How to Study for Quant Trading Interviews: The 12-Week Plan

Most people preparing for quant trading interviews study the wrong things, in the wrong order, with the wrong practice method. This guide gives you the optimal sequence.

The plan assumes you have 12 weeks and about 1–2 hours per day. If you have less time, compress the early weeks and protect the final 3 weeks of simulation practice.

What Quant Interviews Actually Test

Before building a study plan, you need to know what you're preparing for. Quant trading interviews test four distinct skill clusters:

1. Mental arithmetic speed (Optiver, Jane Street, SIG): Pure calculation speed under time pressure. 2-digit multiplication in under 3 seconds. Percentages, fractions, and roots by feel.

2. Probabilistic reasoning (all firms): Expected value, conditional probability, combinatorics, Bayes' theorem. The ability to set up and solve probability problems quickly.

3. Market intuition (Citadel, Two Sigma, mid-career): Order-of-magnitude estimates about real-world quantities. Market caps, GDP, commodity prices, rates.

4. Quantitative reasoning depth (Two Sigma, D.E. Shaw, research roles): Statistics, stochastic processes, machine learning foundations, rigorous mathematical reasoning.

Your target firms determine your mix. For Optiver: heavily weights 1 and 2. For Two Sigma: more 2 and 4. For a senior Citadel research role: 3 and 4.

Week-by-Week Plan

Weeks 1–2: Mental Arithmetic Foundation

Goal: Comfortable with all 2-digit multiplication, division, and fractions. No calculator.

Daily practice (45 min):

• Flashcard drill: multiplication tables through 15 × 15 by heart
• 20 minutes of timed 2-digit × 2-digit multiplication (target: under 5 seconds each)
• Fermiq math category: 30 questions/day

Key techniques to master:

• Multiply by 25 = divide by 4, then multiply by 100
• Near-squares: 48 × 52 = 50² − 2² = 2496
• Percentage decomposition: 17.5% = 10% + 5% + 2.5%
• Powers of 2: memorize 2¹ through 2¹⁵

Benchmark: By end of week 2, you should do 80 simple arithmetic problems in 8 minutes with >90% accuracy.

Weeks 3–4: Probability Foundations

Goal: Fluent with expected value, conditional probability, and basic combinatorics.

Daily practice (60 min):

• Work through the 30 probability interview problems
• Fermiq probability category: 20 questions/day
• Re-derive key formulas from first principles, don't memorize blindly

Topics to master:

• Expected value and linearity of expectation
• Conditional probability: P(A|B) = P(A∩B)/P(B)
• Bayes' theorem and base rates
• Geometric distribution: E[flips to first head] = 1/p
• Counting: combinations C(n,k) and permutations P(n,k)

Classic problems to master cold:

• Expected coin flips to get HH (answer: 6)
• Birthday problem (50% at 23 people)
• Monty Hall (switch, P = 2/3)
• Coupon collector: E[rolls to see all 6 faces] = 14.7

Benchmark: Solve any of the 100 quant interview questions from sections 2–4 in under 2 minutes.

Week 5: Expected Value and Kelly Criterion

Goal: EV calculations are automatic; understand Kelly sizing.

Daily practice (60 min):

• Work through the Expected Value complete guide
• 20 EV problems per day, timed
• Practice making markets: given a random event, produce a bid/ask on the probability

Key concepts:

• EV of a die roll with reroll options (dynamic programming)
• Stopping times: when to stop drawing from a distribution
• Kelly criterion: f* = p − q/b for binary bets
• "Make a market" exercises: quote bid/ask on a probability, defend it

Market-making drill: Pick a statement (e.g., "Will it rain tomorrow?"). Quote a 10% bid-ask spread. Have a partner challenge your quote with larger orders. Update your mid based on their aggression.

Week 6: Market Intuition

Goal: Order-of-magnitude accuracy on major market and economic quantities.

Daily practice (45 min):

• Fermiq markets category: 15 questions/day
• Read one financial news source for 20 minutes (WSJ, FT, Bloomberg)
• Flashcards: market caps of top 20 companies, major index levels

Memorize these reference points:

• S&P 500 level: ~5,500 (as of 2025)
• Apple market cap: ~$3T; Microsoft: ~$3T; NVIDIA: ~$2.5T
• US GDP: ~$27T; US national debt: ~$36T
• 10-year Treasury: ~4.2%; Fed funds rate: ~5.25%
• Crude oil: ~$80/barrel; Gold: ~$2,400/oz

Fermi practice: Every day, estimate 2 quantities you don't know, then look them up. Track your error. Aim to be within 3× by week 8.

Week 7: Statistics (for Research Roles)

Goal: Fluent with the statistical concepts Two Sigma, D.E. Shaw, and Citadel research test.

Daily practice (60 min):

• Work through the statistics for quant interviews guide
• 10 statistics problems from Casella & Berger or a graduate-level statistics course
• Code up 3 concepts per week (run a t-test in Python, compute a confidence interval, simulate a random walk)

Key concepts to master:

• Hypothesis testing: H₀, H₁, p-value, Type I/II errors
• Multiple testing problem: why you need Bonferroni or out-of-sample testing
• Maximum likelihood estimation
• Linear regression and its assumptions
• Sharpe ratio and its estimation error

Skip if you're targeting pure trading roles. Weeks 7–8 are only essential for research tracks.

