Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

Level

AnyCoreIntermediateHard

Type

AnyBrainteaserTechnicalCaseMarket viewFit

1. 062You have made me a market. If the true answer falls inside your market, how much would you risk to win a hundred dollars?Market makingHardtechnicalAkuna CapitalTrading · Chicago · 2025

   Say this

   That depends entirely on how wide I quoted and how confident I am, and those two are linked. If I quoted a tight market I should not be very confident the answer is inside it, so I would risk little. If I quoted wide, I should be confident, and I would risk more. The honest answer is to price my own probability and then bet a fraction of Kelly.

   Then walk it

   1. The question is a consistency check. A tight market is a strong claim, and the interviewer is testing whether my stated width matches my stated confidence. If I said 300 at 310 on the number of Starbucks in New York and then say I am 90 percent sure the truth is inside, one of those is a lie.
   2. So I quantify. Suppose I think there is a 60 percent chance the answer is inside my market. Then risking x to win 100 has expected value 0.6 times 100 minus 0.4 times x, which is positive for x below 150. So fair value is 150 and I would bet meaningfully below that.
   3. Kelly gives the size: bet a fraction of capital equal to edge over odds. At 60 percent on an even-money-ish bet the full Kelly fraction is around 20 percent of capital, and I would take a quarter to a half of that, because my 60 percent is itself an estimate and overbetting Kelly is far more punishing than underbetting.
   4. I would also name the asymmetry in the setup. The interviewer chooses whether to take the bet, so they only take it when they think my price is wrong. That is adverse selection, and it means I should shade my number down from the naive fair value.
   5. So a concrete answer: with a 60 percent belief and an adversary who selects, I would risk around 50 to 70 dollars to win 100, and I would say out loud that I am shading below the 150 fair value because you get to choose whether to trade.

   Where candidates lose it

   Giving a bravado number like I'd risk a thousand, or refusing to name a figure. Both fail. Also failing to notice that your quoted width already implied a confidence level, so an answer inconsistent with your own market gets picked apart immediately. Name your probability, compute fair value, then shade for adverse selection.

   Expect next

   • So tighten your market and answer again.
   • What if I let you choose which side of the bet to take?
   • Explain why you shaded below fair value.

   Reported by candidates at Akuna Capital (Trading, Chicago, 2025). Source: Wall Street Oasis.

2. 066Explain the Kelly criterion, and why do real traders bet less than it says?Market makingHardtechnicalQuant tradingProp trading firms

   Say this

   Kelly maximises the expected growth rate of your capital by betting a fraction equal to your edge divided by the odds. For an even-money bet at probability p, that fraction is 2p minus 1. Real traders bet a fraction of it because Kelly assumes you know your edge exactly, and overbetting is far more damaging than underbetting.

   Then walk it

   1. The derivation in one line: maximise the expected log of wealth, because log wealth is additive across repeated bets and its expectation governs the long-run growth rate. For a bet paying b to 1 with win probability p, the optimal fraction is (pb minus (1-p)) over b.
   2. Numbers: a 55 percent even-money bet gives f equal to 0.1, so ten percent of capital. A 60 percent bet gives 20 percent. That is a lot more than most people's intuition, which is the first surprise of Kelly.
   3. For continuous returns the analogue is mean over variance, which is why a Sharpe ratio maps directly to a leverage level. Full Kelly leverage equals the Sharpe divided by the volatility.
   4. The asymmetry is the key insight. Growth rate as a function of bet size is a concave parabola, so betting half Kelly gives you three quarters of the growth with half the volatility. Betting double Kelly gives you zero growth. Overestimating your edge by a factor of two therefore destroys the entire benefit.
   5. And full Kelly's drawdowns are intolerable in practice: the probability of at some point halving your capital under full Kelly is fifty percent. Nobody running other people's money survives that, and no risk manager permits it. So a quarter to a half Kelly is standard, and the honest reason is parameter uncertainty plus career risk, not mathematics.

   Where candidates lose it

   Reciting the formula without the asymmetry. The gradeable insight is that the growth curve is flat near the optimum and falls off a cliff past it, which is why uncertainty in your edge estimate pushes you to bet less. Also mention the fifty percent chance of a fifty percent drawdown, because it makes the practical argument concrete.

