goal: move from reading the stem to bubbling the correct option in ≤ 1.5 minutes.

Seconds	Action	What you actually do
0–15 s	Read the last line first.	Decide whether you must produce VaR/ES, a tail index, or pick the correct model.
15–30 s	Classify the data sample.	One extreme per block → GEV; many exceedances → GPD/Hill.
30–45 s	Select the formula.	Write the VaRp_pp or Hill estimator on scratch paper; note given inputs.
45–75 s	Plug the numbers.	Store uuu (A), β\betaβ (B), ξ\xiξ (C) in your calculator; compute once—no interim rounding.
75–90 s	Sense-check & commit.	Heavy tail (positive ξ\xiξ) → VaR far above uuu; bounded tail (negative ξ\xiξ) → VaR close to uuu. Bubble.

Practise the sequence under a stopwatch until each micro-step is muscle memory.

5. Five candidate pitfalls & fixes FRM Part I 2025 Quantitative Analysis Extreme Value Theory

Pitfall	Why it hurts	Quick fix
Using Hill on light-tailed data	Hill assumes ξ>0\xi > 0ξ>0; using it when ξ≤0\xi \le 0ξ≤0 biases results.	Check tail type first; if unsure, default to GPD.
Threshold bias	Too low → central data; too high → too few points.	Use a Hill plot; choose kkk where slope stabilises.
Ignoring dependence	EVT assumes i.i.d. extremes; volatility clustering inflates VaR.	De-cluster or block-bootstrap data.
Rounding away ξ\xiξ	Small positive ξ\xiξ (e.g., 0.05) still meaningfully lifts VaR.	Keep three decimals in ξ\xiξ.
Time mismanagement	Spending > 2 min on one EVT question disrupts exam rhythm.	Drill the 90-second routine until automated.

6. Exam-day checklist for EVT questions

Calculator registers pre-labelled (A = uuu, B = β\betaβ, C = ξ\xiξ).
Scratch sheet ready: write the GPD VaR formula and a mini table of tail-index signs.
Hill plot mental cue: slope flattens → pick that kkk.
Pacing rule: by question 25, aim to have ~60 minutes elapsed.

7. Final takeaway

Extreme Value Theory intimidates many FRM candidates, yet its toolbox is compact: two modelling frameworks, one tail-index estimator, one VaR equation, and a handful of conceptual triggers. Combine that minimalist formula sheet with disciplined threshold selection and the 90-second answering routine. You’ll bank reliable marks, conserve exam-time bandwidth, and put yourself on the right side of the pass line in 2025. FRM Part I 2025 Quantitative Analysis Extreme Value Theory

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