Discussion question for trading and research roles.
When to stop looking
The question
You interview n candidates in random order, learn only relative ranks, and must accept or reject each immediately. How do you maximise the chance of hiring the best one?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Reject the first n/e, then take the next candidate better than everyone seen. Success probability about 37 percent.
Consider the family of strategies that observes the first r candidates, then accepts the next record-setter.
The probability this picks the best is roughly (r/n) times ln(n/r), which is maximised when r/n = 1/e.
At that cutoff the success probability is 1/e, about 0.368, and it does not decay as n grows, which is the surprising part.
The practical reading matters in interviews: a fixed fraction of your search should be spent calibrating with no intent to commit.
What it is testing
Whether you can parametrise a strategy class before optimising.
Try these next
Roll a die, take it or reroll
Warm-upYou roll a fair six-sided die and may either keep the value or reroll once and keep the second value. What is the optimal strategy and its expected value?
The larger of two dice
StandardTwo fair six-sided dice are rolled. What is the expected value of the larger?
Cards until the first ace
HardYou deal a shuffled 52-card deck one card at a time. What is the expected number of cards dealt before the first ace appears?
Collecting the full set
StandardA cereal brand hides one of six equally likely toys per box. How many boxes until you expect to own all six?
Preparing properly
Live opportunities
Interviewing soon? See who is hiring
Open vacancies we track at quant firms, grouped by role and city. Adverts are anonymised.
Hiring for these roles? Brief the desk on a hire or check your fit for a role.
Research desk
Speak to a quant market specialist
Ask what a firm really pays, how a desk hires, or where your profile sits. One reply from the research desk, in confidence, no obligation.