   Expect next

   • What is the probability of a fifty percent drawdown under full Kelly?
   • How does Kelly relate to mean-variance optimisation?
   • How would you size when your edge estimate itself has a standard error?
3. 071Here is a scenario. Walk me through how you would analyse the trade.Market makingHardcase studySchonfeldQuantitative Research · New York · 2021

   Say this

   I would structure it as five questions: what is the thesis and what would make it wrong, what is the expected value, how do I size it, how do I hedge what I am not trying to be exposed to, and what is my exit. Then say the number, because a trade analysis without a number is an opinion.

   Then walk it

   1. Thesis first, stated as a falsifiable claim with a horizon. Not this looks cheap, but I think this spread compresses from 80 to 50 basis points over three months because of a specific mechanism, and if it is still at 80 in three months I am wrong.
   2. Expected value: probability times payoff on each branch. If there is a 60 percent chance of making 3 and a 40 percent chance of losing 2, that is 1.8 minus 0.8, so plus 1 with a 5-point range of outcomes. The range matters as much as the mean.
   3. Sizing: from the loss branch, not the win branch. I size so that the bad case is a loss I can carry, which in practice means a fraction of my risk budget, and I say what that fraction is.
   4. Hedging: separate the exposure I want from the ones that come attached. If the view is idiosyncratic, hedge out the market beta, the sector, and the rate duration, then check what basis risk remains after hedging, because that is the risk I did not choose.
   5. Exit and monitoring: the level or the date at which I am out, plus the two or three observables that would tell me the thesis is breaking before the P&L does. And I would name the thing I cannot hedge, because every trade has one and being explicit about it is what makes the analysis credible rather than promotional.

   Where candidates lose it

   Describing the thesis at length and never getting to sizing, hedging or the exit. Anyone can have a view. What a multi-manager platform is hiring for is the risk framework around it, so spend at least half your answer on size, hedge and exit, and name the unhedgeable residual yourself.

   Expect next

   • What is your stop, and why there?
   • What would make you double the position?
   • What risk are you left with after hedging?

   Reported by candidates at Schonfeld (Quantitative Research, New York, 2021). Source: Wall Street Oasis.

4. 073Why do alphas decay, and how would you detect that yours is dying?Time seriesHardsuperdayQuant researchQuant trading

   Say this

   Because a profitable pattern attracts capital until the price moves to where the profit was. Detect it by tracking realised versus expected performance, the signal's own predictive power separately from the P&L, and crowding measures, and set the decision rule before performance deteriorates.

   Then walk it

   1. Mechanisms in order of frequency. Crowding, where other people trade the same signal and the entry price moves. Structural change, where the market feature the signal exploited is regulated or engineered away. Arbitrage by faster participants. And plain overfitting, where the alpha was never there.
   2. Separate the two things that can break. Is the signal still predicting, measured by information coefficient, the correlation between forecast and subsequent return? Or is it predicting but no longer profitable after costs? The first is decay, the second is crowding or impact, and the fixes differ.
   3. Concrete measures: rolling information coefficient, rolling Sharpe, realised transaction cost versus modelled, and the fraction of your expected edge captured on a typical fill. If the signal is intact and the capture rate is falling, other people are in front of you.
   4. Crowding proxies: short interest and borrow costs for the short leg, correlation of your P&L with published factor returns, and how your strategy behaves on days when leveraged players deleverage. A crowded trade has fat negative tails on those days.
   5. The discipline is the answer though. Set the decay threshold in advance, for example halve the allocation if the rolling one-year information coefficient falls below half its backtest level for two consecutive quarters. Deciding in the middle of a drawdown is how people turn a decayed alpha into a large loss, and having the rule written down before you need it is the part an interviewer is actually testing.

   Where candidates lose it

   Answering only markets get more efficient. Be specific about mechanisms and about measurement, and above all separate whether the signal stopped predicting from whether the trade stopped being profitable. A pre-committed decision rule is the piece most candidates never mention.

