DRW screens with an at-home probability test, then turns every later round into a conversation where a brainteaser becomes a market you have to quote.
A school corridor contains lockers numbered through , and every door starts open. Then students file through one at a time: student (for ) flips the state of every locker whose number is a multiple of — closing it if open, opening it if closed. So the first student flips every locker, the second flips lockers , and so on through student . Once everyone has passed, how many lockers stand open?
A fair six-sided die pays you its face value in dollars. The first roll is free. After seeing any roll you may either bank that amount and stop, or pay a fee of and roll again -- as many times as you like, with the fee due before each new roll and no going back to a face you have declined.
(a) What is the optimal policy, and what is the game worth? (b) For which fees would you hold out for a only?
You buy an at-the-money call on a stock trading at with trading days to expiry, paying an implied volatility of , and you delta-hedge it once at the end of each trading day. Work throughout in trading time: a year is trading days, so the option's life is years. Ignore interest rates and dividends.
(a) How large does the stock's daily move have to be, in dollars and in percent, for the position to break even on the day? (b) The stock in fact moves about per day, in a random direction. Do you make or lose money, and how would you describe the trade in one sentence to a risk manager? (c) The option's gamma is per share. What is its theta per trading day?
Reasoning is weighted over speed
Brainteasers arrive mid-conversation
A brainteaser turns into a trading game
DRW covers the travel
At the end of a gala, a flustered coat-check attendant discovers the ticket stubs for all coats have fallen off. Rather than sort it out, he hands the coats back in a uniformly random one-to-one assignment — every guest leaves with exactly one coat. On average, how many guests walk out wearing their own coat?
A grasshopper sits at on the integer number line and repeatedly jumps to the right, each jump covering unit or units with probability each, independently forever. For a positive integer , let denote the probability that the grasshopper ever touches down exactly on . Which maximizes , and what is that maximum probability?
An urn holds 6 tokens: 3 green tokens each worth and 3 orange tokens each worth . You draw tokens one at a time without replacement, banking each token's value as you go, and you may quit whenever you like (including before the first draw). Playing optimally, what is your expected profit?
Under Black–Scholes assumptions, a European put on stock , struck at with expiry , carries a delta of . You build a long straddle at that same strike and expiry — long one call plus long one put. What is the straddle's delta?
A fair coin is flipped repeatedly, and the flipping stops the first time two heads land in a row. Find the probability that the process terminates on flip number 10 exactly.
You roll a fair six-sided die together with a fair ten-sided die (faces through ), and you must call the total before the roll, winning only on an exact match. Which total or totals give you the best chance of winning, and what is that chance?
A dealer picks an amount uniformly from , puts into one envelope and into the other, seals both, and hands you one at random. You open yours and find .
(a) Should you swap? (b) Work out the right policy for every amount you might have seen. (c) A colleague argues: "whatever is in your envelope, the other holds either double or half with equal chance, so swapping is worth -- always swap, and swap again forever." Where exactly does that break, and how much is your correct policy actually worth?
A researcher shows you a strategy with winning trades out of . Take the world to contain only two kinds of strategy: real ones, which win each independent trade with probability , and worthless ones, which win with probability . From experience you believe only submitted strategy in is real.
(a) After seeing wins in trades, what is the probability this strategy is real? (b) The researcher points out the result is "statistically significant at two sigma." Reconcile that with your answer. (c) Roughly how many trades would a genuinely real strategy need before you were convinced?
Three traders are each given a badge, coloured red or blue by an independent fair coin flip. Each of them can see the other two badges but not their own. At a signal, all three simultaneously either name a colour or say "pass" -- no communication of any kind once the badges are on.
The team wins a shared prize if **at least one person guesses and every guess made is correct**. They may agree on a strategy beforehand. What is the best they can do?
Since any individual guess is a fair coin flip, is the ceiling?
A timed, at-home multiple-choice test of about 45 minutes covering probability, expected value, combinatorics and logic puzzles. No calculator, but pen and paper are allowed and you can move freely between questions. It is pitched at medium difficulty and rewards careful reasoning over speed, so most candidates finish with time to spare.
An interviewer poses a scenario and asks you to post a bid and an ask with size. They then trade against whichever side favours them, and you update your quote, manage the inventory you have taken on and explain each move as you make it. It is usually done mentally, without pen and paper, and it often grows out of a brainteaser rather than being announced as a game.
Several weeks end to end: the quantitative challenge, a phone screen, a technical interview, then the Superday in Chicago. After the Superday, decisions typically arrive within one to two weeks. DRW reviews applications on a rolling basis, so apply when the role posts rather than waiting for a deadline.
At the Chicago headquarters, with travel expenses covered by the firm. It is a multi-hour event, often an afternoon technical challenge followed by a full day of back-to-back interviews with traders from different desks: mental math, market-making games and culture-fit conversations.
