Nine Minutes from Two Sand Timers
A pastry chef owns exactly two sand timers — one runs for minutes, the other for — and needs to bake a tart for precisely minutes. How can the chef time the bake using nothing else?
Flow Traders Interview Guide
Flow Traders opens with 60 mental math questions you have six minutes to finish, then spends the rest of the process on ETFs and how you quote them.
Sample Flow Traders questions
Shared Birthdays in a Small Seminar
A seminar has attendees. Assume each person's birthday is independently and uniformly distributed over the days of a non-leap year. What is the probability that some pair of attendees shares a birthday?
Free Money in the Creation Basket
An exchange-traded fund called the Nordic Shipping Trust is built from exactly three listed stocks. One share of the fund is redeemable for a basket of shares of Aker, shares of Borga, and share of Corve. Right now the screens show Aker at , Borga at , Corve at , and the fund itself at . You are an authorised participant, so you may hand a full basket of shares to the fund sponsor and receive fund shares in exchange (creation), or hand in fund shares and receive the basket (redemption), on the same day.
(a) What is the fund's fair value, and what trade locks in a riskless profit? How much per fund share?
(b) You sell fund shares and start buying the basket, but Corve halts for news after you have filled only the Aker and Borga legs. What exposure are you left holding, and how do you stay hedged until Corve reopens?
Online math test
Wrong answers cost a point
What to expect
- 60 arithmetic questions in 6 minutes, six seconds each on average.
- Multiplication, division, decimals, fractions and percentages, with no calculator and no scratch work.
- Scoring is plus one for a correct answer, minus one for a wrong one and zero for a skip, so guessing is punished.
- A second test covers number sequences: 26 questions in 25 minutes, scored the same way.
- Most candidates do not finish, and this test is where the largest share of applicants exit.
How to prepare
- Drill timed arithmetic daily until two-digit multiplication and percentage conversions come without working.
- Practise skipping: a question you cannot finish in six seconds is worth more left blank than guessed.
- Work sequence and pattern sets separately, since the second test is a different skill from the first.
Recruiter call
Expect ETF questions here, not just motivation
What to expect
- A 30 to 45 minute phone or video call with a recruiter.
- Motivation and fit, plus what you know about the business and about ETFs.
- Explaining what a market maker does for an ETF is the bar here, not a bonus.
How to prepare
- Learn the creation and redemption mechanism and be able to explain it in a minute.
- Have a specific reason for Flow rather than any market maker, tied to exchange traded products.
Trader interview
ETF pricing is the firm speciality
What to expect
- A trader-led technical round: probability, expected value and brainteasers.
- Make a market on the value of a card drawn face down from a 52-card deck, then defend the width.
- Pricing an ETF against its underlying basket across exchanges or currencies.
- Explaining why a leveraged ETF decays when the index chops sideways.
- Market discussion: what moved recently and why it matters to a liquidity provider.
How to prepare
- Work through the daily rebalancing math on a 3x fund until the decay is obvious to you.
- Quote two-sided markets on simple random variables out loud, with a width you can justify.
- Read ETF flows and index news the week of the call, so the market discussion is specific.
Assessment day
Includes a live trading game against other candidates
What to expect
- A day onsite with four or five back-to-back interviews of about 45 minutes each.
- A dedicated ETF case study: value the basket, spot the arbitrage, explain the hedge.
- A live trading game where you quote two-sided markets against the other candidates in the room.
- Interviewers watch your inventory and your spread, not just whether you finished ahead.
- Quoting sensibly after a bad fill counts for as much as the fill itself.
How to prepare
- Play market-making games with friends and keep a running count of your inventory.
- Decide in advance how wide you quote and how you skew when you are long or short.
- Rehearse the case study order: basket value, fair price, the arbitrage, then the hedge.
More reported Flow Traders questions
One Seat on the Rowboat
A zookeeper transporting animals reaches a river with a hawk, a snake, and a frog. The rowboat at the bank holds only her plus one passenger per trip. Left unsupervised together, the hawk will attack the snake, and the snake will swallow the frog; each is safe whenever the keeper is present, and the hawk has no interest in the frog. How does she ferry all three across intact?
Subway Days in the First Three Mornings
Every morning a courier independently flips a fair mental coin: bike or subway, each with probability . You learn that across a particular 7-day stretch he took the subway exactly 4 times. Conditional on that, what is the probability he took the subway exactly twice during the first 3 days of the stretch? Give the answer as a fraction in lowest terms.