   Expect next

   • What is an information coefficient and what is a good value?
   • How would you measure crowding in a trade?
   • Would you turn it off, or reduce it, and who decides?
5. 074How would you model market impact and slippage for a strategy you are sizing?Market makingHardtechnicalQuant researchQuant trading

   Say this

   Split the cost into spread, temporary impact and permanent impact. The empirical regularity worth knowing is the square-root law: impact scales roughly with the square root of the order size as a fraction of daily volume, times the volatility.

   Then walk it

   1. The square-root law: impact in volatility units is approximately a constant times the square root of order size over average daily volume, with the constant usually estimated around 0.5 to 1. So trading 1 percent of ADV in a 2 percent daily vol name costs roughly 0.1 times 2 percent, about 20 basis points.
   2. That non-linearity is what caps capacity. Doubling your size only increases impact by 41 percent per share, but total cost grows as size to the power 1.5, so cost eats your edge faster than your edge grows.
   3. Separate temporary from permanent. Temporary impact reverts after you stop trading and is a function of how fast you trade. Permanent impact is the information your trading revealed, and it does not come back. Almgren-Chriss style frameworks trade off the two against the risk of trading slowly.
   4. Estimating it honestly: use your own fills against arrival price, not a vendor model, and regress realised shortfall on participation rate, volatility and spread. You need a lot of trades, and you must control for the fact that you traded more aggressively when you had more signal, which biases the estimate.
   5. And the modelling discipline: be conservative, because impact is the parameter most likely to turn a profitable backtest into a losing strategy. I would rather assume twice the cost and discover I was pessimistic than the reverse. That preference is the answer they want to hear.

   Where candidates lose it

   Assuming linear impact or using the quoted spread as the whole cost. For any size that matters the spread is the small part. Know the square-root law and know that cost scaling as size to the power 1.5 is what determines capacity, because that is the link between a research result and a business decision.

   Expect next

   • Why does cost scale as size to the power one and a half?
   • How do you separate permanent from temporary impact empirically?
   • How does impact determine the capacity of a strategy?
6. 078Given a stream of numbers, return the median after each element arrives.ProgrammingHardtechnicalOld Mission CapitalEquities · Boston · 2024

   Say this

   Two heaps. A max heap for the lower half and a min heap for the upper half, kept balanced so their sizes differ by at most one. The median is the top of the larger heap, or the average of the two tops. Insert is O(log n), query is O(1).

   Then walk it

   1. Insert rule: if the new value is at most the max of the lower heap, push it there, otherwise push to the upper heap. Then rebalance by moving one element across if the sizes differ by more than one.
   2. Query: if the sizes are equal, the median is the average of the two tops. Otherwise it is the top of the larger heap. Constant time either way.
   3. Total cost for n elements is n log n, and memory is O(n) because you must retain everything. That memory cost is the honest limitation, and it is the first thing an interviewer will probe.
   4. If the median must be over a sliding window rather than the whole prefix, the two-heap approach needs deletions from the middle. Use an indexed multiset or two heaps with lazy deletion and a hash of pending removals. That is the version that comes up in practice on a tick stream.
   5. And if approximate is acceptable, which on a trading system it usually is, the right answer is a streaming quantile sketch: t-digest or the Greenwald-Khanna algorithm, giving you any quantile in bounded memory rather than O(n). Naming that unprompted is what turns a correct interview answer into a practical one.

   Where candidates lose it

   Sorting on every element, which is O(n squared log n) overall, or maintaining a sorted list with insertion, which is O(n) per element because of the shifting even though the binary search is fast. Say two heaps immediately, then volunteer the sliding-window and bounded-memory variants, because that is where the conversation is heading.

   Expect next

   • Now do it over a sliding window of the last thousand values.
   • What if you cannot store all the data?
   • How would you get the 99th percentile instead of the median?

   Reported by candidates at Old Mission Capital (Equities, Boston, 2024). Source: Wall Street Oasis.

7. 081Write me an unordered_map class. What is actually inside a hash map?ProgrammingHardsuperdayOld Mission CapitalTrading · Chicago · 2021

   Say this

   An array of buckets, a hash function mapping keys to bucket indices, a collision resolution strategy, and a resize policy driven by load factor. The three decisions that define the implementation are the hash, the collision handling, and when you grow.

