Citadel Securities runs a probability assessment, two phone rounds with traders and a Superday of up to seven interviews, and the bar at every step is fast, independent and correct.
Your new coworker mentions she has exactly two children and, in passing, that at least one of them is a boy who was born on a Tuesday. Model each child independently as boy or girl with probability , with birth weekday uniform over the 7 days and independent of everything else. Given exactly this information, what is the probability that both of her children are boys?
Estimate how many size-5 footballs you could pour into an empty 40-foot shipping container. You have no reference materials -- show the estimate and state what dominates the error.
A casino wheel has 50 equally likely pockets: the numbers 1 through 48, plus two green house pockets. Three bets are offered, each staking \$1: (a) "low", covering numbers 1 through 24, pays 1 to 1; (b) a single number, pays 47 to 1; (c) a column of 16 numbers, pays 2 to 1. Compute the expected profit per dollar for each bet. What do you notice, and what is the general principle?
Strict cutoffs, before any human is involved
Behavioural questions sit inside the technical call
Miami, or virtual
A glazier snaps a glass rod of length at a point chosen uniformly at random. She keeps both pieces, picks up the longer one, and snaps it again at a uniformly random point along it. What is the probability the three resulting shards can be arranged into a triangle?
A stadium scoreboard is an panel of bulbs, and a power glitch sets each bulb on or off independently with probability . What is the probability that every row and every column of the panel ends up containing an even number of lit bulbs?
Two trading desks post daily P&Ls and that are independent standard normal random variables. Today the combined book finished up: . Given that, what is the probability the first desk was itself profitable — that is, ?
A researcher regresses a stock's daily return on signal A alone, with an intercept, and gets . Regressing the same returns on signal B alone gives . She now runs one regression on A and B together. What is the largest that regression could possibly produce, and what would the two signals have to look like for that to happen?
Three trading desks report daily P\&L. A risk manager finds that every pair of desks has exactly the same correlation : . What is the full set of values can take? Then generalize to desks.
An analyst builds a dataset of 100 observations and regresses on a single predictor plus an intercept. By mistake she appends a second, identical copy of the file before running it, so the regression sees 200 rows: every original row appearing exactly twice. Compared with the correct regression, what happens to (a) the estimated coefficients, (b) the , and (c) the reported -statistics?
A ladybug lands at a uniformly random point on a circular wire hoop of radius 3 centered at the origin (uniform along the wire). What is the variance of its -coordinate? Now a satellite is at a uniformly random point on the *surface* of a sphere of radius 3, also centered at the origin. What is the variance of its -coordinate?
A fair coin is flipped 10 times. What is the probability of getting strictly more heads than tails? Do it without summing five binomial terms. What is the answer if the coin is flipped 9 times instead?
A fair six-sided die will be rolled once, and the "settlement price" of the underlying is the number that comes up. Ignore interest rates and assume the true distribution is also the pricing distribution. What is the fair value of a call struck at 4? A put struck at 4? The straddle? Verify that put-call parity holds, and say what the at-the-forward straddle is worth.
A timed multiple-choice test sent shortly after application. For trading roles it centres on probability, with logic puzzles and math alongside; software and quant-developer applicants get HackerRank coding problems instead, graded on hidden test cases and time complexity. Cutoffs are strict and applied before any interview.
An online assessment, two phone or video rounds of 45 to 60 minutes with traders or researchers, then a Superday of four to seven back-to-back interviews. A team-matching conversation with a hiring manager can follow. The whole process usually takes about four to six weeks.
A live round at the Superday for trading candidates. You quote a two-sided market on a security, the interviewer trades against it and feeds in new information, and you reprice while tracking your own inventory and profit. Being slow to reprice, or carrying an unmanaged position, is the most cited reason candidates lose the day.
Historically at the Miami headquarters, and it can also run virtually. It is a single day of quant rounds, behavioural conversations and, for trading candidates, the live market-making game.