The ETF That Trades While Tokyo Sleeps
A New York--listed ETF holds a global equity portfolio: of its value is US stocks and is Japanese stocks. It is a.m. in New York. The fund's last published net asset value, struck at yesterday's US close, was per share -- from the US sleeve and from the Japanese sleeve, where the Japanese holdings were marked at the Tokyo close preceding it, and Tokyo has not traded since.
Since that Tokyo close: Nikkei futures, which trade essentially around the clock, are up , and the yen has weakened against the dollar. The US sleeve is, at this moment, worth exactly per fund share.
What is the ETF worth right now? A client points out that the fund is quoted at , "a premium to NAV," and asks whether that is free money. What do you tell him?
One Constituent Moves the Fund
A technology ETF is quoted at per share. One of its holdings, Nexatek, makes up of the fund by weight. Nexatek prints a trade at , up from a moment ago. Assume every other holding is unchanged and nothing else about the fund has moved.
Where should you now be quoting the ETF? Do it in your head.
The Triple-Leveraged Fund's Nightly Trade
You run the hedging desk for an exchange-traded product that promises the **daily** return of a crude oil index. At last night's close the fund had million of investor equity, so it held million of index exposure via swaps and futures.
(a) Today the index rises . What trade must the fund do into today's close to be correctly positioned for tomorrow, and in which direction?
(b) Suppose instead the index had fallen . What trade then?
(c) The index goes up one day and down the next. The index is then down over the two days. Where is the fund? Explain the gap to a client who expected .
Cross the Spread or Wait in Line
A stock is quoted bid, offered, with shares showing on each side. You want to buy shares and you have a one-minute forecast: with probability the fair value one minute from now is , and with probability it is .
(a) Is it profitable to take the offer at ?
(b) Instead of taking, you could post a passive bid at and wait. Suppose -- realistically -- that the only world in which a seller comes to you is the world in which the price is heading down; that is, your passive bid fills only in the state. What is the expected value of posting?
(c) What is the lesson?
Backing Out the Approval Odds
A single-drug biotech trades at per share. A regulator announces its decision tomorrow morning. Analysts agree that on approval the company is worth per share and on rejection it is worth per share, with no other outcome possible. Ignore the one day of interest.
(a) What probability of approval is the market pricing?
(b) Your own research says the true probability is . What is the trade, and how big is the edge?
(c) Name two reasons the number in (a) might not equal the market's genuine belief.
No Two Faulty Panels Side by Side
A maintenance crew inspects a straight row of solar panels. Independently of one another, each panel is faulty with probability . What is the probability that no two faulty panels are adjacent in the row?
The Gap the Hedger Prefers
You buy a one-month at-the-money call on a stock trading at , paying for it (take the option to cover one share, so all figures are per share). Its delta is , and you immediately delta-hedge by shorting shares at . You re-hedge to delta-neutral once a day at the close, and you hold the position to expiry.
The stock ends the month at either way, but consider two paths:
- **Path A:** overnight, the stock gaps straight from to on bad news, then sits at for the rest of the month. - **Path B:** the stock drifts down about a day for twenty trading days, arriving at at expiry.
The option expires worthless in both cases. Which path makes you more money, and by roughly how much? What general principle is this?
FAQ
What is on the Flow Traders math test?
Sixty arithmetic questions in six minutes with no calculator and no scratch work: multiplication, division, decimals, fractions and percentages. A correct answer scores plus one, a wrong answer minus one and a skip zero, so leaving a question blank beats guessing. A second test covers number sequences, 26 questions in 25 minutes, scored the same way.
How long does the Flow Traders interview process take?
Three to six weeks from application to decision is typical: the online tests, a recruiter call, a trader interview, then an assessment day. The graduate programme recruits all year with four intakes, so there is no single application window.
What happens at the Flow Traders assessment day?
Four or five interviews of about 45 minutes each, an ETF case study, and a live trading game in which candidates quote two-sided markets against each other. Interviewers watch how you manage inventory and spread and whether you keep quoting sensibly after a bad fill. New hires who pass go into a multi-month trader development programme before trading live.
Do you need to know ETFs before interviewing at Flow Traders?
Yes. ETF questions appear in the recruiter call, the trader interview and the final case study: creation and redemption, pricing an ETF against its basket across exchanges or currencies, and why leveraged funds decay in a sideways market. Candidates who prepare only generic probability stall at the trader round.