   Then walk it

   1. Core operations: index equals hash of key modulo bucket count, then search within that bucket comparing keys for equality. Insert, find and erase all follow that pattern, and all are O(1) expected under a good hash.
   2. Collision resolution, and this is the main design choice. Separate chaining stores a list per bucket, which is simple and is what the C++ standard effectively mandates for unordered_map because of its iterator and reference stability guarantees. Open addressing stores entries inline and probes forward, which is far more cache-friendly but complicates erase, since you need tombstones or backward shifting.
   3. Resize: track load factor as elements over buckets, and when it exceeds a threshold, typically 0.75 for chaining or 0.5 to 0.7 for open addressing, allocate a bigger array and rehash everything. Use a power-of-two bucket count so the modulo is a bitmask, but then your hash must mix the high bits or a weak hash collides badly.
   4. The correctness details an interviewer will probe: key equality is separate from the hash, two equal keys must hash the same, iterator invalidation on rehash, and what happens when the key type has a bad hash. A hash that is the identity on integers plus power-of-two buckets means sequential keys with a stride collide catastrophically.
   5. If I were writing this for a trading system I would use open addressing with linear probing over a pre-allocated power-of-two array, reserve capacity up front so no rehash ever happens in the hot path, and store keys and values in separate arrays if the values are large. The reason is tail latency: one rehash mid-session is a millisecond spike, and a millisecond is forever.

   Where candidates lose it

   Describing the interface rather than the internals. The question is about buckets, hashing, collisions and resizing. Also be ready for why is std::unordered_map slow, whose answer is node-per-element allocation and the standard's stability guarantees forcing chaining. And never forget that erase under open addressing needs tombstones, which is the bug candidates ship.

   Expect next

   • How does erase work under open addressing?
   • What load factor would you choose and why?
   • What makes a good hash function, and what happens with a bad one?

   Reported by candidates at Old Mission Capital (Trading, Chicago, 2021). Source: Wall Street Oasis.

8. 082Something in your C++ program is overwriting memory it should not. How do you find it?ProgrammingHardtechnicalTower Research CapitalForeign Exchange · London · 2019

   Say this

   Reach for the sanitisers first. AddressSanitizer catches out-of-bounds writes and use-after-free with roughly a two times slowdown and tells you both the write site and the allocation site. If the corruption is timing-dependent, add ThreadSanitizer for data races.

   Then walk it

   1. Order of tools: compile with -fsanitize=address,undefined and run the failing case. That resolves most buffer overruns and use-after-free immediately. Valgrind memcheck is slower but needs no recompile and catches uninitialised reads that ASan misses.
   2. If the corrupted location is known but the writer is not, set a hardware watchpoint in gdb on that address with watch, and let it break when something writes. Four watchpoints on x86, which is usually enough.
   3. If the corruption is not reproducible, make it reproducible before anything else. Record the inputs, pin the threads, disable randomisation, and consider record-and-replay with rr. A bug you cannot reproduce cannot be fixed, only guessed at.
   4. Common causes to check by inspection while the tools run: writing past the end of a fixed buffer, a dangling reference into a vector that reallocated, a stale pointer into an object that moved, a struct written with memcpy at the wrong size, and two threads writing the same cache line without synchronisation.
   5. And the systems answer for a production trading process where you cannot run ASan in the hot path: build with sanitisers in a test environment and in a canary, add canary values or guard pages around suspect buffers, and turn on the allocator's own debug checks. I would also say plainly that the fastest fix for a class of these bugs is to stop using raw buffers, because bounds-checked containers and spans eliminate the whole category.

   Where candidates lose it

   Answering add print statements. That is the answer of someone who has never used a sanitiser, and at a firm running C++ in production it is disqualifying. Name ASan specifically, name the gdb watchpoint technique for a known address, and say how you would make an intermittent bug reproducible before you try to find it.

   Expect next

   • What does AddressSanitizer not catch?
   • How would you debug this in production where you cannot run sanitisers?
   • What is a data race and why is it undefined behaviour?

   Reported by candidates at Tower Research Capital (Foreign Exchange, London, 2019). Source: Wall Street Oasis.

