Quantitative Researcher Interview Prep: Questions and a Mock Test

The probability round is not a test of memorised formulas. Interviewers are watching how you decompose a problem, whether you sanity-check your answer, and whether you notice when a result is absurd.

The recurring topics are narrow enough to prepare properly: conditional probability and Bayes, expectation and variance including the law of total expectation, distributions and when each applies, order statistics, random walks and stopping times, and simple Markov chains. Expected value questions about games with an optional stopping decision are a staple, because they require you to work backwards from the terminal state rather than forwards from the start.

Two failure modes cost more marks than a wrong answer. The first is silence: an interviewer cannot award credit for reasoning they cannot hear, and the entire point of the exercise is to observe your process. The second is defending a wrong answer after being given a hint. Hints are almost always deliberate, and how you take one is being assessed directly.

The base rate question in some form is nearly universal, because it is the cleanest test of whether someone confuses the probability of the evidence given the hypothesis with the probability of the hypothesis given the evidence. A test with 99 percent accuracy for a condition affecting one person in ten thousand produces far more false positives than true ones, and being able to say why quickly, ideally by imagining a population of a million rather than manipulating symbols, is what a strong answer looks like.

The technical distinction most often probed is between a price series and a return series, and it is not pedantry.

Prices are non-stationary: their mean and variance change over time, and two unrelated non-stationary series will frequently appear strongly correlated purely because both trend. Regressing one on the other produces a spurious relationship with an impressive t-statistic and no predictive content. Returns are much closer to stationary, which is why almost all modelling is done on returns rather than levels.

The properties to be able to state about financial returns: they are approximately uncorrelated in time but not independent, because squared returns are strongly autocorrelated. That is volatility clustering, the observation that large moves follow large moves regardless of sign, and it is the phenomenon that GARCH-type models exist to capture. Returns also have fat tails relative to a normal distribution, so any risk number computed under normality understates the frequency of extreme moves.

Stationarity testing, differencing and cointegration come up in pairs-trading contexts. Two non-stationary price series can be cointegrated, meaning some linear combination of them is stationary, which is precisely the statistical statement behind a mean-reverting spread. The interview follow-up is usually about what happens when the relationship breaks, and the honest answer is that cointegration over a sample period is not a guarantee about the future and needs a stop rule that does not assume reversion.

This section carries more weight than any other, because a candidate who cannot enumerate the ways a backtest flatters a strategy is dangerous rather than merely inexperienced.

Lookahead bias is the first: using information not available at decision time. It hides in ordinary places, a fundamental figure timestamped by its reporting period rather than its publication date, an index constituent list as of today, a daily bar's close used to trade at that day's open.

Survivorship bias is the second: testing on the securities that still exist excludes exactly the ones that failed, which biases every return statistic upward. A point-in-time universe is the fix.

Overfitting is the third and the subtlest. Trying many strategies against one dataset guarantees that some will look excellent by chance, and the more configurations tested, the less a good in-sample Sharpe means. Interviewers probe this by asking how many variants you tried, and the expected instincts are out-of-sample and walk-forward testing, a strong prior toward fewer parameters, and deflating the reported statistic for the number of trials.

Validation methodology transfers directly from machine learning, with one crucial adjustment. As scikit-learn's documentation notes, time series data is "characterized by the correlation between observations that are near in time (autocorrelation)", so standard k-fold assumes an independence that does not hold and effectively trains on the future. Forward-chaining, where "successive training sets are supersets of those that come before them", is the honest structure. In finance you additionally need a gap between train and test to prevent leakage through overlapping labels.

And costs. A strategy that is profitable before transaction costs, market impact and borrow is not a strategy.

Execution is where paper returns go to die, so interviewers check that you understand what happens between a decision and a fill.

The SEC's own description of order types is the right level of precision. A market order "guarantees that the order will be executed, but does not guarantee the execution price", with the explicit warning that "the last-traded price is not necessarily the price at which a market order will be executed". A limit order is "an order to buy or sell a security at a specific price or better", which guarantees price and not execution. A stop order becomes a market order once the stop price is reached, which is why it inherits the market order's lack of price certainty at exactly the moment prices are moving fastest.

That tradeoff is the core of execution: you are choosing between certainty of price and certainty of fill, and the cost of the wrong choice is asymmetric depending on whether you are providing or taking liquidity.

The vocabulary to have ready: the bid-ask spread as the immediate cost of a round trip, the mid as the reference price, slippage as the difference between the decision price and the achieved price, market impact as your own order moving the price against you, and adverse selection as the reason a resting limit order tends to be filled precisely when the market is about to move through it.

The practical consequence is that capacity is a property of a strategy. A signal with a genuine edge on small size can be worthless at scale because impact grows faster than the edge, and being able to say that unprompted is a strong senior signal.

Derivatives questions appear in most quant loops even for roles that do not trade options, because implied volatility is the cleanest example of a market price containing a forecast.

The VIX is the standard reference. Cboe describes it as "a leading measure of market expectations of near-term volatility conveyed by S&P 500 Index (SPX) option prices". Two properties matter in an interview. It is forward-looking, derived from option prices rather than from historical returns, so it is not a measure of what volatility has been. And because it is an expectation extracted from prices, it embeds a risk premium, which is the usual explanation for implied volatility exceeding subsequent realised volatility on average.

On Black-Scholes, the useful position is that its assumptions are known to be false, constant volatility and lognormal returns in particular, and it survives as the market's common language rather than as a belief. Implied volatility is just the number that makes the formula reproduce the observed price, and the volatility smile is the market telling you that the model's distributional assumption is wrong.

Risk questions come last and often decide the interview. Value at risk is a quantile, so it says nothing about the size of losses beyond it, which is why expected shortfall is preferred for tail work. Sharpe ratio scales with the square root of time under an independence assumption that returns violate, so an annualised Sharpe computed from daily data on an autocorrelated strategy is optimistic. And on sizing, the strong answer is that maximising expected log wealth gives an aggressive number that assumes your parameter estimates are correct, which they are not, so practitioners size well below it.