Week 8: Advanced Probability (for Research/Technical Roles)

Goal: Markov chains, random walks, basic stochastic processes.

Topics:

• Random walks: recurrence, expected return time, absorbing barriers
• Markov chains: stationary distributions, absorbing states
• Optional stopping theorem and its applications
• Polya urns, branching processes (for D.E. Shaw types)
• Poisson processes

Key result to understand deeply: The symmetric random walk is recurrent (returns to origin with probability 1) but has infinite expected return time. This counterintuitive result is a classic interview topic.

Weeks 9–10: Interview Simulation

Goal: Apply all skills under interview conditions.

Daily structure:

• 30 min: Fermiq daily drill + one extra category practice
• 30 min: Timed problem sets (20 mixed probability/EV problems in 30 minutes)
• 30 min: Mock interviews with a partner

Partner practice protocol:

• One person plays interviewer, one plays candidate
• Use problems from 100 quant interview questions
• Candidate must explain reasoning out loud
• Interviewer pushes back: "Is that right? What if I told you the answer is different?"

Mental arithmetic speed check: At the start of week 9, do the 80-in-8 simulation. If you score below 60, continue drilling mental arithmetic daily. If above 60, you're arithmetic-ready.

Week 11: Firm-Specific Prep

Goal: Tailor your practice to your target firms' actual formats.

Optiver / Jane Street / SIG:

• 80-in-8 simulations daily: Optiver blitz mode
• Focus on mental multiplication speed and probability
• Read: Optiver guide, Jane Street guide, SIG guide

Citadel / Two Sigma:

• Options Greeks intuition: what is delta, gamma, vega in plain English?
• Market making simulation: quote bid/ask on probabilities
• Read: Citadel guide, Two Sigma guide

HRT / D.E. Shaw:

• Algorithms: LeetCode Hard 2–3× per week
• Advanced probability: Coupon Collector, Polya urn, Markov chains
• Read: HRT guide, D.E. Shaw guide

Week 12: Final Review and Mental Prep

Goal: Sharpen, don't cram. Mental and physical readiness.

What to do:

• Light practice (30 min/day, no heavy cramming)
• Review your error patterns: which problem types were consistently wrong?
• Do 2–3 practice interviews in interview-like conditions (dressed, at a desk, timed)
• Sleep 8 hours. Interview performance tracks cognitive sharpness, and quant interviews require your sharpest thinking.

What NOT to do:

• Don't try to learn new topics in week 12
• Don't grind 4-hour sessions the night before — it dulls thinking
• Don't skip the behavioral prep entirely (tell me about yourself, why trading, tell me about a hard problem you solved)

The Practice Method That Actually Works

Deliberate Practice, Not Volume

Doing 200 probability problems without reviewing errors is much less effective than doing 50 problems with careful analysis of every mistake.

After every wrong answer:

1. Don't look at the solution immediately — try again for 5 minutes
2. Read the solution
3. Write down the key insight in your own words
4. Find 2 similar problems and solve them to lock in the pattern

Timed Practice From Week 3

Quant interviews are time-pressured. The mental friction of "how do I approach this?" needs to be eliminated through timed practice. From week 3 onward, set a timer when you practice.

Targets by week:

• Week 3: 2 minutes per probability problem
• Week 6: 1.5 minutes
• Week 9: 1 minute for basic probability; 2 minutes for complex problems

Making Markets (The Most Underrated Drill)

This is the highest-leverage practice that most candidates skip.

The exercise: Pick a random question (e.g., "How many gas stations are in the US?"). Before you compute, write down your bid/ask range. Then solve. Did your range contain the answer?

Do this 10 times per day. Track what percentage of your intervals contain the true answer. A well-calibrated person should be right about 70% of the time with a 70% interval.

This is exactly what market-making interviews test. Being calibrated — not being right — is the skill.

Calibration: The Meta-Skill

Every firm, in every interview, is testing some form of calibration: your ability to match your expressed confidence to your actual accuracy.

In arithmetic: Don't rush and get wrong answers. Know when you're certain vs. estimating.

In probability: Express answers as ranges when uncertain. "I think this is between 20–30%, let me work it out more precisely."

In estimation: "My best estimate is $500B, I'm about 60% confident it's between $300B and $800B."

Calibration is trainable. Fermiq's scoring system is specifically designed to train calibration — it rewards getting close, penalizes being off by large margins, and tracks your calibration over time.

Realistic Timelines

6 weeks: Adequate for strong math backgrounds targeting Optiver/Jane Street. Mental arithmetic may not be fully optimized.

8 weeks: Recommended for most candidates targeting Tier 1 firms. Enough time for arithmetic fluency plus probability depth.

12 weeks: Optimal. Allows time for statistics depth, firm-specific polish, and extensive simulation.

12+ weeks: For research roles at Two Sigma/D.E. Shaw, or if you're starting from a weaker math base.

The most common mistake: starting too late. Most offers are made 2–4 months after initial outreach, so starting your prep when you begin networking gives you the right runway.

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The daily habit that makes everything else compound: 5 questions every morning. Keeps your quantitative instincts sharp, tracks calibration, and takes 10 minutes. Start today, regardless of where you are in this plan.