9. 084How would you design a system to troubleshoot latency in a trading stack?ProgrammingHardsuperdayCitadelProp Trading · New York · 2026

   Say this

   Timestamp at every hop with one clock, measure distributions not averages, and make the whole path attributable so you can say which segment consumed the microseconds. The design principle is that you cannot fix what you cannot decompose.

   Then walk it

   1. Instrumentation: hardware timestamps at the network card for packet in and packet out, plus software timestamps at each stage, market data decode, book update, strategy decision, order encode, and kernel bypass send. Carry a correlation id through the whole chain so a single event can be reconstructed end to end.
   2. Clocks are the hard part. Use PTP with hardware timestamping across hosts, not NTP, and record clock offset and drift as first-class data. Two hosts disagreeing by fifty microseconds will invent latency that does not exist and hide latency that does.
   3. Statistics: report the median, the 99th, the 99.9th and the maximum. Averages are useless here because the distribution is heavily right-tailed and the tail is exactly what costs money. Track per-segment histograms, ideally with HDR histograms so the tail resolution survives.
   4. Storage and analysis: stream the records off the critical path into a time-series store, then build the two views that actually get used, a per-segment breakdown over time and a drill-down into the slowest individual events. Alert on percentile regressions against a rolling baseline rather than on fixed thresholds.
   5. Then the causes to design for, because the system exists to distinguish them: garbage collection or allocation pauses, page faults, context switches and CPU migration, interrupt coalescing settings, cache misses and false sharing, queueing at the exchange gateway, and simple network congestion. And I would say the measurement must not itself be on the hot path, so lock-free ring buffers with a separate reader thread, because an observability system that adds ten microseconds has destroyed what it measures.

   Where candidates lose it

   Describing logging and monitoring generically. This is a specific systems question and the differentiators are clock synchronisation, percentile rather than mean reporting, and keeping instrumentation off the critical path. Talk in microseconds, and be able to name concrete causes of a tail latency spike.

   Expect next

   • How do you synchronise clocks across hosts, and to what accuracy?
   • Why report the 99.9th percentile rather than the average?
   • Walk me through diagnosing a spike that happens once a day.

   Reported by candidates at Citadel (Prop Trading, New York, 2026). Source: Wall Street Oasis.

10. 092What are the assumptions behind Black-Scholes, and which one fails hardest?Options and derivativesHardtechnicalDerivativesProp trading firms

    Say this

    Constant known volatility, geometric Brownian motion with no jumps, continuous frictionless hedging, constant rates, no dividends and European exercise. The one that fails hardest is constant volatility, and the proof that it fails is the volatility smile.

    Then walk it

    1. If the model were right, every strike and expiry on the same underlying would have the same implied vol. They do not. Equity index options show a pronounced skew, with out-of-the-money puts trading at much higher implied vol than calls, and the smile steepens for shorter expiries.
    2. Two economic reasons for the skew: returns are negatively skewed with crash risk, which a lognormal cannot represent, and there is genuine demand for downside protection that pushes puts rich. Both are real and they reinforce each other.
    3. No jumps is the second failure, and it is the same failure in a different form. Under continuous paths a delta hedge is riskless in the limit; with jumps it is not, and that unhedgeable jump risk is precisely what the skew prices.
    4. Continuous costless hedging fails too, which matters practically. You hedge discretely and pay the spread, so your realised hedging error has a variance proportional to the hedge interval, and a short-gamma book pays that cost repeatedly.
    5. But here is the thing worth saying: the model is still used everywhere despite being false, because it is a lossless translator between price and implied vol. Traders quote in vol, not in price, and Black-Scholes is the shared language. The correct summary is that it is a wrong model used as a coordinate system, with local vol, stochastic vol models like Heston, and jump models layered on top for anything path-dependent.

    Where candidates lose it

    Listing the assumptions without naming the smile as the empirical refutation. That link is the whole point. And do not conclude the model is useless, because that misses why every desk still quotes in Black-Scholes implied vol. Wrong but indispensable as a change of variables is the answer.

    Expect next

    • If you know the model is wrong, why still use it?
    • What is local volatility, and what does it fix?
    • How would you price a barrier option given a smile?

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.